study of the morphology and optical properties of … · 2020-01-16 · study of the morphology and...

Study of the Morphology and Optical Properties ofPropylene/Ethylene Copolymer Films

Christopher M. Fratini

Dissertation submitted to the Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

in

Chemistry

Herve Marand, Chair

Alan R. Esker

Harry W. Gibson

Thomas C. Ward

Garth L. Wilkes

April 14, 2006

Blacksburg, Virginia

Keywords: Polypropylene, Copolymer, Morphology, Film, Haze, Clarity, Transparency, Gloss,

Light Scattering, Surface Roughness

Copyright 2006, Christopher M. Fratini

Study of the Morphology and Optical Properties of Propylene/Ethylene

Copolymer Films

Christopher M. Fratini

(ABSTRACT)

The development of a new catalyst system by The Dow Chemical Company has resulted in the

production of isotactic polypropylene and propylene/ethylene copolymers with a unique defect

and comonomer distribution. This work investigated the morphology and optical properties of cast

and compression molded films made from the homopolymer and copolymers with up to 20 mol%

ethylene comonomer. The defect distribution of the Dow Chemical copolymers resulted in mate-

rials with lower crystallinity than Ziegler-Natta or metallocene-made materials of similar ethylene

content. These materials exhibited a γ-phase crystal content ranging from 0–95%, depending on

ethylene content, processing condition, and catalyst type.

The γ-phase crystal content of quiescently crystallized copolymer films was found to significantly

influence their bulk optical properties, presumably through a change in the spherulite birefrin-

gence. The bulk haze, clarity, and transparency of a homopolymer film were degraded through

annealing treatments, which decreased the fraction of γ-phase crystallinity and increased the thick-

ness of existing lamellae, resulting in an increased intensity of scattered light and a corresponding

degradation in the optical properties of the film. The haze, clarity, transparency, and gloss of the

copolymer films were found to improve at higher comonomer content and higher cooling rates.

The variation in the length scale and degree of disorder in the bulk morphology of films processed

under different conditions was shown to correlate with the optical quality of the films, with smaller

scale morphologies scattering less light and resulting in films with better optical properties.

It was also shown that no single metric can completely describe the optical quality of a poly-

mer film; the relative importance of haze, transparency, and gloss, which depends on the intended

application of the film, was discussed. The influence of surface scattering from the films was con-

trolled through the compression molding of films using substrates of different surface roughness.

The contribution of light scattered from the surface of the films was isolated and found to play a

significant role in the degradation of optical quality.

iii

For Lisa, Kyle, and Gianna . . .

iv

Acknowledgments

I would like to acknowledge and thank the following people for their contributions to this work.

Dr. Herve Marand, for providing guidance, motivation, support, and insight throughout the course

of my residence at Virginia Tech, and for introducing me to the fascinating world of physical

polymer chemistry.

Drs. Alan Esker, William Ducker, Harry Gibson, Thomas Ward, and Garth Wilkes for serving on

my advisory committee, for teaching informative and stimulating classes, and for the many helpful

discussions over the past five years.

Wilson Cheung, Li Tau, Patricia Ansems, and Steve Chum from The Dow Chemical Company,

which provided the funding and materials used in this research, for the opportunity to work on this

project and to contribute to the research program at Dow Chemical.

Drs. Brian Okerberg, Julie Uan-Zo-li, and Zhenyu Huang for their friendship and assistance during

our time together in the Marand group.

Steve McCartney of the Materials Research Institute for the training and use of SEM and AFM

instruments, and for entertaining conversation while waiting for AFM images to scan.

Melvin Shaver, John Miller, and Scott Allen at the Physics Machine Shop and David Simmons

and Darrell Link at the ESM Machine Shop for fabricating many of the parts employed in the

modification of laboratory instruments used in this work.

Tom Wertalik of the Chemistry Glass Shop for crafting the optical cell used in this work, and for

v

useful discussions regarding many other topics relevant to this research.

Drs. Ross Angel of the Geology Department and Lucian Zelazny of the Crop and Soil Science

Department for the education in x-ray diffraction and the use of their instruments.

Jim Coulter, James Hall, Larry Jackson, and Travis Heath of the Chemistry Electronics Shop for

fabricating several devices used in this project and for keeping our computers running.

The dozens of others who have helped me along my way through Virginia Tech.

Finally, and most importantly, I thank my family for enduring my absence over the years and for

their constant support and love. Lisa, Kyle, and Gianna, I could not have achieved this goal without

you.

vi

Contents

1 Introduction 1

2 Literature Review 4

2.1 Morphology of Isotactic Polypropylene and its Copolymers . . . . . . . . . . . . . 4

2.1.1 Polymer Crystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.2 Polymorphism of i-PP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.3 Influence of the Catalyst System . . . . . . . . . . . . . . . . . . . . . . . 16

2.1.4 Copolymer Crystallization . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.1.5 i-PP Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Optical Properties of Polymer Films . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Interaction of Light with Matter . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.2 Small Angle Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2.3 Haze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.2.4 Clarity, Transparency, and Visually Perceived Film Quality . . . . . . . . . 31

2.2.5 Gloss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.3 Surface Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

vii

2.3.1 Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.3.2 Measurement of Surface Roughness . . . . . . . . . . . . . . . . . . . . . 40

3 Experimental 44

3.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2 Film Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.3 Film Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.4 Density Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.5 Refractive Index Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.6 Wide-Angle X-ray Diffraction (WAXD) . . . . . . . . . . . . . . . . . . . . . . . 51

3.7 Polarized Optical Microscopy (POM) . . . . . . . . . . . . . . . . . . . . . . . . 52

3.8 Scanning Electron Microscopy (SEM) . . . . . . . . . . . . . . . . . . . . . . . . 52

3.9 Atomic Force Microscopy (AFM) . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.10 Haze and Clarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.11 Transparency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.12 Gloss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.13 Small Angle Light Scattering (SALS) . . . . . . . . . . . . . . . . . . . . . . . . 54

4 Results and Discussion 56

4.1 Optical Properties of P/E Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.1.1 Extrusion Cast Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.1.2 Compression Molded Films . . . . . . . . . . . . . . . . . . . . . . . . . 63

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4.1.2.1 Preparation of Pressed Films . . . . . . . . . . . . . . . . . . . 63

4.1.2.2 Haze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.1.2.3 Clarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.1.2.4 Comparison of Clarity and Transparency . . . . . . . . . . . . . 73

4.1.2.5 Gloss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.2 Morphology of Pressed Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.2.1 Crystallinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.2.1.1 Room Temperature Physical Aging . . . . . . . . . . . . . . . . 83

4.2.1.2 Refractive Index . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.2.1.3 Polymorphism . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.2.1.4 Bulk Density and Crystallinity . . . . . . . . . . . . . . . . . . 89

4.2.2 Bulk Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.2.3 Lamellar Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.3 Control of Optics by Variation of Bulk Morphology . . . . . . . . . . . . . . . . . 104

4.3.1 Spherulite Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

4.3.2 Spherulite Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

4.4 Control of Optics by Variation of Surface Roughness . . . . . . . . . . . . . . . . 126

4.4.1 Introduction and Sample Preparation . . . . . . . . . . . . . . . . . . . . . 126

4.4.2 Correlation of Surface Roughness with Optical Properties . . . . . . . . . 128

4.5 Comparison of Dow Chemical P/E copolymers to Ziegler-Natta and Metallocene

P/E copolymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

4.6 Cast Films Revisited — Optical Characterization . . . . . . . . . . . . . . . . . . 143

ix

4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

5 Future Work 158

5.1 On the Dow Chemical P/E copolymers . . . . . . . . . . . . . . . . . . . . . . . . 158

5.2 On the Surface Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

5.3 On the Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

A Temperature Controller BASIC Program Listing 180

B Morphology and HV SALS patterns of PE, ZN, and MET copolymers 182

C Derivation of a Model for the Birefringence of an iPP Spherulite with γ-α Branching 194

x

List of Figures

2.1 The fringed micelle model of polymer crystallization. . . . . . . . . . . . . . . . . 6

2.2 The chain-folded lamellar model of polymer crystallization. . . . . . . . . . . . . 6

2.3 Growth stages of a polymer spherulite. . . . . . . . . . . . . . . . . . . . . . . . . 7

2.4 Spherulite of polyvinylidene fluoride. . . . . . . . . . . . . . . . . . . . . . . . . 8

2.5 Determination of the sign of ∆n. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.6 LH model of polymer crystallization. . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.7 Unit cell of α-phase i-PP. View is down the c-axis. . . . . . . . . . . . . . . . . . 13

2.8 Unit cell of γ-phase i-PP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.9 Epitaxial α-α and α-γ branching in i-PP. . . . . . . . . . . . . . . . . . . . . . . . 19

2.10 Schematic drawing of hazemeter. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.11 Schematic drawing of transparency meter. . . . . . . . . . . . . . . . . . . . . . . 32

2.12 Schematic drawing of gloss meter. . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1 Schematic of VT hazemeter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.2 VT haziness vs. Dow Chemical haze for the cast films. . . . . . . . . . . . . . . . 59

4.3 Haziness of cast extruded film separated into total and bulk contributions. . . . . . 60

xi

4.4 VT haziness/mil vs. Dow Chemical haze/mil for the cast films. . . . . . . . . . . . 61

4.5 Haziness/mil for Dow Chemical cast films. . . . . . . . . . . . . . . . . . . . . . . 61

4.6 Sample temperature profile for slow cool. . . . . . . . . . . . . . . . . . . . . . . 65

4.7 Sample temperature profile for bench top cool. . . . . . . . . . . . . . . . . . . . . 65

4.8 Sample temperature profile for ice/water quench. . . . . . . . . . . . . . . . . . . 66

4.9 Sample temperature profile for cooling at 1◦C/min. . . . . . . . . . . . . . . . . . 66

4.10 Sample temperature profile for cooling at 10◦C/min. . . . . . . . . . . . . . . . . . 67

4.11 Pressed film thickness as a function of MW . . . . . . . . . . . . . . . . . . . . . . 68

4.12 Haze – total and bulk scattering contributions for cast film with 7.7%E. . . . . . . 69

4.13 Haze of pressed films vs. ethylene content and cooling rate. . . . . . . . . . . . . . 70

4.14 Bulk haze/mil of pressed films. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.15 Clarity – total and bulk scattering contributions for cast film with 7.7%E. . . . . . 73

4.16 Total and bulk normalized clarity of pressed films. . . . . . . . . . . . . . . . . . . 74

4.17 Schematic drawing of the Haze Gard Plus clarity mode. . . . . . . . . . . . . . . . 75

4.18 Transparency – total and bulk scattering contributions for cast film with 7.7%E. . . 77

4.19 Transparency vs. ethylene content and cooling rate. . . . . . . . . . . . . . . . . . 78

4.20 Normalized bulk transparency of pressed films. . . . . . . . . . . . . . . . . . . . 79

4.21 Total and bulk transparency and thickness of pressed films. . . . . . . . . . . . . . 80

4.22 Gloss–45 of compression molded copolymer films. . . . . . . . . . . . . . . . . . 82

4.23 Density of P/E copolymers versus aging time at 23◦C. . . . . . . . . . . . . . . . . 84

4.24 Haze of quenched P/E copolymers versus aging time at approximately 22◦C. . . . 85

xii

4.25 Clarity of quenched P/E copolymers versus aging time at approximately 22◦C. . . . 86

4.26 Density of quenched P/E copolymers versus refractive index. . . . . . . . . . . . . 87

4.27 WAXD powder pattern of slowly cooled PE00. . . . . . . . . . . . . . . . . . . . 88

4.28 Fraction of γ-phase crystallinity as a function of ethylene content and cooling rate. . 89

4.29 Density of P/E copolymers at 23◦C. . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.30 Crystallinity of P/E copolymers from density analysis. . . . . . . . . . . . . . . . 92

4.31 Morphology and HV SALS pattern of PE0.0 cooled at 1◦C/min. . . . . . . . . . . 94





4.36 Morphology and HV SALS pattern of PE12.3 cooled at 10◦C/min. . . . . . . . . . 96

4.37 Morphology and HV SALS pattern of quenched PE0.0. . . . . . . . . . . . . . . . 96

4.38 Morphology and HV SALS pattern of quenched PE7.0. . . . . . . . . . . . . . . . 97

4.39 SEM image of PE0.0 crystallized at 1◦C/min. . . . . . . . . . . . . . . . . . . . . 99

4.40 SEM image of PE8.2 crystallized at 1◦C/min . . . . . . . . . . . . . . . . . . . . 100

4.41 SEM image of PE13.3 crystallized at 1◦C/min . . . . . . . . . . . . . . . . . . . . 101

4.42 SEM image of PE8.2 crystallized at 1◦C/min — densely packed lamellae . . . . . 101

4.43 SEM image of PE8.2 crystallized at 1◦C/min — both morphologies . . . . . . . . 102

4.44 AFM image of PE12.8 crystallized at 1◦C/min — both morphologies . . . . . . . . 103

4.45 HV SALS patterns and POM micrographs for PE5.4. . . . . . . . . . . . . . . . . 106

xiii

4.46 HV SALS quadrant average for PE5.4 quench. . . . . . . . . . . . . . . . . . . . . 106

4.47 HV SALS pattern smoothing with Gaussian blur. . . . . . . . . . . . . . . . . . . 108

4.48 µ = 45◦ intensity profile for MET13.5 cooled at 1◦/min. . . . . . . . . . . . . . . . 108

4.49 µ = 45◦ intensity profiles for PE films cooled at 90◦/min. . . . . . . . . . . . . . . 109

4.50 Haze/mil as a function of spherulite radius. . . . . . . . . . . . . . . . . . . . . . 111

4.51 Normalized clarity as a function of spherulite radius. . . . . . . . . . . . . . . . . 112

4.52 Normalized transparency as a function of spherulite radius. . . . . . . . . . . . . . 113

4.53 Density and crystallinity of PE0.0 cooled at 1◦C/min and subsequently annealed . . 114

4.54 POM images of PE0.0 crystallized at 1◦C/min before and after annealing. . . . . . 115

4.55 Optical properties of PE0.0 crystallized at 1◦C/min and subsequently annealed. . . 116

4.56 AFM images of PE0.0 crystallized at 1◦C/min (before annealing). . . . . . . . . . 117

4.57 AFM images of PE0.0 crystallized at 1◦C/min (after annealing). . . . . . . . . . . 118

4.58 WAXD patterns of PE0.0 crystallized at 1◦C/min and subsequently annealed. . . . 118

4.59 DSC melting traces for PE0.0 crystallized at 1◦C/min and subsequently annealed. . 119

4.60 Optical properties of PE3.3 crystallized at 1◦C/min and subsequently annealed. . . 121

4.61 WAXD patterns of PE3.3 crystallized at 1◦C/min and subsequently annealed. . . . 122

4.62 DSC melting traces for PE3.3 crystallized at 1◦C/min and subsequently annealed. . 122

4.63 Polarized haze of PE0.0 crystallized at 1◦C/min and subsequently annealed. . . . . 124

4.64 Repeatability of RMS roughness measurements for three films of PE4.8. . . . . . . 127

4.65 Roughness of Kapton film and of PE4.8 film using Kapton substrate. . . . . . . . . 128

4.66 RMS roughness of PE4.8 and PE13.3 vs. image size and substrate type. . . . . . . 129

xiv

4.67 Haze, clarity, and Gloss-45 of PE13.3 films with different surface roughness. . . . 130

4.68 Bulk haze and clarity of PE13.3 films of different roughness. . . . . . . . . . . . . 131

4.69 Crystallinity of PE, ZN, and MET films versus cooling rate. . . . . . . . . . . . . . 133

4.70 Xγ of PE, ZN, and MET films crystallized at 1 and 10◦C/min. . . . . . . . . . . . . 134

4.71 Bulk morphology of ZN4.4 versus cooling rate from the melt. . . . . . . . . . . . 135

4.72 Bulk morphology of MET5.2 versus cooling rate from the melt. . . . . . . . . . . 136

4.73 Bulk morphology of PE5.4 versus cooling rate from the melt. . . . . . . . . . . . . 137

4.74 Bulk haze/mil of PE, ZN, and MET films versus cooling rate. . . . . . . . . . . . . 138

4.75 Normalized bulk clarity of PE, ZN, and MET films versus cooling rate. . . . . . . 139

4.76 Normalized bulk transparency of PE, ZN, and MET films versus cooling rate. . . . 140

4.77 POM images and HV SALS patterns of MET13.5 cooled at 1◦C/min and 10◦C/min. 142

4.78 AFM height and phase images of MET13.5 cooled from the melt at 1◦C/min. . . . 142

4.79 AFM height image of cast film 43-2. RMS roughness = 7.4 nm. . . . . . . . . . . 144



4.82 5×5 µm2 AFM height image of cast film 43-6. . . . . . . . . . . . . . . . . . . . 145

4.83 HV SALS patterns from cast film 43-4 . . . . . . . . . . . . . . . . . . . . . . . . 147

4.84 AFM section through 25 nm high particle on cast film 43-4. . . . . . . . . . . . . . 148

4.85 Total and bulk haze of cast films 43-2, 43-4, and 43-6. . . . . . . . . . . . . . . . . 149

4.86 Gloss-45 of cast films 43-2, 43-4, and 43-6. . . . . . . . . . . . . . . . . . . . . . 150

4.87 Total and bulk clarity of cast films 43-2, 43-4, and 43-6. . . . . . . . . . . . . . . . 151

xv

4.88 Total and bulk transparency of cast films 43-2, 43-4, and 43-6. . . . . . . . . . . . 152

B.1 Morphology and HV SALS pattern of PE0.0 cooled at 1◦C/min. . . . . . . . . . . 183










B.11 Morphology and HV SALS pattern of PE12.3 cooled at 10◦C/min. . . . . . . . . . 186





B.16 Morphology and HV SALS pattern of ZN4.4 cooled at 1◦C/min. . . . . . . . . . . 188





xvi


B.22 Morphology and HV SALS pattern of MET5.2 cooled at 1◦C/min. . . . . . . . . . 190






B.28 Morphology and HV SALS pattern of MET11.1 cooled at 10◦C/min. . . . . . . . . 192

B.29 Morphology and HV SALS pattern of MET13.5 cooled at 10◦C/min. . . . . . . . . 192



xvii

List of Tables

3.1 Dow P/E copolymer physical data. . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.2 Dow P/E copolymer tacticity and regio-error data. . . . . . . . . . . . . . . . . . . 47

3.3 Dow cast film physical data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.4 Ziegler-Natta and Metallocene copolymer physical data. . . . . . . . . . . . . . . 49

4.1 Differences between VT haziness meter and ASTM D 1003 specification. . . . . . 58

4.2 Estimates of R0 by HV SALS and POM for PE5.4. . . . . . . . . . . . . . . . . . 105

4.3 Estimated scattering angles and RMS roughness for cast films. . . . . . . . . . . . 147

4.4 Cast films ranked using VT haze, clarity, and transparency. . . . . . . . . . . . . . 153

xviii

Chapter 1

Introduction

Isotactic polypropylene (i-PP) is one of the most widely used commodity polymers, with sales of

18 billion pounds in 2004, second only to polyethylene.1 The low cost, low density, high melting

temperature, and good mechanical properties of i-PP are desirable for applications such as packag-

ing materials and fibers. The properties of i-PP are often modified through the copolymerization of

propylene with α-olefins or ethylene. At low levels of incorporation the inclusion of comonomer

typically improves the toughness, impact resistance, and optical properties of the resin, while high

levels (∼ 30%) of ethylene comonomer incorporation result in ethylene-propylene monomer rub-

ber (EPM).2

Most commercial i-PP is produced using Ziegler-Natta catalyst systems, but the newer metallocene

catalyst systems allow for improved control over defect and comonomer incorporation and molec-

ular weight distribution. Recently, The Dow Chemical Company developed a new catalyst for the

synthesis of i-PP and its copolymers, which produces resins with a unique defect distribution that

results in materials with a low density, broad melting range, good optical properties, and processing

characteristics suitable for film and fiber applications.3, 4

One of the most important characteristics of a polymer film is its optical quality. The great dif-

ficulty of optical quality evaluation is that the ‘true’ value of quality is not some quantitatively

1

2

measurable or calculable material property, but is instead defined by the subjective opinion of

a human observer. The establishment of standard illumination conditions, test geometries, and

sample preparation methods serves to limit the variations in reported quality, but in the end a mea-

surement technique can only be considered successful if it predicts film quality in agreement with

subjective evaluations by human observers.

Such a problem was one of the earliest investigated during the current research. The optical char-

acterization techniques routinely used by Dow Chemical scientists were unable to distinguish be-

tween several polymer films with a different visual appearance. This example is suggestive of a

more widespread problem in the polymer film industry, since the Dow Chemical tests employed

widely available commercial instruments and followed well-established procedures defined by sev-

eral standards organizations.

The present study examined the morphology and optical properties of films made from the new

Dow Chemical propylene/ethylene (PE) copolymers. The morphology and surface roughness of

the films were controlled through variation of the ethylene comonomer content, cooling rate, and

the substrate used during compression molding. Correlations between the bulk morphology and the

observed optical properties of the copolymer films were found. In addition, a significant effort was

made to evaluate the theoretical basis and applicability of optical testing methods used in industrial

settings to determine their ability to predict film quality as perceived by a human observer.

Following a brief background and literature review (Chapter 2), the experimental methods used

for film production and evaluation are presented (Chapter 3). The results and discussion of the

studies on the copolymer films are presented as six sections of Chapter 4. The evaluation of cast

and compression molded films using both a fabricated haziness meter and commercial haze and

transparency meters is discussed in Section 4.1. The crystallinity, bulk morphology, and lamellar

structure of these films is presented in Section 4.2. The influence of the bulk morphology and

surface roughness on the optical properties of the films is described in Sections 4.3 and 4.4, re-

spectively. Section 4.5 shows the results of a comparison of the morphology and optical properties

of the Dow Chemical PE copolymers with Ziegler-Natta and metallocene-made materials with

3

similar ethylene contents. Section 4.6 reports on the optical and morphological characterization

of three cast films reported by Dow Chemical to have similar haze, clarity, and gloss values but a

different visual appearance. A seventh section summarizes the general conclusions of this work.

Chapter 5 describes several avenues for the extension of this work and suggests opportunities for

related investigations utilizing the materials and methods employed in the current project.

Chapter 2

Literature Review

This chapter presents a brief review of several topics relevant to the present work. A discussion

of the micro- and macroscopic crystallization behavior of polymers in general and of isotactic

polypropylene in particular is given to introduce the variety of morphologies expected from the

materials used in this study. The scattering of visible light and its importance in the evaluation of

polymer properties is then reviewed. Finally, a summary of the measurement of surface roughness

and its effect on optical properties is presented. With the background information provided in this

chapter, the reader should be well equipped to evaluate the results of this project.

2.1 Morphology of Isotactic Polypropylene and its Copolymers

2.1.1 Polymer Crystallization

Crystallinity in polymeric materials was first discovered by x-ray diffraction methods in the early

20th century. Subsequent work led to the fringed micelle model of polymer crystallization, which

proposed that the polymer chains, in a randomly coiled state in the melt or in solution, could

align to form small crystalline domains scattered throughout the bulk of the material (Figure 2.1).

4

5

A single chain could participate in several crystalline domains. This model was consistent with

the observation of somewhat diffuse diffraction spots in wide-angle x-ray diffraction patterns, due

to the very small size of the crystals (on the order of 10 nm). The model also accounted for

the presence of an amorphous halo, caused by the randomly arranged noncrystalline chains. The

model also emphasized the concept that polymer crystallization does not reach completion —

both crystalline and noncrystalline regions existed in all ‘crystalline’ polymers, which are more

correctly designated semicrystalline polymers.

Continued study of polymer morphology revealed shortcomings of the fringed micelle model, par-

ticularly its difficulty in explaining single crystals grown from dilute solution and the spherulitic

morphology observed in crystal aggregates grown from more concentrated solutions or the melt of

several polymer systems. The randomly oriented array of small crystals described by the fringed

micelle model was incompatible with faceted single crystals or the development of radially sym-

metric spherical objects tens of micrometers in diameter.

Examination of polyethylene single crystals using electron microscopy and electron diffraction

revealed that the polymer chains were oriented nearly perpendicular to the crystal surfaces and

led Keller to the conclusion that the polymer chains must fold back and forth to produce the ex-

perimentally observed thin plate- or ribbon-like lamellar crystals.5, 6 A schematic drawing of a

chain-folded lamellar crystal is shown in Figure 2.2. Polymer lamellar crystals are typically on

the order of 10 nm thick but may span tens of µm in the other two dimensions. The concept of a

chain folded lamellar crystal could account for the formation of both polymer single crystals and

spherulitic morphology. Subsequent studies have shown this to be the general mode of crystalliza-

tion for flexible-chain semicrystalline polymers under quiescent crystallization conditions.7

With the lamellar crystal established as the building block of polymer microstructure, attention

was turned to the spherulitic aggregates grown from polymer melts under quiescent conditions.

Spherulites were shown to form by a process of lamellar splaying and branching from a central

nucleus, which progressed continuously through an axialite/hedrite stage with a sheaf-like appear-

ance to eventually form a three dimensional spherically symmetric crystalline aggregate composed

6

Figure 2.1: The fringed micelle model of polymer crystallization.

Figure 2.2: The chain-folded lamellar model of polymer crystallization.

7

of radial chain-folded lamellae (Figure 2.3).7, 8 Poorly crystallizable, short, or defective chains;

loose folds and loops; and interlamellar links (tie chains) occupy the regions between stacks of

lamellar crystals and between spherulite boundaries and constitute the amorphous phase of the

bulk polymer. The internal structure and resultant optical properties of isotactic polypropylene

spherulites in particular will be discussed in more detail in Section 2.1.5.

Under isothermal conditions, spherulites grow radially at constant rates until impingement with

other spherulites. Spherulite impingement signifies the end of primary crystallization in the bulk

polymer. A stage of secondary crystallization can then occur in which existing lamellae thicken

to increase their thermodynamic stability and/or small crystallites may form in the initially amor-

phous interlamellar regions.10, 11

Polymer spherulites display interesting optical properties due to their symmetry and internal struc-

ture. Spherulites are typically observed using polarized optical microscopy (POM). When the

Figure 2.3: Growth stages of a polymer spherulite. Reprinted with permission from J. Schultz, Polymer

Crystallization, Oxford University Press, 2001. Copyright 2001 American Chemical Society.9

8

extinction directions of the polarizer and analyzer are oriented at 90◦ relative to each other, a con-

dition known as the crossed polarization position occurs. Under these conditions, well-formed

spherulites display the characteristic Maltese cross of extinction along the axes of the polarizer

and analyzer as shown in Figure 2.4. Concentric banding is observed in some polymer spherulites

due to cooperative twisting of the radial lamellae.

An important optical characteristic of a spherulite is its birefringence, ∆n, defined as the differ-

ence in refractive index in the radial direction of the spherulite, nr, and the refractive index in the

tangential direction, nt (see Section 2.2 for an introduction to the interactions between light and

matter).

Most polymer spherulites are formed from radially oriented lamellae, which typically places the

chain axis nearly tangential to the radius. Since the chain axis is normally the high-index direction

of the polymer crystal, most polymer spherulites are negatively birefringent. The birefringence can

Figure 2.4: Spherulite of polyvinylidene fluoride observed between crossed polars. The characteristic

Maltese cross extinction pattern is clearly visible.

9

be measured using a polarized optical microscope equipped with a compensator. The compensator

is used to measure the optical path difference, PD, of the spherulite and the birefringence can be

estimated using the relation ∆n = PD/t, where t is the thickness of the spherulite.12

The sign of ∆n can be determined by inserting a retardation plate, also known as a wave plate or

λ-plate, into the microscope between the polarizer and analyzer and at a 45◦ angle to the extinction

directions of the crossed polarizer and analyzer. The retardation plate is a thin slab of birefrin-

gent material, typically gypsum, of an appropriate thickness to induce an optical retardation of

approximately 550 nm. This retardation, when viewed between crossed polarizers using white

light, produces the first-order red or sensitive-tint interference color. The small phase differences

introduced by slightly birefringent objects such as polymer spherulites are clearly visible as color

changes when viewed under these conditions.

To measure the sign of spherulite birefringence, the polarizer and analyzer of the microscope are

crossed in the North-South and East-West positions, and the λ-plate is inserted between them

with its fast, or low index, axis in the NW-SE position. Negatively birefringent spherulites will

show a yellow color in their upper-right and lower-left quadrants and blue in the other two. The

arrangement of colors will be reversed for a positively birefringent spherulite. These color changes

occur due to the addition or subtraction of optical path differences due to the orientation of the

chain axis in the spherulite (Figure 2.5).

Observations of spherulite growth rates, which are representative of the crystal growth rates in

spherulites where the lamellar growth is in the radial direction, have shown that the growth rate,

G is an exponential function of 1/(T ∆T ), where T is the crystallization temperature and ∆T is

the undercooling, defined as T 0m − T , where T 0

m is the melting temperature of an infinitely thick

crystal (i.e., the equilibrium melting temperature).10, 14 This behavior supports the hypothesis that

polymer lamellae grow by a process controlled by secondary nucleation.14 Changes in the slope

of logG vs. 1/(T ∆T ) have been observed in polyethylene and other polymers and attributed to

changes in crystal growth regimes.10, 15

The Lauritzen-Hoffman (LH) theory of polymer crystallization has been used to successfully

10

Figure 2.5: Determination of the sign of polymer spherulites using a retardation plate. The addition or

subtraction of optical path difference produces the observed color changes. Left: negatively birefringent

spherulite. Right: positively birefringent spherulite. Reprinted from G. N. Meeten, Ed., Optical Properties

of Polymers, Chapter 4, Elsevier, 1986. Copyright 1986 Elsevier.13 With kind permission of Springer

Science and Business Media.

model this secondary nucleation concept and explain the relationship between G and the under-

cooling and the presence of growth regimes.10, 15 Although a lengthy discussion of this theory is

beyond the scope of this work, the relevant details are summarized below.

The LH theory uses a mean field approach to model the polymer crystallization process as the de-

position of polymer stems onto the crystal growth front in a two-step process. First, an initial stem

deposits onto a clean crystal surface with rate i (the secondary nucleation event), then subsequent

stems zip down the crystal face to complete the layer with chain folding at rate g, leading to the

overall crystal growth rate G, as shown in Figure 2.6.

where l is the thickness of the lamellar crystal, a is the width of the stem, b is the thickness of the

stem, σ is the lateral surface free energy, σe is the fold surface free energy, and L is the substrate

length. The LH model predicts the lamellar growth rate G to be:

11

Figure 2.6: LH model of polymer crystallization. Reprinted from N. B. Hannay, Ed., Treatise on Solid State

Chemistry, Volume 3, Chapter 7, Plenum Press, 1976. Copyright 1976 Plenum Press. With kind permission

of Springer Science and Business Media.

G = G0 exp[

−U∗

R(T −T∞)

]exp[−Kg

T ∆T

](2.1)

where G0 is a prefactor not heavily dependent on T , U∗ is the activation energy for chain transport

through the melt, R is the gas constant, T∞ is the temperature at which cooperative chain motions

cease, and Kg is the nucleation rate constant incorporating material parameters such as b, σ and σe,

and in Regime II has half the value as in Regimes I or III.10, 15 The model predicts the observed

decrease in G at low (approaching T∞) or high (approaching T 0m) crystallization temperatures.

A key factor in polymer crystal growth is the dependence of the initial lamellar thickness, l∗g on

crystallization temperature. Hoffman showed that l∗g is proportional to (∆T )−1; in other words, the

initial lamellar thickness increases with crystallization temperature.10 The lamellar crystals may

subsequently undergo thickening to decrease their surface to volume ratio, and thereby increase

12

their thermodynamic stability, if allowed to remain at high temperature or during subsequent an-

nealing.

2.1.2 Polymorphism of i-PP

The development of stereospecific polymerization catalysts by Ziegler and Natta in the 1950’s led,

among other advances, to the production of high molecular weight isotactic polypropylene. This

material quickly gained commercial importance due to its low cost and desirable mechanical prop-

erties and, at the same time, garnered scientific interest as a result of its interesting crystallization

behavior and morphology.

Polypropylene is one of many polymers that exhibit stereoisomerism due to the presence of an

asymmetric carbon center in its repeating unit. The polymer chains may be isotactic, where each

asymmetric carbon has the same configuration; syndiotactic, where alternating asymmetric carbons

have the same configuration; or atactic, where there is no regular configuration of the asymmetric

carbon. The regular structure of the isotactic and syndiotactic forms facilitates their crystallization,

while atactic polymers are often amorphous. Additional irregularities arise from misinsertion of

monomer units during the polymerization reaction. Errors such as head-to-head and 1,3 misinser-

tions are classified as regio-errors.

Only isotactic polypropylene and its copolymers with ethylene were used in the present work;

therefore, all subsequent discussions will pertain to this stereoisomer. The first and most common

crystalline phase of i-PP, now known as the α-phase, was discovered by Natta et al. who also

determined its crystal structure.16 Subsequent work confirmed the monoclinic unit cell with only

slight alterations from Natta’s original determination.17–19 The unit cell dimensions as determined

by Turner-Jones are: a = 6.66 A, b = 20.78 A, c = 6.495 A, and γ = 99.62◦.18 The polymer chains

were arranged in 31 helices with four chains, each making one turn of the helix, per unit cell for

a calculated density of 0.943 g/cm3.18 A schematic drawing of the α-phase unit cell is shown in

Figure 2.7.

13

Figure 2.7: Unit cell of α-phase i-PP. View is down the c-axis. The arrows show the chirality of the helices

and the dotted lines indicate the positions of ‘up’ or ‘down’ helices. Unit cell dimensions are: a = 6.66 A,

b = 20.78 A, c = 6.495 A, and γ = 99.62◦.18 Reprinted from Polymer, 37, B. Lotz, J. C. Wittmann, and

A. J. Lovinger, Structure and morphology of poly(propylenes): a molecular analysis, Pages 4979–4992,

Copyright 1996 Elsevier, and Copyright 1960 Societa Italiana di Fisica.16, 20 With permission from Elsevier

and Societa Italiana di Fisica.

The α-phase crystal structure consists of alternating layers, parallel to the a-axis, of right- and

left-handed helices, which alternate along the b-axis. The helices also possess an ‘up’ or ‘down’

orientation of the methyl groups which determines the space group of the unit cell. The C2/c,

Cc, and P21/c space groups represent various forms of disorder in the up/down arrangement of

helical layers but the particular arrangement of up/down symmetry has little influence on the bulk

morphological behavior of α-phase i-PP.21

The α-form is the most common in practice and generally forms during crystallization from so-

lution or rapid cooling from the melt. Its formation is favored when long defect-free isotactic

sequences are available for crystallization. The crystallographic branching, or crosshatching, of α-

14

phase lamellar aggregates is unique in polymer science and plays an important role in the optical

properties of i-PP spherulites. This topic will be discussed further in the following section.

A second crystalline form of i-PP was discovered in 1959 by Padden and Keith, but the crystal

structure of this β-form remained unsolved until 1994.12, 20, 22, 23 The β-phase was shown to have an

unusual frustrated hexagonal unit cell but the polymer chains were still found in the characteristic

i-PP 31 helix.23 However, this polymorph rarely forms unless specific crystallization conditions

or nucleating agents are used, and transforms into the α-phase upon heating or into a disordered

paracrystalline phase upon mechanical deformation.17, 18 The β-polymorph was not seen in the

present investigation and will not be discussed further.

A third, γ-form, was noticed in the previously mentioned studies.17, 18 The γ-phase crystals trans-

formed into the α-phase during attempts to produce oriented samples, which limited the evaluation

of its crystal structure.18, 21 The structure was finally solved by Bruckner and Meille in 1989 and

displayed a surprising non-parallel arrangement of 31 i-PP helices.24 Subsequent studies validated

this model and led to a more complete understanding of the unusual morphologies seen in i-PP.25, 26

Figure 2.8 depicts the orthorhombic γ-phase unit cell with dimensions: a = 8.54 A, b = 9.93 A, and

c = 42.41 A.24, 25 Alternating bilayers of right- and left-handed helices lie parallel to the diagonals

of the unit cell with each bilayer tilted at 81◦ to each other. This structure, unique in polymer

science, enabled researchers to propose a mechanism for the characteristic branching seen in i-PP

lamellar crystals which will be discussed further in the following section.

The γ-phase was first promoted through the use of low molecular weight or poorly crystallizable

fractions and slow cooling from the melt or high temperature isothermal crystallization.18, 24, 25, 27

The γ-phase was found to be the dominant mode of crystallization at high pressure for high molar

mass i-PP.26, 28–30

The copolymerization of propylene with other olefins has been shown to promote the γ-phase,

with higher comonomer content producing a higher proportion of the γ-polymorph.27, 31, 32 Work

by Alamo et al. and De Rosa et al. has shown that γ-phase is promoted by the existence of short

crystallizable isotactic sequences.33–35 Bruckner et al. have suggested that the γ-phase lamellae can

15

Figure 2.8: Unit cell of γ-phase i-PP. The asterisk denotes the basic bilayer structure composed of left (levo-

gyre) and right (dextrogyre) helices and the dotted lines indicate the positions of ‘up’ or ‘down’ helices. Unit

cell dimensions are: a = 8.54 A, b = 9.93 A, and c = 42.41 A.24, 25 Reprinted from Polymer, 37, B. Lotz,

J. C. Wittmann, and A. J. Lovinger, Structure and morphology of poly(propylenes): a molecular analysis,

Pages 4979–4992, Copyright 1996 Elsevier, and Copyright 1989 Macmillan Publishers Ltd: Nature.20, 24

With permission from Elsevier and Macmillan Publishers Ltd: Nature.

better accommodate defects at or near the crystal surface due to the large tilt angle of the crystalline

stems, somewhat reminiscent of a fringed micellar crystal which is favored in this particular case

due to the energetic benefits of the 40◦ chain tilt angle in the γ-phase i-PP crystal.26

A fourth pseudo-crystalline polymorph can form when i-PP is quenched very rapidly.36 This form,

often referred to as smectic or mesomorphic, is characterized by diffuse x-ray reflections and a

small crystalline ‘blob’ morphology and could be transformed into α-phase by annealing.36, 37

Additional details on the history and identity of this phase were reviewed by Bruckner et al.21

Because the formation of this phase requires very rapid cooling conditions, it was not likely to be

encountered in significant amounts during the present work and will not be discussed further.

16

2.1.3 Influence of the Catalyst System

As mentioned previously, the presence of short crystallizable chains promotes the formation of the

i-PP γ-phase. For a given chain length and defect content, the distribution of defects along the chain

will be important. If the defects are clustered in blocky regions or sequestered in noncrystallizable

chains, then the remaining chains will have long defect-free sequences and crystallize in the α-

phase. Conversely, a random defect distribution will result in few long crystallizable sequences

and many short ones, thereby promoting the formation of γ-phase crystals.

Defect and comonomer segregation occurs when propylene is polymerized with the traditional

Ziegler-Natta (ZN) catalyst systems.38 The broad molecular weight and defect distributions per-

mit the fractionation of ZN polymers by crystallization or dissolution temperature where the

comonomer concentration is highest in the low melting/dissolving fractions.18, 39–41 The high

molecular weight and highly isotactic chains in ZN homo- and copolymers promote the crystal-

lization of α-phase lamellae at high temperature.

Modern metallocene catalyst systems can be tailored to produce a variety of chain architectures.42

The molecular weight distribution of metallocene-made materials is typically narrower than that

achieved with ZN catalysis. Most metallocene-type catalysts favor the random incorporation of

comonomer units and defects.33–35, 38, 39, 43–48 The random defect distribution in metallocene-made

homo- and copolymers results in short crystallizable propylene sequences which favors the forma-

tion of the γ crystal phase as discussed above.

2.1.4 Copolymer Crystallization

The incorporation of a small fraction of foreign comonomer units into a normally crystallizable

chain may have a significant impact on the crystallization behavior. Two options are available for

the minority component upon crystallization: either the minority units are at least partially incor-

porated into the crystal phase of the majority component (inclusion model), or the minority units

are completely rejected from the crystals (exclusion model). The archetypical copolymer crystal-

17

lization models are Flory’s exclusion model and the inclusion model of Sanchez and Eby.49–51

Both models predict that copolymers will crystallize at lower temperatures and over a broader

temperature range than the corresponding homopolymer. In studies on copolymers of propylene

with other olefins, it has been shown that ethylene and 1-butene units are partially included into

the propylene crystals, while higher α-olefins, such as 1-hexene or 1-octene are generally ex-

cluded.33, 35, 44, 46, 48, 52, 53 In particular, Uan-Zo-li has recently shown that the inclusion model of

Sanchez and Eby is applicable to the PE copolymers used in the present work.50, 53

2.1.5 i-PP Morphology

The spherulitic morphology of i-PP was studied in solution by Khoury and in the melt by Padden

and Keith, who identified five types of spherulites.12, 54 Type I and II spherulites were most com-

mon, depending on crystallization temperature, and were both shown to be composed of α-phase

crystals. Padden and Keith observed that Type I i-PP spherulites, crystallized at a lower tempera-

ture than Type II, had a small but positive birefringence.12 Type II spherulites had a slightly nega-

tive birefringence. A significant number of spherulites formed with a ‘mixed’ birefringence, where

regions of positive and negative ∆n existed within the same spherulite. The mixed spherulites were

also found to be composed of α-phase crystals. The much rarer Type III and IV spherulites were

negatively birefringent and shown to be composed of β-phase crystals. Subsequent reviews have

reinforced this classification of the spherulitic morphologies of i-PP.55–57

Studies of solution-grown i-PP crystals and spherulites by Khoury revealed the unique cross-

hatched morphology only found in α-phase i-PP.54 Pre-spherulitic square crosshatched crystals

were isolated and termed ‘quadrites’ by Khoury. Electron micrographs showed profuse lamellar

branching at a characteristic 80◦ angle. The same crosshatched morphology was seen in spherulites

and sheaf-like crystals grown from the melt.55, 58, 59

Binsbergen and De Lange proposed a model to explain the observed birefringence changes as a

function of the level of crosshatching.58 The α-phase i-PP is seen experimentally to be composed

18

of radially (parent) and tangentially (daughter or crosshatched) oriented lamellae. Because the

chain axis is oriented approximately perpendicular to the lamellar basal surface, the radial index

of refraction is given by:

nr = rna + tnc, r + t = 1 (2.2)

where na and nc are the refractive indexes along the a and c unit cell axes, respectively, r is the

fraction of radially oriented lamellae, and t is the fraction of tangentially oriented lamellae. The

tangential index of refraction is given by:

nt = r(nb +nc)/2+ t(na +nb)/2 (2.3)

where nb is the refractive index along the b unit cell direction. Making the assumption that nc >

na ≈ nb, the spherulite birefringence is then:

∆n = (nc−na)(t− r/2) (2.4)

This relationship predicts that crosshatched spherulites will have positive birefringence when t

exceeds 1/3 and negative ∆n when t is less than 1/3. Experimental observations generally agree

with this model, where positive spherulites (Type I) crystallized at lower temperature and showed

profuse crosshatching while negative spherulites (Type II) grown at higher temperature were com-

posed of primarily radially oriented lamellae.55, 58, 59 The degree of crosshatching has been shown

to decrease with increased tacticity and crystallization temperature.60, 61 Mixed spherulites have

been shown to be composed of domains with varying degrees of crosshatching and flat-on radial

lamellae which have near zero ∆n, leading to regions of positive and negative birefringence within

the spherulite.55

The unique crosshatched branching occurs because of a fortuitous similarity in the a and c α-phase

unit cell dimensions. Additionally, when an i-PP helix is oriented at an 80◦ angle to the ac face of

19

an existing α-phase crystal, and both the depositing helix and those composing the face of the crys-

tal are of the same hand, the methyl units can pack without hindrance. The result of this ‘mistake’

in the alternation of helical hand results in homoepitaxial crystallographic branching.20, 58, 62–64

Growth of these daughter branches results in the crosshatched morphology. The solution of the

γ-phase crystal structure revealed its close relationship to this α-α branching process.

The α-α branching occurs when the normal alternating right- and left-handed helical layer struc-

ture of α-phase i-PP is disrupted by the deposition of a helix of the same hand as the current

layer.20, 63, 64 There is no significant energy penalty for this addition, provided that the depositing

helix rotates the 80 degrees required for methyl interdigitation. If successive chiral layers resume

their normal alternating habit, then the typical crosshatched α-α branching occurs. The ‘mistakes’

can also continue, resulting in the deposition of the alternating isochiral tilted bilayers of the γ-

phase. Figure 2.9 shows a schematic drawing of both types of crystallographic branching. This

epitaxial α-γ branching is believed to be the primary nucleation process for γ-phase i-PP.20, 63, 64

No such branching is expected or observed for pure γ-phase i-PP because the process that leads to

branching in the α-phase is the normal growth process of the γ-phase.21

Figure 2.9: Epitaxial α-α and α-γ branching in i-PP. Reprinted from Polymer, 45, I. L. Hosier, R. G. Alamo,

and J. S. Lin, Lamellar morphology of random metallocene propylene copolymers studied by atomic force

microscopy, Pages 3441–3455, Copyright 2004, with permission from Elsevier.48

20

2.2 Optical Properties of Polymer Films

This project dealt primarily with the optical properties of polymer films. A brief review of light

scattering is presented, followed by a discussion of the optical characterization techniques com-

monly used to evaluate polymer films. An introduction to the small-angle light scattering (SALS)

method follows.

2.2.1 Interaction of Light with Matter

The interaction of light with matter determines the appearance of the world around us. Generalized

theories exist to accurately predict the behavior of light in condensed systems, but these theories

become mathematically intractable for many real world problems. Therefore, the study of light-

matter interactions typically requires the use of approximations to obtain calculable results.

Light may be modeled using a particle or a wave approach, with the latter more suitable for the

present discussion. The wave theory models light as a transverse electromagnetic disturbance or

wave packet (photon) which propagates through free space at a constant velocity c = 3×108 m/s.

The disturbance can be modeled as orthogonal electric, E, and magnetic, B, fields oscillating in

phase. The wave is characterized by its frequency, ν, or its wavelength, λ, which are related

by c = νλ. This model describes the properties of electromagnetic waves from very long (radio

waves) to intermediate (visible light) to very short (x-rays and γ-rays) wavelengths. The illumi-

nation perceived as ‘white’ light is composed of a mixture of wavelengths in the visible range of

approximately 400–700 nm.

Upon entering a dense medium, the interaction of the varying electromagnetic field with the

charged electrons of the atomic or molecular species in the medium results in a reduction in the

propagation velocity of the wave. The speed reduction is quantified by the refractive index of the

material, n = c/v, where v is the velocity of light in the medium. Since n depends on ν, refractive

index measurements are reported at a standard wavelength of light (monochromatic illumination),

typically the 589 nm D line produced by a sodium lamp. Such values are reported as nD.

21

The index of refraction is a property of the bulk material. The corresponding microscopic para-

meter is the polarizability, α, of the molecule. The index of refraction and the polarizability are

related, in the absence of absorption, by the Lorentz-Lorenz equation:

n2−1n2 +2

=NAρα

3Mε0(2.5)

where NA is Avogadro’s number, ρ is the density of the material, M is the molar mass, and ε0 is the

permittivity of free space.65

Light may interact with matter in other ways, which can be classified into the groups of reflec-

tion, absorption, and scattering. Reflection occurs at the interface between two media of different

refractive index, and often contributes significantly to the visual appearance of polymer films.

Absorption occurs when some of the energy of the light wave is transferred to the medium. Pref-

erential absorption of some wavelengths in the visible region gives rise to colored materials. The

polymers used in the current study showed no appreciable absorption of visible light and had a

colorless appearance. Therefore, the phenomenon of absorption will not be discussed further.

Light may also interact with the medium in an elastic manner, where the net result is the redirection

of the photons in a process known as elastic or nonresonant scattering. A redirected photon main-

tains the same energy it had before the interaction. Elastic scattering is the primary mechanism for

image degradation in non-absorbing media, and will be discussed in more detail below.

An important property of light waves is their state of polarization. A beam of light composed of

many photons with their electric field vectors oriented in all directions is said to be unpolarized.

Such an unpolarized beam is produced from common incandescent sources. Isolation of only one

electric field vector orientation results in a linearly polarized beam. Polarization of an initially

unpolarized beam is typically achieved through the use of a polarizing film or by reflection off a

surface at an appropriate angle. Although the human eye is insensitive to the polarization direction

of light, the use of polarized light is common in the laboratory setting to facilitate comparison to

theoretical predictions.

22

The materials used in the present research undergo virtually no magnetic interactions with the light

wave, therefore these interactions will be neglected and future discussions will focus only on the

electric field of the electromagnetic wave. The electric field, Ex(z, t), of a harmonic plane wave

traveling in the z direction of a cartesian coordinate system is given by:

Ex(z, t) = iE0x cos(kz−ωt) (2.6)

where E0x is the maximum amplitude of the field, i is the unit vector in the x-direction, k is the

wave number equal to 2π/λ, z is the position along the z-axis, ω is the angular frequency equal to

2πν, and t is time.66 The argument of the cosine function is known as the phase, φ, of the wave.

Interference occurs when waves occupy the same space. Constructive interference, when the waves

are in-phase, results in an increased total amplitude, while destructive interference , when the waves

are out-of-phase, results in decreased total amplitude. If two waves are out-of-phase by 180◦ (π

radians) then complete extinction occurs.

Wave interference explains many observed phenomena, such as the appearance of extra fringes

or rings around narrow slits or small pinhole apertures, that are not compatible with a particle

model of light. A specific application of the diffraction effect is the diffraction grating, a device

exhibiting periodic optical variations on a spacing comparable with that of visible light. A beam of

light passed through or reflected from such a particular arrangement of optical variation, grooves

for example, produces a corresponding pattern of points. Wave theory predicts these patterns based

on interference phenomena. The grating equation for transmission is:

asinθm = mλ, m = 0,±1,±2, . . . (2.7)

where a is the spacing between lines on the grating, θm is the angle that the mth diffraction spot

makes with the main beam (0th order), m is the diffraction order, and λ is the wavelength of incident

light.66

If x-rays, which are simply light waves with a wavelength on the order of 0.1 nm, are passed

23

through a crystalline material a pattern is obtained corresponding to the specific arrangement and

type of atoms in the crystal. The pattern forms because the crystal acts as a three-dimensional

diffraction grating due to the regular spacing of the constituent atoms. The Bragg equation predicts

diffraction maxima to occur when:

2d sinθ = mλ, m = 0,±1,±2, . . . (2.8)

where d is the spacing between planes of atoms in the crystalline lattice, and θ is the scattering

angle.66 These relationships illustrate a characteristic feature of diffraction phenomena, that small

objects or spacings scatter at large angles, and vice versa.

When the objects of interest are much larger than the wavelength of light, the approximations

of geometrical optics become extremely useful. In this case the diffraction and wave nature of

light may be ignored, and the beams of light are treated as rays that obey simple trigonometric

relationships based on bulk material properties.

Two predictions of geometrical optics relevant to the present work are the laws of reflection and

refraction. The law of reflection simply states that θi = θr, where the i and r indicate the angles of

incidence and reflection, respectively. The law of refraction, or Snell’s Law, is:

ni sinθi = nt sinθt (2.9)

where the subscript i indicates the incident medium and the t indicates the second medium through

which the transmitted beam travels.66

When the interface between the two media is rough, some fraction of the incident beam will be

scattered away from the specular direction predicted by the law of reflection. This behavior is

known as diffuse reflectance. The prediction of the precise intensity and angular distribution of the

light reflected from a rough surface is difficult, and approximate solutions to the problem are known

only for periodic or random surface profiles in which either the roughness is small (perturbation

theory) or in which the roughness varies slowly (Kirchoff theory).67

24

Because the transition from smooth to rough surface is continuous, there is no sharp transition

between the two. The most commonly accepted criterion for a rough or smooth surface is the

arbitrary one set forth by Lord Rayleigh, which is known as the Rayleigh criterion. For a rough

surface the path difference of two parallel light rays is:

∆φ =4πhcosθ

λ(2.10)

where ∆φ is the phase difference between the two parallel rays striking nearby points on the surface,

h is the difference in height between the two points, θ is the incident angle measured from the

surface normal, and λ is the wavelength of light.68 The Rayleigh criterion is based on a phase

argument; when the two rays are out-of-phase by π, they will destructively interfere and transmit

no intensity in the specular direction. Rayleigh proposed that the surface be considered smooth

when ∆φ < π/2, or by substitution into Equation 2.10:

h <λ

8cosθ(2.11)

This relation shows that a surface will appear smoother when viewed at larger angles, i.e., closer

to the grazing angle, and when viewed using longer wavelengths of light.

All real surfaces possess some degree of roughness, and will therefore exhibit a finite diffuse

reflectance. To minimize this diffuse scattering, a liquid with the same refractive index as the

sample, to eliminate refraction at the liquid/sample interface, can be applied to the surface or used

as an optical coupling medium between the rough surface and a known smooth surface, such as a

polished glass sheet. The liquid will flow to fill the irregularities of the rough surface, resulting in

a smooth surface for the incident beam to strike, thus reducing surface scattering.

Regions of inhomogeneity in bulk materials also lead to light scattering. Again, various approxi-

mations are employed depending on the magnitude of the refractive index fluctuations in the ma-

terial and the comparative size of the variations and the wavelength of light used. Fluctuations in

density and orientation on the length scale of the wavelength of the incident light lead to variations

25

in refractive index in the material which results in the scattering of light. Non-random density and

orientation fluctuations in objects such as polymer spherulites may lead to complex scattering pat-

terns which depend on the symmetry and internal structure of the object. Scattering from polymer

spherulites is discussed below.

2.2.2 Small Angle Light Scattering

The bulk morphology of many quiescently crystallized polymers is composed of spherulites. In an

attempt to explain the patterns produced by the scattering of polarized light at small angles from

polymer spherulites, Stein and Rhodes developed a model to predict the scattering profile of an

anisotropic sphere.69 This model, valid for scattering at small angles, has proven to be successful at

predicting the angular range and intensity of light scattered from polymer spherulites, and was later

extended to predict scattering patterns from sheaf-like crystals and rods.69–73 A brief summary of

the theory follows.

The small-angle light scattering (SALS) theory models a spherulite as an anisotropic sphere, where

the radial birefringence, nr, is not equal to the index of refraction in the tangential direction, nt .

The spherulite is embedded in a surrounding medium of uniform refractive index, ns. The theory

of Stein and Rhodes employs the Rayleigh-Gans-Debye approximation for light scattering, which

considers each small volume element in the sphere to be a separate scattering entity.13, 69 The

scattered amplitude from each element is summed to produce the total scattered amplitude, which

will have a particular distribution due to the interference between waves scattered from different

volume elements. This approximation is valid only when the refractive indexes of the object and

medium are similar, and when the phase difference between light scattered from nearby volume

elements is small.13 The first condition is normally satisfied for polymer systems since a spherulite

will be found either growing in the melt or surrounded by other spherulites, each of which has a

refractive index similar to the spherulite in question. The second condition typically holds when,

for visible wavelengths of light, the spherulite radius is on the order of 10 µm or less.

26

These experiments are carried out using monochromatic illumination, typically from a laser, which

is linearly polarized. The light beam passes through the sample, which must be thin to avoid mul-

tiple scattering and is often coated with an oil of matching refractive index to eliminate surface

scattering, and the scattered light then passes through the analyzer. Two positions of the analyzer

are commonly used: alignment of the analyzer extinction direction parallel with that of the po-

larizer for the VV condition, and alignment perpendicular (crossed polars) for the HV mode. The

resulting pattern is collected using a flat plate of photographic film, multichannel analyzer, or a

charge-coupled device (CCD) sensor.

The theoretically predicted scattered intensities for the VV and HV modes, IVV and IHV respectively,

are given as a function of the radial scattering angle θ and the azimuthal scattering angle µ by:

IVV = Aζ2V 2

0 (3/U3)2{(αt −αs)(2sinU −U cosU −SiU)

+(αr −αs)(SiU − sinU)+(αr −αt)[cos2(θ/2)/cosθ]

×cos2 µ(4sinU −U cosU −3SiU)}2 (2.12)

IHV = Aζ2V 2

0 (3/U3)2{(αr −αt)[cos2(θ/2)/cosθ]

×sinµcosµ(4sinU −U cosU −3SiU)}2 (2.13)

where A is a proportionality factor, V0 is the volume of the sphere, αt is the tangential polarizabil-

ity of the sphere, αr is the radial polarizability of the sphere, and αs is the polarizability of the

surroundings. The geometric polarization correction term ζ is given by:

ζ = cosθ

√cos2 θ+ sin2

θcos2 µ (2.14)

SiU is the sine integral given by:

27

SiU =Z U

0

sinxx

dx (2.15)

and is solved using a series expansion. U is the shape factor for a sphere, and is given by:

U =4πR0

λsin(θ/2) (2.16)

where R0 is the radius of the sphere and λ is the wavelength of light in the medium.69, 72

The VV mode patterns generally show anisotropy along the polarization axis due to the cos2 µ term,

which is maximum when µ = 0. VV scattering is sensitive to fluctuations in both density and

orientation of the volume elements, but can be difficult to perform experimentally due to the high

intensity of the transmitted incident beam. No VV scattering studies were performed in the current

work.

HV SALS, while sensitive only to fluctuations in orientation, is simple to perform experimentally

due to the extinction of the main beam by the crossed polarizers and provides useful information

about the spherulite dimensions, as will be discussed below. HV scattering patterns from well-

formed spherulites display a characteristic four-leaf clover appearance due to the maxima of the

sinµcosµ factor at µ = 45◦ intervals around the pattern. Furthermore, when the azimuthal scat-

tering angle is maximum, µ = 45◦, the scattered intensity increases from zero at θ = 0 and goes

through a maximum at U = 4.1 before decreasing.69 Under these conditions, Equation 2.16 can be

rearranged to:

R0 =4.1λ

4πsin(θmax/2)(2.17)

This equation can be used to estimate the average size of the spherulites by measuring θmax from

the experimentally obtained HV pattern. Alternatively, the angle at which maximum scattering will

occur under HV polarization conditions can be predicted if the spherulite radius is known. This

technique can estimate the radius of spherulites too small to be observed in an optical microscope

28

and rapidly provides an average size of all spherulites illuminated by the incident beam. Equation

2.17 is used as a powerful tool for the investigation of the spherulitic morphology in polymer films.

The convenience and utility of the HV SALS technique has led to extensions of the basic model

to incorporate corrections such as spherulite truncation, internal disorder, interference between

spherulites, and a distribution of spherulite sizes.74–80 Models have also been developed for sheaf-

like crystal aggregates.71, 73, 81 These deviations from perfect spherulite structure generally in-

crease the intensity at low and high angles, and may cause the intensity maximum to shift from the

typical U = 4.1 location. The general predictions of the basic model still hold, and it is the original

model of Stein and Rhodes that is typically employed for analysis of experimental patterns due to

the mathematical complexity introduced by the previously mentioned corrections.69

Using the basic model it can be shown that the maximum scattered HV intensity (θmax) occurs

along the µ = 45◦ line when U = 4.1; from Equation 2.13 the following can then be shown:

I ∝ R60 (∆n)2 (2.18)

Thus the HV scattered intensity at θmax increases rapidly with spherulite radius and increases to

a lesser but still significant extent as the birefringence increases. Equation 2.18 also predicts that

the scattered intensity will approach zero, even for large spherulites, as ∆n approaches zero. Thus,

spherulitic films of polypropylene with low or mixed birefringence should scatter relatively small

amounts of light and display good optical properties. The interplay between scattered intensity,

the angular distribution of the scattered light, and the observed macroscopic optical properties is

discussed in more detail in the following sections.

2.2.3 Haze

The quantification of film optical quality is a difficult task due to the large number of variables

including illumination conditions, viewing angle, orientation of the film and target object with re-

spect to the observer, and variation in human perception. Haze, clarity, transparency, and gloss

29

are examples of parameters that have been defined in an attempt to measure film quality under

standardized conditions. Standardized haze and gloss measurements correlate well with the milk-

iness and sheen, respectively, of thin polymer films. However, the development of a meaningful

measurement of film clarity or transparency is more difficult.

The next several sections divide the discussion of optical quality evaluation into loosely defined

areas concentrating on the visual properties of interest and the testing methods established to quan-

tify them. The measurement of the cloudiness or milkiness of a polymer film is typically evaluated

using a haze metric. The loss of resolution of objects viewed through the film is due to a reduction

in film clarity, the measurement of which is the subject of some debate. While the haze and clarity

of a film are influenced by light scattered from both surface and bulk features, the sheen or gloss

of a material is overwhelmingly dependent on the surface quality. The description of the theory

of optical property measurement and its application to the development of measuring instruments

is necessary for a thorough evaluation of the results of the current research project, which are

presented in Chapter 4.

The perceived cloudiness of a film, which is a manifestation of the loss of contrast of objects

viewed through the film, had been successfully characterized by the haze metric. The evaluation of

film haze by subjective visual methods is effective for materials of generally poor optical quality,

but for fine differentiation of relatively non-hazy films a more quantitative method is required.

Experimental work by Barnes and Stock led to the development of a haze measuring instrument and

an American Society for Testing and Materials (ASTM) standard for the determination of haze.82

This basic design has remained relatively unchanged and the standard procedure was codified as

ASTM D 1003.83 A schematic drawing of this type of hazemeter is shown in Figure 2.10.

The illumination from an incandescent source is corrected to a standard spectrum, typically CIE

Illuminant C with a color temperature of approximately 6500K and designed to simulate overcast

daylight, and shaped by an optical system into a parallel beam approximately one inch in diameter.

The beam passes through the center of the entrance port of an optical integrating sphere, travels

through the sphere, and is extinguished by a light trap at the exit port of the sphere. A photosen-

30

Figure 2.10: Schematic drawing of hazemeter.

sitive detector is placed 90◦ from the main beam axis and baffled from the entrance port so as to

receive no direct illumination.

A provision is made for either tilting the sphere so the main beam strikes the sphere surface rather

than the light trap, or by providing a movable door to block the light trap and diffuse the main beam

into the sphere interior. This step is required for calculation of the haze result which is described

below. Sample films, or liquids if placed into an optical cell, are measured by placing the film flush

with the sphere entrance port.

The geometrical restrictions of ASTM D 1003 result in a hazemeter that discriminates between

light scattered in a forward direction above and below an average of 2.5◦. The haze measured by

this technique is defined as:

haze =(Φs)

902.5

Φt +(Φs) f×100% (2.19)

where (Φs)902.5 is the light scattered between 2.5 and 90◦, Φt is the intensity of the undeviated trans-

mitted beam measured with the sample in place, and (Φs) f is the forward scattered fraction, or the

intensity scattered away from the main beam but still in a forward direction.68, 83, 84 The denom-

inator of Equation 2.19 constitutes the total flux transmitted by the specimen and is measured by

31

tilting the sphere or blocking the light trap as described above.

Thus, the haze measurement quantifies the fraction of light transmitted by a specimen that is scat-

tered at large angles (2.5◦). High haze values indicate a film with poor optical properties. The

physical basis for the haze measurement can be described with geometrical optics arguments.

Light traveling from a target object to the observer’s eye may be scattered when passing through

a polymer film. If some portion of this light is scattered at large angles within the film, it will not

enter the observer’s eye and the target object will appear less bright. In addition, some light emitted

from the object at a wide angle that would normally miss the observer’s eye may be scattered

through a large angle and enter it. This light would appear to have originated from some point near

the object which would cause the background to appear brighter. The net effect is a dimming of the

object and a brightening of the background. This loss of contrast gives the film and objects viewed

through the film a cloudy or milky appearance and causes colors to appear faded and washed-out.

These effects are normally undesirable in packaging film applications, and haze measurements are

frequently used to rank the quality of such films.85–96

2.2.4 Clarity, Transparency, and Visually Perceived Film Quality

The inability of the haze measurement to completely classify the optical properties of polymer

films was demonstrated by Webber, who photographed test targets through films of different ma-

terials and showed that films with high haze could permit good resolution of the targets and that

the converse was also true.97 Using a high resolution photogoniometer constructed by Aughey and

Baum, Webber showed that the direct transmittance, or transparency, of the films correlated well

with rankings of film quality performed by human observers, provided that the cutoff angle at the

receiving aperture was very small.97, 98 Correlations between perceived quality and transparency

were lost if the acceptance angle exceeded 0.1◦.

The distinction between haze, the loss of contrast, and transparency, the loss of resolution, is now

widely accepted. Subsequent studies have used different techniques and terminology for the per-

32

ceived loss of resolution, and the terms see-through clarity, transparency, clarity, and see-through

are often used to describe this effect.99–102 The point of agreement among all of these authors is

that the receptor aperture must be very small to retain the correlation between the instrumental

results and human perception, as originally found by Webber.97

An ASTM testing standard for transparency was published in 1960 as ASTM D 1746.103 This

standard specifies conditions for the measurement of transparency based on Webber’s work, but

without the requirement of a movable detector system. This provision reduces complexity and

cost, but relegates the standards-compliant transparency meter to the role of a testing device, rather

than a research instrument. A drawing of an ASTM D 1746 style transparency meter employing

an incandescent source is shown in Figure 2.11

Figure 2.11: Schematic drawing of transparency meter.

where L is a lens system designed to produce a symmetric and slightly converging beam, S is the

sample, P is a pinhole of appropriate size to exclude light scattered by more than 0.1◦, and D is a

photosensitive detector. ASTM transparency is calculated using the simple relation:103

T =II0×100% (2.20)

where I is the transmitted light intensity with the specimen in the beam path and I0 is the trans-

mitted light intensity with no specimen in the beam path.103 Again, the key specification in the

geometry of this instrument is the very small angle used to exclude light from the main beam at the

receptor aperture. Further discussions of the meaning of transparency and clarity measurements

33

are presented in Section 4.1.2.4.

The loss of resolution of objects viewed through the film is due to the scattering of light at small

angles. Consider a bright point object on a dark background viewed through a film with poor

transparency. The light emitted by the point will be scattered at small angles when traversing

the film. Thus the originally narrow light beam will be blurred or spread out by the small angle

scattering and the point will appear to be surrounded by a luminous halo. Two points in close

proximity will cease to be resolved when their luminous halos overlap as described by the Rayleigh

or Sparrow criteria for resolution.66 The loss of resolution of a target object viewed through a film

is dramatically increased as the film to target distance, d, increases. The angular separation of any

two points decreases as d increases, so even luminous halos of small angular width can cause a

loss of resolution.68 Polymer films are often used in commercial packaging applications where

the film is in contact with or very close to the target object. In these cases, the transparency

(clarity) measurement may be less useful than haze because the image degrading effects of poor

clarity are minimized for small values of d. Conversely, applications where the important criteria

is the resolution of detail in distant objects viewed through the film or sheet, such as windows or

windscreens, will be most affected by poor clarity.

Therefore, it is clear that the haze and transparency of a film are relatively independent properties,

with each effect arising from a different origin. For example, a film composed of large hetero-

geneities may scatter light intensely at small angles but relatively weakly at large angles. Such a

film would have poor clarity but relatively good haze and may be suitable for a packaging applica-

tion in which the film is in close proximity to the target object and the deleterious optical quality

effects of poor clarity are minimized. Conversely, a film containing small inclusions or density and

orientation fluctuations would scatter light at large angles and show good transparency but high

haze.

It is important to realize that the ASTM standard tests described above all utilize measurements of

transmitted light to evaluate the optical properties of the specimen. In common applications such

as packaging films, the light source is typically on the same side of the film as the observer. Little

34

work has been reported on the measurement of film haze or transparency using reflected light.

In addition, the effect of backscattered light on optics is typically neglected, but may be partly

responsible for discrepancies in visually observed and measured optical properties. Although the

ASTM standard test methods for haze and transparency employ illumination conditions that are

not always encountered in practice, the results of these tests have been shown to correlate with

visually perceived optical properties. Considering the issues discussed above, the ASTM haze and

transparency tests are useful for the characterization of polymer film optical properties in a general

sense, but the limitations of the measurements must be recognized.

2.2.5 Gloss

The third general category of optical property measurement, gloss, depends strongly on the surface

properties of the film. Gloss measurements attempt to quantify the perceived shininess or sheen of

the film. Typically, some measure of the reflectance of the film is compared to the reflectance of a

smooth standard.

Gloss measurements for plastic films are typically based on the reduction in specular reflectance

from the film, as specified in ASTM D 2457.104 The measurement described by this standard is

known as specular gloss or gloss, where the angle of reflectance must also be reported. The gloss

measurements used in the current work adhered to the ASTM standard and employed a 45◦ angle

of incidence and will therefore be referred to as gloss-45.

The ASTM gloss test geometry is shown in Figure 2.12.

where θ is the angle of incidence/reflection. Light generated by an incandescent source is shaped

by a lens system into a parallel beam which strikes the surface at an angle θ. Light that is specularly

reflected from the film at the same angle θ will enter the photodetector. The intensity reading

collected from the film is normalized by the intensity of a standard measured under the same

conditions and the result scaled to give a value between 1 and 100 gloss units. Polished black glass

plates are typically used as reflectance standards.

35

Figure 2.12: Schematic drawing of gloss meter.

To minimize the detection of stray light, the specimen must be mounted on a light absorbing fixture

so that only the reflected main beam enters the detector. Either a flat black surface or a black cavity

placed behind the film is sufficient for this purpose. Additionally, the surface of the film must

be completely flat and taut to avoid the loss of measured intensity due to reflection from wavy or

sloped regions of the film.

The sensitivity of the gloss measurement to sample preparation and mounting typically leads to

variations in the gloss values determined for a given sample. Therefore, the average gloss taken

from many regions of the sample is reported along with the measured deviations to give a more

representative gloss characterization. Care must also be taken when comparing gloss values from

different instruments or when different standards have been used for the normalization procedure,

as slight variations in angle or intensity could significantly alter the gloss results.

As shown previously in Equation 2.11, a surface will appear smoother when viewed from larger

angles. Consequently, the gloss of a film increases as it is measured closer to the grazing angle.

Several standard incident angle geometries, including 20, 45, 60, and 85 degrees, have been spec-

ified for use with materials of different gloss levels. The high angle measurements are used to

evaluate products such as paper sheets which display a matte finish. The low angle measurements

36

are used for high gloss metallic and painted surfaces. Polymer films typically have some interme-

diate surface finish and therefore are measured using the 45 and 60 degree gloss geometries.

For a smooth surface the specular reflectance, Rs is given by the Fresnel equation:

Rs =Ir

I0=

12

(cos i−√

n2− sin2θ

cos i+√

n2− sin2θ

)2

+

(n2 cos i−

√n2− sin2

θ

n2 cos i+√

n2− sin2θ

)2 (2.21)

where Ir is the intensity of the specularly reflected beam.68 This equation predicts that the re-

flectance increases as θ increases and, for a given angle, as n increases. Care must be taken, then,

when comparing gloss values of materials with different values of n.

A rough surface will scatter some light in non-specular directions, reducing the measured gloss

value. Equation 2.11 shows that, at a given angle and wavelength, there will be a transition from

smooth to rough surface when the average surface height variation reaches a critical value. A more

realistic model of reflectance from a surface with random height variations which are distributed

with a Gaussian probability shows that the specular reflectance predicted by the Fresnel equation

is reduced by:

Rr = Rs exp

[−(

4πσcosθ

λ

)2]

(2.22)

where Rr is the reflectance from the rough surface and σ is the root mean square (RMS) roughness

of the surface.68, 105 So, as the roughness of the surface increases, the light intensity transmitted in

the specular direction decreases, leading to a lower value of gloss. The reduction of gloss with in-

creased roughness has been shown in several studies of metal surfaces and polymer films.85, 106–111

As a final note on the gloss measurement technique, it must be realized that the distribution of the

diffusely scattered light is not considered. However, this distribution may significantly affect the

appearance of a material. For example, a surface with periodic surface variations may scatter light

in some narrow but non-specular direction, which could have an undesirable appearance when

viewed from particular angles. Therefore, a more thorough characterization of the light scattered

37

from a surface would involve the measurement of the angular dependence of the diffusely scattered

light in addition to the determination of the intensity of the specularly reflected beam.

38

2.3 Surface Roughness

The previous discussions on light scattering and the optical properties of polymer films have shown

that the surface quality of the material is of particular importance. Rough surfaces will scatter light

diffusely and lead to a reduction in the optical quality of the specimen. In the case of thin polymer

films the surface scattering is often the primary cause of the degradation in optical quality. The

classification and measurement of surface topology is discussed below.

2.3.1 Characterization

The review of light scattering presented previously implied that the scattering of light becomes

important when fluctuations in density or orientation of volume elements in a material occur on a

length scale comparable to the wavelength of light. Thus, for visible light, scattering is expected for

fluctuations on the order of 100 nm to 10 µm. The presence of roughness due to the crystallization

of spherulites or sheaf-like crystals near the surface often occur on this length scale and constitute

one origin of surface roughness in semicrystalline polymer films. Physical variations such as ma-

chining marks from the dies and rolls used to manufacture the film and melt flow instabilities that

lead to an orange-peel or sharkskin surface texture may also cause fluctuations on this scale and

contribute to scattering. Therefore, the processing conditions play a primary role in the develop-

ment of surface roughness, and therefore optical properties, of polymer films.86–91, 95, 106, 109

The characterization of roughness on the sub-micrometer scale is performed with stylus or optical

profilometers or, more recently, with scanning probe microscopes (SPM). Each of these techniques

provides information on the height of the surface at a given lateral position. The techniques are

differentiated primarily by the limit of their lateral resolution, which is approximately 1 µm for op-

tical profilers, 0.2 µm for a mechanical profilometer equipped with a submicron radius stylus, and

1 nm for SPM instruments.112, 113 Optical profilometers provide information on the average rough-

ness in the two dimensional area illuminated by the light beam. Traditional stylus profilometers

drag a diamond stylus across the surface of the specimen while recording the variation in height,

39

providing a high resolution profile along one scan line. The scanning probe microscopes generally

sense the height of the surface through noncontact methods and achieve two dimensional lateral

resolution using a raster scan technique. The scanning probe microscope has become the dominant

surface profiling instrument in the polymer science field due to its convenience and nondestruc-

tive probe-sample interaction. The measurement of roughness with the atomic force microscopy

(AFM) variant of SPM is discussed in Section 2.3.2.

The roughness of a surface can be quantified in several ways. The most reported parameters are the

mean or average roughness, Ra, and the root mean square (RMS) roughness, σ, which are given by

the following equations for roughness in one dimension:

Ra =1N

N

∑i=1

|Zi−< Z >| (2.23)

σ =

√1N

N

∑i=1

(Zi−< Z >)2 (2.24)

where N is the number of data points in the data set, Zi is the height at point i, and < Z > is the

mean surface level chosen so that the following expression is satisfied:112, 113

N

∑i=1

(Zi−< Z >) = 0 (2.25)

The two dimensional version of these equations is similar. Both of these parameters are simple

to calculate and are widely used. In addition, the RMS roughness often appears in theoretical

treatments of light scattering by random rough surfaces as seen in Equation 2.22. However, neither

of these parameters contain spatial information.

To quantify the correlations of surface variations, several other metrics may be used. The autoco-

variance function, its Fourier transform, the power spectral density, or the autocorrelation function

describe the probability that a surface feature will repeat itself over a given length.112 This para-

meter is useful in the characterization of surfaces with some repeated feature, such as a spherulitic

40

surface morphology or the presence of streaks or grooves formed during film processing.

More recent studies have examined the self-affine nature or fractal dimension of polymer film

surfaces. A self-affine roughness exponent may be calculated from line profiles obtained from one

dimensional height images; the value of the roughness exponent varies from 0 to 1, where the value

of unity represents a smooth surface.114 Fractal dimension parameters may be determined from

either 1 or 2 dimensional data sets.115 In this case, a higher fractal dimension indicates a rougher

surface. These analysis techniques require more intensive calculations than the average roughness

parameters and correlation functions described previously, which limits their widespread use.

The RMS roughness as measured by tapping mode AFM was used exclusively during the present

work due to its convenience and suitability for the purpose of the study, which was primarily

concerned with estimating the surface roughness of polymer films for comparative purposes. The

following section discusses the use of AFM for the determination of surface roughness.

2.3.2 Measurement of Surface Roughness

Over the past 15 years, the measurement of surface topology, which was previously characterized

by stylus or optical profilometery, has become dominated by the use of scanning probe microscopy.

Atomic force microscopy in particular has become a popular tool for surface metrology in polymer

science due to its ease of use, ability to sample three-dimensional space at nanometer resolution,

and the low probe-sample interaction forces used which allow for the imaging of soft surfaces

such as amorphous or poorly crystalline polymers.90, 91, 93–96, 109, 114–119 A comprehensive review

of the considerations required for accurate measurement of surface features with AFM is given

by Griffith and Grigg.120 The following discussion highlights several of the issues relevant to the

current work.

Although AFM instruments and their associated software packages are easy to use, several issues

arise in the measurement of surface roughness. The resolution of the AFM in tapping mode may

be on the order of one nanometer or less, but the total image is limited to fixed resolution, often a

41

512 x 512 pixel square. At this image resolution a 1×1 µm2 image is composed of pixels less than

2 nm on each side, in a 20×20 µm2 image each pixel is a 39 nm square, and for a 100×100 µm2

image each pixel spans 195 nm. Therefore, polymer lamellae, which were typically a few tens of

nanometers in thickness, typically cannot be resolved in AFM images larger than 10–20 µm. The

pixel size also influences the measured height of the surface, although not always in a well-defined

manner, as shown by Heymann et al.121

At the opposite end of the sampling spectrum, the maximum image size of the AFM is limited by

the motion of the scanner tube. The scanner tubes are piezoelectric devices that move the tip or

sample stage with nanometer precision. The maximum travel of these devices is limited to about

100 µm. However, large travel distances lead to large corrections in image post-processing due

to the flexing motion of the scanner tube. Practically, AFM images are limited to 40–100 µm in

length, depending on the particular sample studied and the ambient conditions.

The maximum image size is important when looking at correlation lengths of surface features. For

example, the characteristic dimension of a morphology composed of 50 µm diameter spherulites

would be difficult to detect in a 40 µm image. Since one of the goals of the present study was to

correlate surface roughness with visible light scattering, objects from 20 nm up to a few microm-

eters in dimension were of particular interest. Features of this size could be reliably imaged over

the practical operating conditions of the AFM.

The image size is well known to affect the measured surface roughness.96, 112, 115, 118, 122–124 Typi-

cally, an increase in RMS roughness with increasing image size is observed. Changes in the slope

of a σ versus image size indicate that surface variations of different characteristic lengths are in-

cluded in the measurement. A plateau region may be reached where the RMS roughness becomes

independent of image size.122, 124 In this region, rarely seen in practice, all surface correlations

lengths below the upper cut off point (the image size) are resolved.

Experimental determinations of σ by AFM are therefore carried out at a fixed image size to avoid

the measurement of different sets of correlation lengths at different image sizes. The image size

acts as a bandpass filter, removing the fine detail of small features due to the averaging of height

42

data within an image pixel, and excluding large scale surface variations due to the limited sampling

length defined by the overall size of the image.118 Alternative approaches to surface characteri-

zation, such as the fractal dimension analysis mentioned previously, account for the image size or

sampling length and may allow for better comparisons of surface roughness.

The effects of the raster-scan nature of the AFM on the measured image are also worth consid-

eration. The cantilever tip, which typically oscillates at 100–300 kHz in tapping mode, scans

back-and-forth in the x-direction while rapidly sampling height data. The tip then jumps down

one scan line; the distance of the jump is determined by the image size as discussed above. The

result is that the x-direction of the image is composed of many samples of the surface, while in

the y-direction, the surface is sampled at only a limited number of points (once per line). This

scanning mode may lead to inaccurate measurements of a periodic surface such as a diffraction

grating if the grooves are aligned parallel to the x-direction. Because the films used in the current

study had nominally isotropic surfaces, this was not a crucial issue.

The interaction of the probe tip and the samples must lead to some distortion of the true sample

surface. Since the tip has a finite size and radius of curvature, the measured image will be a

convolution of the shapes of the surface and the tip.125–131 The sample tip convolution problem is

well known from earlier work with stylus profilometry, where these effects are more important due

to the much larger size of the profilometer stylus.132, 133 These issues were not of great importance

in the present work because the interest here was in the characterization of trends in roughness, not

in establishment of the absolute surface geometry.

Simpson et al. have raised concerns that high tip velocities, normally encountered at large image

sizes, can cause the surface profile to be measured in error.123 The electronic feedback system of

the AFM may not respond quickly enough to changes in surface height when the probe is moving

at high linear velocities, leading to a misrepresentation of the surface features. However, this

effect can be minimized by utilizing scan rates slow enough to allow the probe enough time to

adequately sample the surface at each data point (image pixel). At large image sizes, where the

linear tip velocity is inherently high, a balance must be found between slower scan speeds that

43

minimize measurement errors and faster scan speeds that minimize drift and image artifacts due to

fluctuations in temperature, vibration, and from contamination of the tip.

The caveats discussed above must be considered when AFM is used to evaluate the RMS rough-

ness of surface. Many of the potential problems can be minimized with the appropriate selection

of experimental conditions. The superior resolution, three-dimensional sampling capability, and

convenience of the AFM technique make it an invaluable tool in the study of surface topology.

The discussion in this chapter briefly reviewed polymer and copolymer crystallization, polymer

morphology, and the interesting and unique properties of i-PP; the interactions of light with matter,

which leads to scattering from the surface and the bulk of polymer films; the optical parameters of

haze, transparency, and gloss used to evaluate the optical quality of polymer films; and the princi-

ples and techniques of surface characterization. The following chapters present the experimental

methods used in the current research, the results obtained from these measurements, a discussion

of the results, the conclusions drawn from this work, and a section highlighting potential avenues

for subsequent work in this area.

Chapter 3

Experimental

3.1 Materials

Propylene/ethylene copolymers were provided by the Dow Chemical Company. The novel catalyst

system developed by Dow Chemical produced isotactic polypropylene homo- and co-polymers

which exhibited physical properties that were desirable for commercial applications such as films

and fibers.3 These polymer chains contained a different distribution of regio-defects than was

commonly seen with conventional metallocene or Ziegler-Natta catalysts.

The copolymers were designated as PEX.X, where the X.X indicated the mole percent of ethylene

comonomer. The sample name, series (batch) number, comonomer content, molar mass and distri-

bution, catalyst type, and melt flow rate (MFR) are listed in Table 3.1. The series numbers indicate

different production runs on the pilot- or mini-plant scale. The tacticity and regio-error content of

these materials as determined by NMR analysis is listed in Table 3.2.

Two variants of the catalyst were used for most of the syntheses, designated A and B (see Table

3.2). Recent analysis of these materials revealed that those made with catalyst B exhibited a broad

melting peak with a long high-melting tail, especially the series VII materials.53, 134 This was

attributed to the catalyst’s pseudo-blocky comonomer insertion behavior, which resulted in the

44

45

presence of some long crystallizable sequences even at high comonomer contents. Catalyst A

appeared to produce a material with a more alternating sequence distribution based on analysis of

NMR data provided by Dow Chemical; these polymers displayed broad melting peaks, but did not

have the high-melting tail indicative of long i-PP sequences.

The interesting melting and crystallization properties of these copolymers suggested their use for

practical applications such as fibers and packaging films.3, 4 Test films of these materials displayed

better optical properties than propylene/ethylene copolymers with similar ethylene content but

produced with conventional Ziegler-Natta or metallocene catalysts. Extruded cast films made from

these resins and their blends were provided for study, although with more limited characterization

data than the bulk resins. These films had complicated designations from Dow Chemical and were

given an abbreviated identification number and a simple index number. Data for these films is

listed in Table 3.3.

Several P/E copolymers synthesized using Ziegler-Natta and metallocene catalysts were also sup-

plied by Dow Chemical in pellet form for comparison purposes. These resins were designated

ZNX.X and METX.X, respectively, and are described in Table 3.4. While the four MET materi-

als were synthesized using ‘metallocene’ catalysts, the same catalyst was not used in each case.

The variety of single-site metallocene-type catalyst systems available could produce very differ-

ent chain architectures as discussed in Section 2.1.3. Therefore, systematic trends in physical and

optical properties for the MET series should not be expected a priori.

3.2 Film Fabrication

Copolymer pellets received from Dow Chemical were compression molded into films using a

Carver Model C hydraulic press equipped with heated platens. These films were typically pre-

pared using 0.3 to 0.5 grams of polymer pellets placed between two 6× 6 or 4× 4 inch square

sheets of 0.005 inch thick KaptonTM film, which lined the mirror polished faces of two stainless

steel plates. The assembly was placed in the heated press, normally at 200◦C for the P/E copoly-

46

Table 3.1: Dow P/E copolymer physical data.

Sample Series Ethylene Content Mw Mw/Mn Catalyst MFR

Name Number mol% kg/mol Type g/10 min

PE0.0 I 0.0 320 2.7 A 2.5

PE8.2 I 8.2 300 2.2 A 2.2

PE13.6 I 13.6 290 3.1 A 2.3

PE19.4 I 19.4 260 2.4 A 2.0

PE4.4 II 4.4 320 N/A A 1.9

PE7.8a III 7.8 160 2.2 A 24.9

PE12.4 III 12.4 160 2.3 A 23.1

PE14.8 III 14.8 160 2.3 A 20.4

PE15.0 III 15.0 120 2.0 A 88.3

PE3.3 VII 3.3 230 2.3 B 7.4

PE5.4 VII 5.4 157 2.4 B 30.0

PE6.7 VII 6.7 325 2.3 B 1.8

PE7.0 VII 7.0 168 2.3 B 24.7

PE12.3 VII 12.3 305 2.4 B 1.7

PE12.8 VII 12.8 154 2.2 B 26.4

PE16.6 VII 16.6 154 2.3 B 26.4

PE17.4 VII 17.4 290 2.4 B 1.8

PE21.2 VII 21.2 275 2.4 B 1.8

PE4.8 VIII 4.8 314 2.4 B 2.2

PE7.8 VIII 7.8 219 2.4 B 8.2

PE13.3 VIII 13.3 289 2.7 B 2.3

PE6.5 IX 6.5 217 N/A C 8.2

47

Table 3.2: Dow P/E copolymer tacticity and regio-error data.

Sample Regio-errors %mm %mr %rr

Name mol%

PE0.0 1.18 93.7 4.6 1.6

PE8.2 0.47 94.3 2.2 3.4

PE13.6 0.34 96.4 0 3.6

PE19.4 0.18 95.2 0 4.8

PE4.4 0.57 93.5 4.1 2.4

PE7.8a 0.41 95.0 2.8 2.2

PE12.4 0.21 97.3 0 2.7

PE14.8 0.31 93.8 1.9 1.9

PE15.0 0.30 97.2 0 2.8

PE3.3 0.87 92.8 5.3 1.8

PE5.4 0.89 93.6 4.7 1.8

PE6.7 0.52 95.4 2.6 2.0

PE7.0 0.46 95.3 2.7 2.0

PE12.3 0.37 97.3 0 2.7

PE12.8 0.32 97.7 0 2.3

PE16.6 0.24 97.3 0 2.7

PE17.4 0.41 91.7 0 8.3

PE21.2 0.2 96.2 0 3.8

PE4.8 0.8 94.9 N/A N/A

PE7.8 0.8 95.1 N/A N/A

PE13.3 0.9 94.8 N/A N/A

PE6.5 0.5 95.4 N/A N/A

48

Table 3.3: Dow cast film physical data.

Sample Index Ethylene Content Mw Mw/Mn MFR Thickness

Name number mol% kg/mol g/10 min mil

14-1 1 0.7 N/A N/A 2.6 1.60

14-45 2 6.3 N/A N/A 7.0 1.80

14-7 3 7.7 N/A N/A 7.0 2.30

38-06 4 7.0 307 2.40 2.0 2.50

38-07 5 4.6 215 2.56 8.5 1.90

38-08 6 5.9 225 2.70 7.0 1.00

38-09 7 4.4 322 2.00 2.0 1.50

38-10 8 5.2 308 2.50 2.0 2.10

38-11 9 7.3 212 2.50 8.0 1.30

38-12 10 6.5 216 2.55 8.0 2.20

42-1 11 7.3 N/A N/A 8.0 2.05

42-2 12 7.3 N/A N/A 8.0 1.50

42-3 13 7.3 N/A N/A 8.0 1.45

43-2 14 N/A N/A N/A N/A 2.10

43-4 15 N/A N/A N/A N/A 2.20

43-6 16 N/A N/A N/A N/A 2.50

49

Table 3.4: Ziegler-Natta and Metallocene copolymer physical data.

Sample Ethylene Content Mw Mw/Mn

Name mol% kg/mol

ZN4.4 4.4 N/A N/A

ZN8.3 8.3 255 3.5

MET5.2 5.2 222 2.7

MET6.5 6.5 308 2.5

MET11.1 11.1 147 2.1

MET13.5 13.5 117 2.0

mers, and the platens closed to allow the pellets to melt for one minute. Loads of 1, 2, 3, and/or 5

metric tons were then applied in cycles of 10 to 15 seconds to mold the film. Maximum pressures

ranged from approximately 100–400 psi. In some cases, brass or aluminum shims were used to

control film thickness and shape. After pressure cycling, the films were allowed to relax at the melt

temperature, typically for one minute, before cooling/quenching. Films were aged for 3–4 days at

room temperature before any measurements were taken.

Thin films for light scattering and microscopic analysis were prepared by pressing small portions

of a copolymer film between two 16 mm diameter glass coverslips on a hot plate heated to 180–

200◦C. The resulting films were approximately 20 µm thick. These films were melted and recrys-

tallized at either 1, 10, or 90◦C per minute in a Linkam THM 600 hotstage with a TP91 controller

under a nitrogen atmosphere before any measurements were taken.

3.3 Film Thickness

A Starrett Model 230 micrometer was used to measure the thickness of the films to ±0.0001

inch (2.5µm). Approximately 5–30 measurements were made on each film to obtain an average

50

thickness. In many cases, the center region of the film was measured in a systematic fashion to

obtain the thickness profile.

3.4 Density Measurements

Samples for density analysis were prepared in several ways. In some cases, simple geometric

shapes were cut from pressed films and used as-is. For other experiments, small samples of copoly-

mer film were cut from pressed sheets and placed on glass coverslips. The samples were melted at

180–200◦C for several minutes in a Linkam THM 600 hot stage with TP91 controller and recrys-

tallized by cooling at either 1, 10, or 90◦C per minute.

For very well defined temperature control and for comparison to existing thermal data, disks of

copolymer film were sealed in standard Perkin–Elmer aluminum DSC pans.53 The encapsulated

samples were melted at 180–200◦C for several minutes and recrystallized by cooling at either

1◦C, 10◦C, or 90◦C per minute using a Perkin-Elmer Pyris 1 DSC. An ice/water bath or liquid

nitrogen system was used during cooling, depending on the desired cooling rate. The films were

then removed from the pans and cut into simple shapes for density analysis.

A Techne model DC–2/DC–4 density gradient column apparatus was used to measure the density

of the copolymer film samples in general accordance with ASTM D 1505–98.135 Blends of iso-

propyl alcohol and distilled water were used to establish a linear density gradient ranging from

approximately 0.8400g/cm3 to 0.9200g/cm3. The glass density column was immersed in a water

bath thermostatically controlled to 23± 0.05◦C. Calibrated glass floats from American Density

Materials were used to create a linear calibration curve for the column as recommended by the

Techne Instruction Manual.136 Typically, 12–14 floats spaced approximately 0.005g/cm3 apart

were used for each calibration.

The prepared copolymer samples were dipped in an alcohol/water solution and dropped into the

density column. Fewer than 25 samples were placed into the column at a time to avoid overcrowd-

ing. Samples were typically allowed to equilibrate for 3–4 days before measurements were taken.

51

The positions of the samples and floats were read concurrently, then the density of the samples was

determined using the calibration curve created from the float data. A fresh column was used for

each batch of samples.

3.5 Refractive Index Measurements

The refractive index of the copolymer films was measured with an Abbe refractometer manufac-

tured by the Milton Roy Company. Tap water was used to maintain the sample temperature at

24±1◦C. The scale of this instrument was calibrated to provide indexes of refraction correspond-

ing to measurements made with illumination from the Sodium D line (nD) with a wavelength of

589 nm. The copolymer film samples were cut into 1×3 cm rectangles to cover the refractometer

prisms. Cargille Series A refractive index oil of n = 1.510 was utilized to optically couple the film

to the glass prisms. An oil with a refractive index value intermediate between the refractive index

of the sample (∼1.49) and the refractometer prism (∼ 1.75) was used to insure that the liquid layer

did not affect the measurement of the film refractive index.65 Replicate samples were measured to

obtain average readings.

3.6 Wide-Angle X-ray Diffraction (WAXD)

X-ray powder diffraction patterns were collected with a Scintag XDS 2000 diffractometer in re-

flection mode employing the Bragg-Brentano θ/2θ focusing geometry and using CuKα radiation

with λ = 1.54 A.137 Samples for X-ray analysis were compression molded into either one inch

diameter disks or 1.25×1.5 inch rectangular plaques approximately 1 mm thick using the Carver

Model C press following procedures similar to those used to fabricate film samples. All diffraction

patterns were collected at room temperature.

Because the WAXD analysis was used only to estimate the γ/α ratio of the copolymer samples,

diffraction patterns were collected over the limited angular range of 15–25, 16–21, or 17–21 de-

52

grees 2Θ. A step-scan was used with a step size of 0.04◦ 2Θ and 10s count time per step. No

corrections were made to the raw data.

3.7 Polarized Optical Microscopy (POM)

Polarized optical microscopy was performed using a Zeiss Axioplan microscope in transmis-

sion mode. Micrographs were taken using either an SBIG ST8-XMEI CCD still camera or a

COHU CCD video camera, both of which were interfaced to personal computers. The sign of the

spherulite birefringence was determined using a λ-plate as described in Section 2.1.5.

3.8 Scanning Electron Microscopy (SEM)

A LEO 1550 Field-Emission SEM operating at 2–5 kV was used to image the copolymer samples

which were recrystallized under the desired conditions in the Linkam hotstage as described above.

The film surfaces were coated with approximately 4 nm of gold using a BAL-TEC SCD sputter

coater to reduce charging problems. Even at the low accelerating voltages used, the copolymers

were rapidly degraded by the electron beam, which necessitated rapid focusing and image capture.

Even so, some beam damage was visible in several micrographs.

The permanganic etching techniques first described by Olley and Bassett were used to improve

contrast and remove amorphous polymer on the surface of the films.138–140 A freshly prepared

solution of 1% by weight KMnO4 in a 2:1 mixture of (concentrated H2SO4):(85% H3PO4) was

used to etch the films at room temperature for 1 hour. The samples were removed and rinsed

successively with cold dilute H2SO4, 30% hydrogen peroxide, and acetone. This procedure did

produce the desired results for some samples, but also introduced a level of contamination not

found in unetched samples. Therefore, the etching procedure was not used in every case.

53

3.9 Atomic Force Microscopy (AFM)

Atomic Force Microscopy was carried out in tapping mode using both a Digital Instruments Di-

mension SPM with a Nanoscope IIIa controller and a Digital Instruments MultiMode SPM with a

Nanoscope IVa controller. All experiments utilized silicon cantilever probes with a resonant fre-

quency of approximately 100 to 350 kHz. The silicon probe tips were pyramidal in shape with a

nominal tip radius of 5-10 nm.113

Sample films were either cut from pressed films or prepared in the hotstage under the desired

conditions. The samples were affixed to the AFM magnetic disk sample holders using double-sided

tape. Height and phase images were collected simultaneously over a size range of 1 to 100 µm,

depending on the desired resolution. Height images were flattened using the Digital Instruments

software package. Phase images were generally left unaltered. Surface roughness of whole or

partial height images or of one-dimensional sections through the image was calculated using the

Digital Instruments software.

3.10 Haze and Clarity

The haze and clarity of P/E films were measured using a BYK-Gardner Haze Gard Plus hazemeter

equipped with a CIE illuminant C source and using the appropriate measurement mode and port.

The instrument was calibrated at least daily and the haze and clarity values were verified using

standards from BYK-Gardner. Samples were typically held in place by static electric or manual

forces. Several spots near the center of each film were measured to get an average haze or clarity

value.

54

3.11 Transparency

Film transparency was measured with a Zebedee CL-100 Clarity Meter equipped with an incan-

descent source. The instrument was calibrated every 10–15 minutes to ensure accurate readings.

Samples were held in place manually or by static electric forces. Several spots near the center of

each film were measured to get an average transparency value.

3.12 Gloss

Gloss was measured using a hand held BYK-Gardner micro-gloss 45◦ instrument. The glossmeter

was calibrated before each series of measurements. Films were placed in a custom ring clamp

designed to pull the film surface taut without causing significant deformation. The interior of the

clamp was painted flat black and the clamp was placed on a flat black surface before the gloss

measurements were taken to reduce errors from reflected stray light. Alternately, films were pulled

taut and affixed to a flat black plate with adhesive tape. Typically six to eight gloss readings were

taken near the center of the film to average out any surface or orientation effects.

3.13 Small Angle Light Scattering (SALS)

Small angle light scattering patterns were produced using an apparatus similar to that described

in Section 2.2.2. HV scattering patterns were collected with an SBIG ST8-XMEI CCD camera

interfaced to a personal computer. The camera sensor was cooled to approximately −11◦C to

reduce dark current noise.

Due to the small size of the camera’s sensor, a system of lenses was employed to reduce the size of

the scattering pattern. A reduction of 0.343 was typically used. In this configuration, calibration

was performed using a diffraction grating with 100 lines/mm and Equation 2.7 to determine the

angular location of the first-order diffraction spots. In cases where the patterns were very small,

55

the lenses were removed and the camera was brought close to the analyzer. In this case, the

angles were determined by measuring the distance from the sample to the camera sensor and using

the appropriate trigonometric relations while correcting for refraction of the light beam at the

sample/air interface.

The resulting patterns were digitally blurred using the Gaussian blur filter in the ImageJ image

processing software package.141 This procedure smoothed out the noise and speckle in a manner

analogous to the placement of a frosted glass screen in front of the CCD sensor or film. Quadrant

averaging and line intensity profiles were calculated using ImageJ tools.

Chapter 4

Results and Discussion

4.1 Optical Properties of P/E Films

This section presents the optical characterization of the copolymer films using the techniques de-

scribed in the previous chapter. The haze, clarity, transparency, and gloss of extrusion cast and

compression molded copolymer films were measured to quantify the contributions of surface and

bulk light scattering. Ethylene content and cooling rate were varied to obtain a wide range of

morphologies and corresponding optical properties in the compression molded films.

4.1.1 Extrusion Cast Films

The studies of the optical properties of the copolymer films began with the investigation of the haze

of extrusion cast films provided by The Dow Chemical Company. Researchers at Dow Chemical

had noticed discrepancies between the optical test results of several polymer films and the film’s

visual appearance. In one example, three cast extruded polypropylene/ethylene copolymer films

with very similar test results looked different to the naked eye.142 Therefore, this portion of the

research project evaluated the optical testing methods used in industry and endeavored to resolve

the discrepancy between those test results and human perception.

56

57

For this investigation, Dow Chemical provided samples of sixteen cast extruded propylene/ethylene

copolymer films, including the three films mentioned above. These films ranged in thickness from

about 1–4 mil (1 mil = 0.001 inch = 25.4 µm) and in ethylene comonomer content from 0.7–

7.7 mole percent. At that time, a commercial hazemeter was not available at VT, so the laboratory

small-angle light scattering apparatus was heavily modified (Figure 4.1) to measure haze follow-

ing, as closely as possible, the specifications of ASTM D 1003.83

A six inch diameter integrating sphere (Oriel model 70451) was coupled to a photomultiplier tube

and electronic shutter mounted perpendicular to the main beam axis to measure light scattered

at large angles. The copolymer films were affixed to a sample holder which, when mounted,

positioned the film surface flush with the entrance port of the integrating sphere. A 10mW HeNe

laser (λ = 633 nm) was used for illumination. The main beam and light scattered through small

angles (see Table 4.1) were allowed to exit the integrating sphere and were deflected away from

the sphere and/or absorbed by a light trap. The components were mounted on an optical rail to

allow for centering and alignment.

He/Ne Laser

λλλλ = 633 nm

Neutral Density

Filter; OD = 2

Sample Holder

6-inch Integrating

Sphere

Light Trap

PM Tube (Detector)

Baffled from Entrance PortElectronic

Shutter

Figure 4.1: Schematic of VT hazemeter.

58

Deviations from the ASTM specification are summarized in Table 4.1; refer to Section 2.2.3 for

the details of ASTM haze. To avoid confusion, results from this instrument will be designated as

‘haziness’ rather than ‘haze’ because this configuration did not fully comply with ASTM D 1003.

This custom haziness meter was used to analyze the haziness of the cast extruded P/E copolymer

films provided by Dow Chemical to determine the correlation between VT haziness and the haze

measured by Dow Chemical in accordance with ASTM D 1003. At least thirty points were mea-

sured on each film to provide an average haziness value due to the small beam diameter of 0.8mm

and the nonuniform nature of the films. The haziness data for the cast films was compared with

the haze data reported by Dow Chemical and the results shown in Figure 4.2.

It was clear that there was no correlation between the VT haziness and the haze values reported by

Dow Chemical. Furthermore, the scatter in both data sets was large. Examination of the film rolls

revealed significant variations in thickness and film quality. Several of the cast films displayed

long-range cyclic variations in thickness from less than one to more than five mils over a period

of approximately thirty centimeters. It was also clear that the measured film thicknesses did not

agree with the Dow Chemical thickness data in many cases. Therefore, the effect of film thickness

on haze/haziness was investigated.

Stacks of cast films were used to explore the thickness dependence of haziness. Samples of uniform

thickness were carefully selected from clear regions of the films. In addition, the contributions from

Table 4.1: Differences between VT haziness meter and ASTM D 1003 specification.

Parameter VT hazemeter ASTM D 1003

Entrance Cutoff Angle ∼60◦ 90◦

Exit Cutoff Angle ∼7◦ 2.5◦

Illuminant He/Ne λ = 633 nm white light

Beam Diameter 0.8 mm ∼20 mm

59

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

Dow Chemical Haze, %

VT Haziness, a.u.

Figure 4.2: VT haziness vs. Dow Chemical haze for the cast films.

surface and bulk scattering from these film stacks were measured using the following procedure.

The total scattering was measured for the stack of dry films, then Cargille Series A refractive index

oil of n = 1.4900–1.5000 was applied directly to the film surfaces and smeared with a brush or glass

rod to form a smooth layer of oil between each film (see Section 4.2.1.2 for a discussion of the

choice of refractive index oil). The haziness of the stacks was then remeasured, now accounting

only for scattering from the bulk. The difference in the two measurements was attributed to surface

scattering. Typical results of these experiments are shown in Figure 4.3.

Haziness was seen to increase proportionally to thickness, regardless of whether the total, bulk,

or surface contributions were considered. This suggested that a normalized haziness value would

be useful to compare films of different thicknesses. Therefore, subsequent haziness measurements

will be reported as haziness/mil, which was obtained from the slopes of the haziness vs. thickness

plots. It was also seen that the surface contribution to scattering was significant.

The haziness/mil metric was employed to eliminate the variable of film thickness from the data

60

0

5

10

15

20

25

0 1 2 3 4 5 6

Number of layers

Haziness, a.u.

Total

Bulk

Figure 4.3: Haziness of cast extruded film separated into total and bulk contributions.

shown in Figure 4.2. Dow Chemical haze/mil data was calculated from the thickness data and

deviations that they provided. The results, seen in Figure 4.4, again revealed a poor correlation

(R2 = 0.51) between the two measurements. Therefore, factors other than thickness, such as the

inhomogeneity of the films, contributed to the film haziness.

A comprehensive study was undertaken to examine the contribution from surface scattering in all

sixteen films provided by Dow Chemical using the dry/oiled film stacking method described above.

The composition of the films was not important to this study as only the bulk/surface contribution

was evaluated. The haziness/mil metric was used to directly compare films of unequal thickness.

The results of this work are shown in Figure 4.5.

In most of the cast films the majority of the haziness arose from surface scattering, as expected from

previous studies of polymer film optics.86–93, 95, 96, 107 However, the errors in the measurements

were too large for any trends to be observed. Attempts to observe a systematic trend in the Dow

Chemical haze/mil and VT total and bulk haziness/mil data as a function of comonomer content

61

0

1

2

3

4

0 1 2 3

Dow Chemical Haze/mil, %/mil

VT Haziness/mil, a.u.

Figure 4.4: VT haziness/mil vs. Dow Chemical haze/mil for the cast films.

0

1

2

3

4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Cast Film Number

Haziness/mil, a.u.

Total

Bulk

Figure 4.5: Haziness/mil for Dow Chemical cast films.

62

were also unsuccessful.

The errors in the previous study arose from several sources. The cast films were generally of

poor quality and exhibited rough surfaces with obvious processing marks in the machine direction,

large-scale thickness variations as described previously, heterogeneities such as dirt and inclusions

of apparently unmelted polymer within the film, and regions where the surface displayed a spot-

ted appearance — perhaps due to poor incorporation of processing additives. All of these issues

contributed to variations in the optical property and thickness measurements.

While film samples for this work were carefully selected from relatively defect-free and uniformly

thick regions of the films, samples evaluated at Dow Chemical may not have been. Thickness de-

terminations may have been made by different personnel and on different samples than those used

for haze measurements.142 Although this procedure may not cause difficulties with the evaluation

of uniform materials, the highly variable surface, defect, and thickness characteristics of these cast

films dictated that careful sample selections and measurements were necessary to obtain data for

comparative purposes.

These films were also unsuitable for investigations into the influence of bulk morphology on op-

tics because the bulk morphological features of the films were too small to be seen by optical

microscopy, and the films did not produce consistent HV SALS patterns. In addition, complete

characterization data was not provided by Dow Chemical for all of the films. For these reasons and

the film quality issues discussed above, the majority of the subsequent work used films fabricated

from bulk P/E pellets under controlled conditions in our laboratory. The compression molding

conditions were chosen to produce films without significant orientation. Examination of the Dow

Chemical cast films by polarized optical microscopy and by refractive index measurements taken

parallel and perpendicular to the film machine direction revealed no significant degree of birefrin-

gence, which indicated that the cast films were also relatively unoriented.

The VT haziness meter, although capable of measuring haziness, was labor-intensive to operate as

the narrow beam required the measurement of many (20–30 spots per sample was typical) regions

of the film to obtain a representative average. Figure 4.5, for example, was compiled from 4800

63

individual measurements. The use of monochromatic illumination, incorrect acceptance angles,

and the lack of a standardization procedure prohibited the direct comparison of VT haziness to

ASTM haze. Modification of the apparatus to comply with ASTM D 1003 was considered, but

the purchase of a commercial instrument was determined to be preferable. The BYK-Gardner

Haze Gard Plus was the de facto standard hazemeter in industrial testing labs, complied fully with

ASTM D 1003, and also had a mode for measurement of film clarity. Subsequent experiments

would utilize this instrument exclusively.

4.1.2 Compression Molded Films

The lessons learned from the cast film studies allowed for a focused approach to film fabrication in

the laboratory. It was apparent that smooth surfaced films processed under well-defined conditions

were necessary for the measurement of meaningful optical data. The manufacture of films in

the lab also allowed for the control of the starting materials and crystallization conditions, which

could be tailored to produce bulk morphologies suitable for examination by optical microscopy and

SALS. This would enable the correlations between bulk morphology and bulk optical properties to

be systematically examined.

4.1.2.1 Preparation of Pressed Films

Films were prepared by compression molding copolymer pellets in a heated Carver press. The

cooling rate was varied to produce different bulk morphologies in the films, which are discussed

further in Section 4.2.2. Three scenarios were initially chosen due to their immediate convenience:

rapid cooling by quenching in an ice/water bath, slow cooling achieved by shutting down the press

heaters but allowing the sample to remain in the press until it reached room temperature, or an

intermediate cooling rate realized by removing the sample from the press and allowing it to cool

on the benchtop. These cooling conditions will be referred to as quench, slow cool, and bench top

cool, respectively.

64

Thermal analysis done by Uan-Zo-li had shown that the homopolymer and copolymers used in

this work crystallized in the 140–30◦C range.53 The press cooling profiles described above were

expected to be nonlinear and would be difficult to reproduce with other equipment such as a mi-

croscope hotstage or a DSC.

To determine the linearity of the press cooling profiles in the 140–30◦C range, a 0.005 inch diam-

eter type E thermocouple was sandwiched between two layers of P/E copolymer film and 0.005

inch thick KaptonTM film to measure the temperature at the center of the simulated P/E film. A

temperature monitor from Omega Corporation was interfaced to a personal computer and a custom

BASIC program was written to collect temperature data from the thermocouple at regular intervals.

The program code is listed in Appendix A.

Examination of the slow cool and bench top cool profiles revealed that they were repeatable but

highly nonlinear in the samples’ crystallization range of 140–30◦C, as shown in Figures 4.6 and

4.7. Therefore, the constant cooling conditions of 1◦C/min and 10◦C/min were chosen to replace

the slow cool and bench top cool, respectively. These cooling rates could easily be achieved in the

DSC and hotstage but the Carver press required modification as described below. Rapid cooling

by quenching was deemed acceptable; the temperature profile is shown in Figure 4.8.

To achieve more control over the press cooling rates, an auxiliary set of 6×6×1 inch aluminum

platens which contained 1/2 inch square serpentine channels was fabricated and installed into the

press to provide a means for controlled cooling. Pressurized room temperature or chilled air was

blown through the platen channels to attain the desired cooling rate. The original heating controller

was replaced with a ramp/soak PID controller from Omega Corporation to improve control of the

heating and cooling rates, which were measured using a thermocouple probe embedded near the

center of the lower auxiliary platen.

The temperature profiles for cooling at 1◦C/min and 10◦C/min are shown in Figures 4.9 and 4.10,

respectively. The profiles show that reproducible and constant cooling rates were obtained in the

region where the copolymers undergo crystallization, approximately 140–30◦C.

Although the auxiliary press plates allowed for consistent temperature control, the thickness of

65

0

50

100

150

200

250

0 6000 12000 18000 24000

Elapsed Time, s

Sample Temperature, °C

Run 1

Run 2

140°C

30°C

Figure 4.6: Sample temperature profile for slow cool.

0

50

100

150

200

250

0 1500 3000 4500 6000 7500

Elapsed Time, s


Run 1

Run 2

140°C

30°C

Figure 4.7: Sample temperature profile for bench top cool.

66

0

50

100

150

200

250

0 20 40 60 80 100 120

Elapsed Time, s


Slope from 198.4 to 22.4°C is 5000°C/min

R2 = 0.988

Figure 4.8: Sample temperature profile for ice/water quench.

0

50

100

150

200

250

0 1500 3000 4500 6000 7500 9000

Elapsed Time, s

Sam

ple

Tem

pera

ture

, °C

Run 1

Run 2

Run 3

Slope from 140 to 30°C is 1°C/min

R2 = 0.998

140°C

30°C

Figure 4.9: Sample temperature profile for cooling at 1◦C/min.

67

0

50

100

150

200

250

0 300 600 900 1200 1500

Elapsed Time, s


Run 1

Run 2

Run 3

Run 4

Run 5

Slope from 140 to 30°C is 9°C/min

R2 = 1.000

140°C

30°C

Figure 4.10: Sample temperature profile for cooling at 10◦C/min.

the films was found to vary both within a film and between films of different materials. The

intrafilm thickness variation was somewhat repeatable; the region toward the rear of the press

tended to be thicker than the region near the front of the press. The Carver Model C press has no

adjustment mechanism along this axis. The change in thickness from front to back was variable but

a difference of 50µm was typical. Similarly wedge-shaped films were produced with other heated

hydraulic presses on campus.

The Carver press plates were shimmed to reduce the wedge effect. Thickness variations tended

to be minimized in the center region of the film, from which the optical measurements were con-

ducted. The thickness of this region was typically measured 20–30 times to obtain an average

thickness for use in the haze/mil calculations and for comparison of clarity and transparency val-

ues among films.

Interfilm thickness variations were traced back to the relatively large differences in molar mass

among the series of copolymers. Since the same temperature, pressure, and pressing time were

68

used for each series of pressed films, the final thickness of the films was a function of the melt

viscosity, which depends strongly on molar mass.143 The change in film thickness as a function of

weight-average molar mass, as reported by Dow Chemical, is shown in Figure 4.11.

0

2

4

6

8

100 150 200 250 300 350

MW, kg/mol

Film Thickness, mil

Quenched

Figure 4.11: Pressed film thickness as a function of MW . The trendline is only present to guide the eye.

4.1.2.2 Haze

Initial studies with the Gardner Haze Gard Plus, hereafter referred to as simply the ‘hazemeter’

and described in Section 2.2.3, attempted to confirm the trends seen in the studies of cast films

with the improvised haziness meter. Analysis of stacked cast films using the hazemeter (Figure

4.12) showed a trend similar to that measured by the improvised haziness meter (recall Figure

4.3), where both total haze (dry films) and bulk haze (oiled films) increased proportionally with

thickness. Since haze was proportional to thickness, the haze/mil metric was used to compare haze

between films of different thicknesses.

A series of films covering the range of 0–13 %E were pressed and cooled at either 1 or 10 K/min

69

0

10

20

30

40

50

0 5 10 15 20 25

Cumulative Film Thickness, mil

Haze, %

Total

Bulk

Figure 4.12: Haze – total and bulk scattering contributions for cast film with 7.7%E. The error bars for each

sample represent one standard deviation as calculated from measured data.

or quenched in an ice/water bath. The cleaned smooth face of KaptonTM film was used as the

substrate material during compression molding to minimize the variation in surface roughness

from film-to-film.

The average normalized haze of these films is shown in Figure 4.13. Studies of the haze/mil for

many samples showed that a variation of ±0.5 haze/mil units was typical. The haze/mil decreased

linearly with comonomer content for the quenched films. The scatter in the data proved to be too

large to distinguish between the films cooled at 1◦C/min or 10◦C/min, preventing the unambiguous

determination of which set of films displayed lower haze. However, the composite trend for these

two sets clearly revealed a monotonic decrease in haze/mil as the ethylene content increased.

The surface scattering contribution was expected to be small due to the careful sample preparation

techniques described above. The simple methods for oil application such as smearing with a glass

rod or brush or sandwiching the films between oiled glass plates were found to be more difficult to

use with the commercial hazemeter. Additionally, the horizontal light beam orientation of the Haze

70

0

2

4

6

8

10

0 3 6 9 12 15

Comonomer Content, mol %

Haze/mil

1K/min

10K/min

Quenched

Figure 4.13: Haze of pressed films vs. ethylene content and cooling rate. The dashed trendline includes

both the 1K/min and 10K/min samples. Error bars are ±0.5 haze/mil units.

Gard Plus allowed for the possible contamination of the integrating sphere if oiled surfaces came in

contact with the measurement port. Therefore, a 50×45×3 mm glass cuvette was fabricated and

filled with Cargille Series A refractive index oil of n = 1.4900, which was close to the refractive

index of the films. The film holder of the hazemeter was modified to position the center of the

cuvette flush with the haze measurement port. Immersion of the films into the oil-filled cell allowed

for the measurement of the bulk contribution to haze.

The haze produced by the oil filled cuvette was found to be small, typically less than 0.5% haze

when the cell faces were kept clean. Pressed copolymer films were trimmed so that the same

spot previously measured for total haze would align with the hazemeter measurement port when

submerged in the cell. Oiled film haze was corrected for the cell contribution by subtracting a

constant value, typically 0.5% haze, from the measured haze before calculation of haze/mil. The

results of this study are shown in Figure 4.14

Compression molding with smooth KaptonTM film substrates succeeded in reducing the surface

71

0

2

4

6

8

10

0 3 6 9 12 15


Haze/m

il

1K/min - total

1K/min - bulk

10K/min - total

10K/min - bulk

Quenched - total

Quenched - bulk

Figure 4.14: Bulk haze/mil of pressed films. The data and trendlines from Figure 4.13 (total haze) are

included for comparison. Error bars are ±0.5 haze/mil units.

scattering contribution of the copolymer films to within the uncertainty of the haze/mil measure-

ments. In contrast to the nonuniform cast film samples provided by Dow Chemical, the compres-

sion molded films provided a consistent sample set for subsequent studies. A systematic decrease

in haze/mil with increased comonomer content was found, and the effect of fast (quench) or slow

(1◦C/min or 10◦C/min) cooling rate was significant, with faster cooling leading to better haze/mil.

The correlations between the haze/mil and bulk morphology of these films will be discussed in

Section 4.3.

4.1.2.3 Clarity

The BYK-Gardner Haze Gard Plus, introduced in 1996, is designed to measure haze in accordance

with ASTM D 1003 but is also equipped with a clarity mode. Although this clarity measurement

has not been shown to correlate with perceived loss of resolution and did not specifically adhere to

72

ASTM D 1746 transparency standard, it has been reported in publications and is used in industrial

settings as a transparency-like metric without qualification.142, 144, 145 This confusion may arise

through the mention of a discontinued Gardner clarity meter in the ASTM D 1746 transparency

standard. Extensive studies to determine the practical and theoretical validity of the clarity mea-

surement were conducted using the copolymer films. In the following discussion, the term ‘clarity’

was reserved for the clarity measurement mode of the Haze Gard Plus, while ‘transparency’ was

used exclusively for ASTM D 1746 compliant measurements.

Measurements of clarity were conducted contemporaneously with the haze measurements de-

scribed above. The convenient layout of the hazemeter allowed for rapid measurement of clarity

by sliding the sample film from the haze port to the clarity port. The oil-filled cuvette was used

to effectively measure bulk clarity in a manner similar to that for haze. The cuvette reduced the

maximum clarity by about 0.5%; bulk clarity measurements of copolymer films were corrected for

this reduction. The results of the clarity measurements for the initial experiments on cast films are

shown in Figure 4.15.

Like haze, clarity degraded linearly with thickness, regardless of whether total or bulk scattering

was considered. Therefore, a normalized clarity metric was used to compare films of different

thickness. The normalized clarity represented the clarity of a one mil thick film and was calculated

using the following expression:

Normalized Clarity = 100%−(

100%− claritythickness

)(4.1)

Normalized clarity measurements of the 0–13%E pressed film series used in the haze study above

are plotted in Figure 4.16. The typical error of replicate film measurements was found to be

approximately ±1%, which prevented the discrimination of the samples cooled at 1 and 10◦C/min.

The total and bulk normalized clarity values were similar, indicating that light scattered from the

compression molded copolymer film surfaces did not contribute greatly to the loss of clarity. De-

spite the scatter in the data, the samples crystallized at slower cooling rates, taken together, showed

73

70

80

90

100

0 5 10 15 20 25


Clarity, %

Total

Bulk

Figure 4.15: Clarity – total and bulk scattering contributions for cast film with 7.7%E. The error bars for

each sample represent one standard deviation as calculated from measured data.

a general trend of increased clarity at higher comonomer content, while the quenched samples

showed uniformly high clarity.

4.1.2.4 Comparison of Clarity and Transparency

As a result of the previous investigations, the applicability of the clarity measurement to the visual

appearance of polymer films was questioned. Most films that looked relatively clear tested very

high on the clarity meter, often at 98% or above. Even very cloudy films gave results above 60%.

A careful reading of the Haze Gard Plus operating manual revealed no reference to an accepted

standard for the clarity mode measurement, only that “Clarity can be evaluated at angles of less

than 2.5◦.”146 Recall from Section 2.2.4 that the correlation between observed and measured film

quality was lost if the measurement angle exceeded 0.1◦. Therefore the statement quoted above has

no significance; the exact angles involved in the clarity measurement must be known to evaluate

74

90

92

94

96

98

100

0 3 6 9 12 15


Norm

alized Clarity, %

1K/min - total

1K/min - bulk

10K/min - total

10K/min - bulk

Quenched - total

Quenched - bulk

Figure 4.16: Total and bulk normalized clarity of pressed films. The dashed trendline includes both the

1K/min and 10K/min total normalized clarity samples. Error bars are ±1% clarity.

its suitability for optical measurements.

Upon request, BYK-Gardner provided schematic drawings of the Haze Gard Plus instrument de-

tailing the angles and tolerances involved in the haze and clarity measurements. A simplified

version of this schematic is shown in Figure 4.17. It was found that the Haze Gard Plus was of an

entirely different design and utilized a different geometry and detector system than the old Gardner

clarity meter, which was ASTM D 1746 compliant.

The Haze Gard clarity values were calculated using:

Clarity =Icenter − Iring

Icenter + Iring×100% (4.2)

where Icenter is the intensity received by the center photosensor and Iring is the intensity received

by the ring photosensor. The differences between clarity and transparency measurements were

immediately obvious. The ring sensor measures light intensity which is clearly in the range of haze

75

Figure 4.17: Schematic drawing of the Haze Gard Plus clarity mode.

(> 2.5◦), while the center sensor covers much too large of an area (1.4◦ of angular width) to be

sensitive to light scattered less than the 0.1◦ required for meaningful transparency measurements.

Equation 4.2 was given with no theoretical basis. It appears that this relation was designed to

produce results on a 0–100% scale with 100% defined as maximum clarity, in the manner of a true

transparency reading. However, in the case of transparency, a value of 100% indicates that the

transmitted light beam did not diminish in intensity upon passing through the sample as shown in

Equation 2.20. In the clarity case, a value of 100% simply shows that no light was detected in the

angular range of 3.2–4.0 degrees.

The transparency measurement depends only on light attenuation by the sample in a very narrow

angular range. Conversely, the clarity measurement is sensitive to both attenuation of the main

beam, detected by the center sensor, and light scattered through the angular range of 3.2–4.0◦, de-

tected by the ring sensor. This arrangement has more in common with haze than with transparency

— both clarity and haze compare light scattered at large angles to a background value with a rela-

76

tively higher intensity. In contrast to haze, the clarity calculation is arranged in such a manner to

give 100% as the optimum value (good clarity) rather than haze where 0% is the optimum value

(no haze).

An explanation for the clarity meter’s lack of sensitivity for relatively clear films was also found.

If little light is scattered in the narrow range covered by the ring sensor, then the clarity value

would be close to 100%. Although the area of the ring sensor exceeds that of the center sensor

by a factor of 1.5, much more light is expected to strike the center sensor for relatively clear

specimens because this entire area is illuminated by the main beam of 2.8◦ angular width. Many

polymer films destined for packaging applications would appear relatively clear and show little

differentiation using this definition of clarity.

Finally, the zero points of clarity and transparency measurements are completely different. A zero

transparency indicates a completely opaque or diffuse scattering specimen. A zero value of clarity

occurs when the specimen scatters an equal intensity of light over the areas of the 1.4◦ disk of the

center sensor and in the 3.2–4.0◦ annulus of the ring sensor.

The clarity and transparency measurements were found to be entirely different, with the clarity

more similar to haze than transparency. In hindsight, this was not surprising since the Haze Gard

Plus was designed as a haze measuring instrument with a secondary clarity mode. The compact

0.67 m length of the instrument was also a hint of some discrepancy as transparency meter designs

typically call for lengths of 2–5 m to obtain the required angular resolution.98, 100, 101

The only commercially available clarity meter in compliance with ASTM D 1746 is the CL–100

clarity meter from the Zebedee Corporation. Arrangements were made for the loan of a CL–100

from Zebedee to evaluate the differences in results from a true transparency meter and Haze Gard

clarity. In contrast to the Haze Gard Plus, the CL–100 was a large instrument (1.6 m long) designed

only to measure transparency.

Upon the arrival of the CL–100, a new series of experiments were performed to evaluate the instru-

ment. Transparency measurements were conducted with and without the oil-filled cuvette. In cases

where the cuvette was used, the instrument was set to read 100% transparency with the oil-filled

77

cell in the beam path. Adjustment of the receiving aperture was required as insertion of the cell into

the beam path caused a deviation of the beam, as had been noted previously.102 The transparency

reading of the oil cell without a sample was checked between each measurement and reset to 100%

if necessary.

The thickness dependence of transparency was examined in experiments similar to those used to

evaluate haze and clarity. Stacks of cast films were measured as received to establish the total

transparency and remeasured in the oil-filled cuvette to determine the bulk transparency. The

results are shown in Figure 4.18.

0

20

40

60

80

100

0 5 10 15 20


Transparency, %

Total

Bulk

Figure 4.18: Transparency – total and bulk scattering contributions for cast film with 7.7%E. The error bars

for each sample represent one standard deviation as calculated from measured data.

The bulk transparency decreased linearly with film thickness, in a manner similar to clarity. The

total transparency did not follow a linear trend and quickly decreased to less than 10% as thickness

increased. Recall that the surfaces of the cast films were irregular and had a spotty appearance

which could scatter light. Wavy or non-parallel film surfaces may deviate the transmitted light

beam causing reduced intensity at the receiving aperture of the transparency meter. The trans-

78

parency measurement is sensitive to these variations in surface quality which results in a rapid

nonlinear decline in measured transparency as the number of film-air interfaces increases. The

clarity measurements were not significantly affected by these surface variations becuse of its wide

acceptance angles and poor sensitivity, as discussed previously.

The total and bulk transparency of a series of compression molded copolymer films was measured

and the results, together with the average film thickness, are shown in Figure 4.19. The error bars

in the figure correspond to ±2% transparency.

0

20

40

60

80

100

0 3 6 9 12 15


Tra

nsp

are

ncy,

%

0

3

6

9

12

15

Fil

m T

hic

kn

ess,

mil

1K/min - total

1K/min - bulk

10K/min - total

10K/min - bulk

Quenched - total

Quenched - bulk

Average film thickness

Figure 4.19: Transparency vs. ethylene content and cooling rate. Error bars are ±2% transparency.

The contribution to the loss of total transparency due to scattering from the compression molded

film surfaces was significant and variable for the pressed films due to the high sensitivity of the

transparency meter. The thickness dependence of the bulk transparency was accounted for by

utilizing the same normalization procedure as was used for clarity. This data is presented in Figure

4.20.

Again, the 1◦C/min and 10◦C/min data are indistinguishable due to measurement error, but the

79

70

80

90

100

0 3 6 9 12 15


Norm

alized Bulk Transparency, %

1K/min

10K/min

Quenched

Figure 4.20: Normalized bulk transparency of pressed films. The dashed trendline includes both the 1K/min

and 10K/min data. Error bars are ±2% transparency.

general trend of these slowly cooled samples is toward transparency increasing with ethylene con-

tent. The quenched samples all exhibited high transparency.

All three optical measurement techniques studied thus far established similar trends for the com-

pression molded PE copolymer films. The films crystallized by cooling from the melt at either

1◦C/min or 10◦C/min had similar optical properties, within the uncertainty of the measurements,

which showed a general improvement with increasing comonomer content. Samples quenched

from the melt followed a separate trend; all quenched samples displayed good optics regardless of

ethylene content.

Significant differences were found between the clarity and transparency data. If the Haze Gard Plus

measured true ‘clarity’, synonymous with transparency, the Haze Gard clarity and the transparency

values should have been correlated. Figure 4.21 shows that this is clearly not the case. Samples

with total transparencies over 20% typically registered 98% or higher for total clarity. The film

with the highest total transparency (38%) had a lower total clarity (93%) than many samples of

80

lower transparency. Furthermore, most total clarity values were 80% or higher, while none of the

films had a total transparency over 40%.

0

20

40

60

80

100

0 20 40 60 80 100

Transparency, %

Clarity, %

1K/min - total

1K/min - bulk

10K/min - total

10K/min - bulk

Quenched - total

Quenched - bulk

1:1 Correspondence

Figure 4.21: Total and bulk transparency and thickness of pressed films. Clarity error bars are ±1% and

transparency error bars are ±2%.

The different surface scattering dependence of total clarity, which decreases proportionally with

the number of surface/air interfaces (Figure 4.15), and total transparency, which decreases rapidly

as more surface/air interfaces are measured (Figure 4.18), may also contribute to the poor corre-

lation observed between total clarity and transparency. The presence of surface defects affects the

transparency measurement in a different manner than the clarity measurement, which results in a

poor correlation between the total clarity and total transparency data.

The correlation of bulk clarity and transparency (oiled films) was more pronounced. Although

there was not a 1:1 correspondence, all data points fell on the same curve and were closer to the

proportionality line. Although the clarity measurements were relatively unaffected by the removal

of surface scattering, the transparency values increased dramatically. The transparency measure-

ment was clearly more sensitive to scattering from surface roughness than was clarity. Alterna-

81

tively, these compression molded films may simply not scatter much light in the 3.2–4.0◦ range,

outside of which the Haze Gard Plus clarity measurement is relatively insensitive.

The excellent trend followed by all of the bulk optical data in Figure 4.21, in contrast with the large

amount of scatter observed in Figures 4.19 and 4.20, suggests that comonomer content and cooling

rate (e.g. the bulk morphology) were not the only variables affecting bulk clarity and transparency.

The studies described above attempted to correlate film optical properties with comonomer content

while keeping all other factors, such as cooling rate and surface texture, constant and correcting

for variations in film thickness.

The data presented in Figure 4.21 implies that some other parameter influences the optical proper-

ties of the films. The effect of this ‘random’ variable is to increase the scatter in the optical property

data (Figures 4.19 and 4.20) and obscure the influence of the comonomer content. The scatter in

the bulk optical property measurements may have been caused by inhomogeneities such as dirt

or void inclusions, local variations in temperature or orientation during crystallization leading to

variable morphologies, and incomplete mixing of the melt at the borders of the copolymer pellets

used in the compression molding process. Plotting the clarity and transparency data taken from the

same areas of the same films against each other removed the influence of these random variable

and revealed the trend seen in Figure 4.21.

The experiments described above emphasize the importance of sample preparation and selection.

Even films processed under the most controlled conditions available in the laboratory showed sig-

nificant variation in optical quality. Large-scale commercial film processing lines likely produce

material of higher uniformity than the films used in the present study, but local random fluctu-

ations in film characteristics such as degree of orientation, crystallization temperature, additive

concentration, and the incorporation of inclusions such as dust or voids may lead to variable opti-

cal properties throughout the film. Therefore, care must be taken to sample an adequate portion of

the film to ensure representative optical characterization data. Further investigations that combine

data obtained by different techniques but from the same samples, as shown in Figure 4.21, may

offer new insights into the influence of material parameters on the optical properties by minimizing

82

the impact of random fluctuations.

4.1.2.5 Gloss

Gloss was a function of the surface characteristics of the sample. Because all of the films used

for this study were fabricated to have smooth surfaces, they all exhibited similar gloss values

as shown in Figure 4.22. Gloss measurements are sensitive to sample mounting conditions and

surface irregularities, which typically led to a variation of ±2 gloss units after the exclusion of

outlying data points. A slight trend toward improved gloss with increased comonomer content was

seen. The small decrease in gloss was likely due to slight surface roughening by crystallization at

or near the surface, with a more pronounced effect for the samples of higher crystallinity. Further

investigations into the relationship between surface roughness and optical properties are deferred

to Section 4.4

40

60

80

100

0 3 6 9 12 15


Gloss-45

1K/min

10K/min

Quenched

Figure 4.22: Gloss–45 of compression molded copolymer films. The dashed trendline includes all of the

data. Error bars are ±2 gloss units.

83

4.2 Morphology of Pressed Films

The studies of the optical properties of the compression molded films discussed in the previous

section revealed that changes in ethylene content and cooling rate had a significant influence on

film optics. The differences in bulk haze, clarity, and transparency between films of different

comonomer content and fabricated under different crystallization conditions were presumed to

arise from the variation in the bulk morphologies that developed in these films during cooling.

This section presents the results of several investigations to characterize the bulk morphology of

the PE copolymer films as a function of ethylene content and cooling rate.

4.2.1 Crystallinity

The scattering of light from the bulk of the copolymer films arose primarily from the differences

in the indexes of refraction of the amorphous and crystalline phases. As will be discussed later,

the angular range and intensity of the light scattering, which directly impacts the haze, clarity, and

transparency of the films, depends strongly on the orientation and state of aggregation (spherulites,

rods, sheaves) of the crystalline lamellae. To assist in the identification of morphological features

from microscopy data, the bulk crystallinity and the fraction of crystal phases present in the sam-

ples were measured. After a brief aside regarding the effects of room temperature physical aging,

this section presents the results of the bulk crystallinity and polymorphism investigations.

4.2.1.1 Room Temperature Physical Aging

The room temperature physical aging of polypropylene and semicrystalline polymers in general

is well known.147–154 The physical properties of a crystallizable material undergo an initial rapid

change during cooling/quenching from the melt to room temperature as the material crystallizes

(primary crystallization). Typically, the properties continue to change, although at a much smaller

rate, as the material is stored at room temperature where secondary crystallization and physical

84

aging can take place. The aging properties of the Dow Chemical P/E materials were not a focus

of this research, but studies were carried out to determine the conditions under which physical and

optical measurements could be made without a significant impact from physical aging.

Figure 4.23 shows the increase in density for several ice/water quenched and slowly cooled (ac-

cording to the profile shown in Figure 4.6) samples over time. The samples remained in the density

gradient column at 23◦C during the study. The density increase was most rapid during the first 50

hours.

A series of pressed films were fabricated and quenched to observe the effect of aging on haze and

clarity. Immediately after the quench, the films were mounted on sample holders to insure that the

same region of film was measured at each time interval. The samples were aged at room temper-

ature, approximately 22◦C, and covered with aluminum foil between measurements to minimize

exposure to dust and light. The haze and clarity aging data are shown in Figures 4.24 and 4.25,

0.85

0.86

0.87

0.88

0.89

0.90

0 50 100 150 200

Elapsed Time, hours

Density, g/cm

3

PE4.4 - quenched

PE7.8a - quenched

PE8.2 - quenched

PE12.4 - quenched

PE7.8 - slow cooled

PE8.2 - slow cooled

PE12.4 - slow cooled




Figure 4.23: Density of P/E copolymers versus aging time at 23◦C. The trendlines are logarithmic fits to

the data. The error in density of 0.0002 g/cm3 is within the data points.

85

respectively. No significant aging effect was observed. Based on the conclusions discussed above,

all copolymer samples, including those used in the previous section, were allowed to age at room

temperature for 3–4 days before study.

0

4

8

12

16

20

0 50 100 150 200 250

Elapsed Time, hours

Haze, %

PE0.0

PE7.0

PE7.8

Figure 4.24: Haze of quenched P/E copolymers versus aging time at approximately 22◦C. The trendlines

are logarithmic fits to the data. The error bars for each sample represent one standard deviation as calculated

from measured data.

4.2.1.2 Refractive Index

The interaction of light with the polymer films is a primary focus of this research. One of the fun-

damental optical properties of transparent objects is the index of refraction of the material. This

information was required in the optical property studies to select an appropriate oil of matching

index for the elimination of surface scattering, and as a material constant in the small-angle light

scattering model calculations performed in subsequent sections.69 Average refractive index values

of i-PP are available from reference sources, but the unique microstructure of the Dow Chemi-

cal i-PP homopolymer and PE copolymers was expected to induce a different crystallinity, and

86

90

91

92

93

94

0 50 100 150 200 250

Elapsed Time, hours

Clarity, %

PE0.0

PE7.0

PE7.8

Figure 4.25: Clarity of quenched P/E copolymers versus aging time at approximately 22◦C. The trendlines

are logarithmic fits to the data. The error bars for each sample represent one standard deviation as calculated

from measured data.

consequently different refractive index, to these materials.

The refractive index of a set of compression molded quenched copolymer films was measured using

an Abbe refractometer, and the density was measured using an isopropanol/water density gradient

column. The refractive index increased linearly with density as expected from the predictions of

the Lorentz-Lorenz equation (Equation 2.5) as shown in Figure 4.26.

The refractive index and density of the PE copolymers show a positive correlation, as expected.

The refractive index values ranged from 1.483–1.492, with a median value of 1.490. Therefore,

a Cargille Series A refractive index oil of n = 1.4900, which was a close match for all samples,

was used as an index matching liquid in the optical property studies of the pressed films. The

same value was used in the small-angle light scattering analysis for all films. Refractive index

values of the cast films provided by Dow Chemical were slightly higher, so oils in the range of

n = 1.490–1.500 were used in those studies.

87

0.86

0.87

0.88

0.89

0.90

1.480 1.484 1.488 1.492 1.496

Index of Refraction

Density, g/cm3

Figure 4.26: Density of quenched P/E copolymers versus refractive index. The density errors of

0.0002 g/cm3 are within the data points and the refractive index error bars are ±0.001.

4.2.1.3 Polymorphism

As discussed in Section 2.1.2, isotactic polypropylene may crystallize in several different crystal

phases. Both the α- and γ-phases formed in the materials used in this study, in various proportions

depending on the processing conditions and comonomer content. The specific arrangement of

crystalline lamellae, which in i-PP is partially dependent on the crystal phases present, may have

significant impact on the optical properties of the spherulites.

Wide-angle x-ray diffraction was used to estimate the fraction of α- and γ-phase in the copolymer

samples. The WAXD powder diffraction patterns were analyzed using a method similar to that of

Turner-Jones,27 with the exception that peak areas were used rather than peak heights. A third-

order polynomial equation was fit to the local minima around the (117)γ and (130)α reflections and

used as the baseline. Figure 4.27 shows a typical WAXD powder pattern over the angular range of

interest for the calculation of the γ-phase fraction.

88

17 18 19 20 21

Scattering Angle, degrees (2ΘΘΘΘ)

Norm

alized Intensity, a.u.

(130)αααα (117)γγγγ

Figure 4.27: WAXD powder pattern of slowly cooled PE00.

The peak areas were integrated over the 0.04◦ (2Θ) steps and were used to estimate the fraction of

total crystallinity in the γ-phase, Xγ using:

Xγ =Aγ

Aα +Aγ

(4.3)

where Aγ and Aα are the areas under the (117)γ and (130)α reflection peaks, respectively. Variations

of the γ-phase fraction, Xγ, of the copolymer films as a function of ethylene content and cooling

rate is shown in Figure 4.28.

Recall from the discussion in Section 2.1.2 that the γ-phase is promoted by defective chains, which

in the case of the PE copolymers included regio-errors and ethylene units, and crystallization at

high temperature such as during the slow cooling rates in the present study. For the PE copolymers,

Xγ increases as ethylene content increases and cooling rate decreases, which is consistent with the

results of the previous studies discussed in Section 2.1.2. The implications of Xγ on the bulk

morphology of the copolymer films will be discussed further in Section 4.2.2.

89

0

0.2

0.4

0.6

0.8

1

0 3 6 9 12 15


Xγγ γγ

PE Slow Cool

PE 1K/min

PE 10K/min

PE Quench

Figure 4.28: Fraction of total crystallinity in the γ-phase as a function of ethylene content and cooling rate.

4.2.1.4 Bulk Density and Crystallinity

The crystallinity of the materials used in this study was expected to vary greatly due to the wide

range of comonomer and defect contents in the resins and the different cooling conditions used in

the sample preparation. Therefore, the density of the copolymer samples processed under various

conditions was measured to estimate their degree of crystallinity.

Although the determination of density was straightforward, the calculation of crystallinity from

the density data was less obvious. Recent thermal analysis work by Uan-Zo-li showed that the

two-phase model was applicable to the Dow Chemical copolymers.53 This model assumes that the

sample is composed of crystalline and amorphous phases and any interface between those phases

is negligibly small. According to the two-phase model:

ρ = ρCXVC +ρAXVA, XVC +XVA = 1 (4.4)

90

where ρ is the density of the sample, ρC and ρA are the densities of the crystalline and amorphous

phases, and XVC and XVA are the volume fractions of the crystalline and amorphous phases. When

solved for XVC , Equation 4.4 gives:

XVC =ρ−ρA

ρC −ρA(4.5)

Crystalline fraction by mass, which was more desirable for comparison to thermal data, is defined

as:

XmC =mC

mC +mA(4.6)

where mC and mA are the masses of the crystalline and amorphous phases in the sample. The

degree of crystallinity by mass was designated XC and defined as:

XC = XmC ×100% =(

ρ−ρA

ρC −ρA

)(ρC

ρ

)×100% (4.7)

The choice of density values was also discussed by Uan-Zo-li.53 Following the discussion of Uan-

Zo-li, an amorphous density of ρA = 0.854 g/cm3 was used for all copolymers since the amorphous

densities of polyethylene and polypropylene had that same value and it was reasonable to conclude

that their copolymers would as well.44, 53, 155 Determination of the crystalline density was more

complicated.

Three corrections were considered to the standard α-phase i-PP unit cell density value of ρC =

0.946 g/cm3 as determined by Isasi et al.44 The dilation of the α-phase unit cell in samples con-

taining defects and/or comonomer was known from previous studies.43, 44, 156, 157 The dilation is

relatively constant regardless of defect or ethylene content or cooling conditions. Therefore, the

dilated unit cell density value of 0.919 g/cm3 was used as the starting point for the corrections

discussed below.44, 53, 156

A second issue was the partitioning of ethylene units into the α-phase i-PP crystals. Incorporation

91

of less massive ethylene units in place of propylene units will reduce the overall unit cell mass, thus

lowering the density. Alamo et al. showed that 42% of the total ethylene content of metallocene-

based random propylene/ethylene copolymers was incorporated into the α-phase crystal.46 This

correction was shown to be appropriate for the Dow Chemical PE copolymers and was applied on

a per-sample basis in this work.53

A final consideration is the fact that many of the samples used in this study contained large fractions

of γ-phase crystals. Hosier et al. have shown that defects and ethylene comonomer units partition

into α- and γ-phase crystals in approximately the same proportion.35 Therefore, it would be ap-

propriate to apply the 42% ethylene partition coefficent correction to the γ-phase crystal fraction

as determined by WAXD. However, data on the γ-phase unit cell expansion upon incorporation of

defect and ethylene units was not available. Since this correction could not be accurately applied,

no correction was made for the γ-phase content.

The application of the α-phase corrections detailed above to the calculation of the total crystal

density made the implicit assumption that the α- and γ-phase unit cells expanded in the same

manner upon incorporation of defects and ethylene units. This assumption is plausible considering

that the two phases have nearly identical defect-free unit cell densities and similar defect/ethylene

crystal phase partitioning coefficients.35 The crystallinity values calculated in the present work for

samples cooled at 10◦C/min are therefore very similar to those obtained by Uan-Zo-li.53

Samples used for density analysis were carefully crystallized in sealed aluminum pans in a Perkin-

Elmer Pyris 1 DSC to ensure controlled cooling rates of 1, 10, or 90◦C/min, where the last cooling

rate attempted to simulate the quench conditions used during compression molding (∼ 5000◦C).

The samples were removed from the pans and cut into simple geometric shapes with a sharp razor

blade before density analysis. Triplicate samples were used to confirm the uniformity of crys-

tallization. Errors in density were typically less than ±0.0002 g/cm3. The results of the density

measurements and corresponding crystallinity calculations are shown in Figures 4.29 and 4.30,

respectively.

Several samples taken from compression molded quenched films are included in Figures 4.29 and

92

0.86

0.87

0.88

0.89

0.90

0.91

0.92

0 4 8 12 16 20

Comonomer Content, mol%

Density, g/cm

3

1K/min

10K/min

90K/min

Quenched

Figure 4.29: Density of P/E copolymers at 23◦C. Errors are within the data points.

20

40

60

80

100

0 4 8 12 16 20


Crystallinity, wt%

1K/min

10K/min

90K/min

Quenched

Figure 4.30: Crystallinity of P/E copolymers from density analysis. Error bars are ±1% crystallinity.

93

4.30 for comparison to the DSC samples cooled at 90◦C/min. The two rates are clearly different,

with the quenched samples exhibiting significantly lower crystallinity than those cooled 90◦C/min.

Although the samples prepared by cooling at 90◦C/min and ice/water quenching exhibited different

crystallinities and likely had different bulk morphologies, the disparity was one of degree, rather

than kind. Both of these cooling rates were ‘fast’ when compared to the 1◦C/min and 10◦C/min

‘slow’ cooling rates.

The study of the PE copolymer density showed that the density/crystallinity decreased as ethylene

content and cooling rate increased. This behavior was consistent with studies of other propy-

lene/ethylene copolymer systems.27, 31, 43, 44, 46, 156, 158–160

4.2.2 Bulk Morphology

Much of the optical study focused on the bulk scattering contributions to haze, clarity, and trans-

parency. The primary source of light scattering from the bulk in these copolymers is the presence

of spherulites or sheaves. Therefore, the bulk morphology of the copolymer films was examined

using polarized optical microscopy and HV small angle light scattering. The two approaches pro-

vided complementary information regarding the angular range of scattering expected from the bulk

morphology.

The large pressed films prepared for optical property measurements proved to be too thick for

microscopic observations or for SALS analysis due to multiple scattering caused by the large

number of crystallites in the light beam’s path. Therefore, films of these materials approximately

20 µm thick were prepared between glass coverslips on a hot plate and recrystallized in a Linkam

hotstage. Cooling rates of 1◦C/min, 10◦C/min, and 90◦C/min were used for these samples to allow

for comparison between the optical characterization data and the observed bulk morphologies. The

thin films were used for all of the micrographs and SALS patterns discussed in this section. Optical

micrographs were taken with the microscope’s polarizer and analyzer crossed in the North-South

and East-West positions.

94

P/E copolymers cooled at 1◦C/min generally had a spherulitic morphology with weakly positive or

mixed birefringence, which transitioned to a mixed morphology dominated by sheaf-like crystals

at higher ethylene content as shown in Figures 4.31–4.33. The structures in the homopolymer

were similar to the Type I (positive) or mixed spherulites described by Padden and Keith.12 The

corresponding HV SALS pattern exhibited a four-leaf clover appearance characteristic of spherulite

scattering, with some diffuse scattering due to spherulite disorder and truncation.69

The morphology of the copolymer materials was less distinctly organized, being composed pri-

marily of sheaf-like crystal aggregates rather than spherulites. At 16.6%E, the morphology was

exclusively composed of small crystalline bundles or sheaves; the HV pattern from this sample was

more diffuse and had less symmetry than for the lower %E materials (Figure 4.34).

Figure 4.31: Morphology and HV SALS pattern of PE0.0 cooled at 1◦C/min.

Films cooled at 10◦C/min showed similar morphologies, where the transition from spherulitic to

bundle/granular crystal morphology occurred around 12% ethylene (Figures 4.35 and 4.36). The

spherulites were generally smaller than those in the 1◦C/min samples, while the HV patterns were

correspondingly larger.

Films cooled at 90◦/min all had morphologies composed of crystalline bundles or sheaves as shown

in Figures 4.37 and 4.38. No distinct morphology was visible by optical microscopy or HV SALS

for materials with more than 8% comonomer. A more extensive collection of micrographs and HV

SALS patterns is included as Appendix B.

95




96



Figure 4.37: Morphology and HV SALS pattern of quenched PE0.0.

97

Figure 4.38: Morphology and HV SALS pattern of quenched PE7.0.

Morphologies of this type, with a transition from spherulitic to sheaf-like morphology with in-

creasing comonomer and/or defect content, had previously been described for propylene/ethylene

copolymers.4, 31, 48, 134, 156, 161 Thomann et al. showed a similar bundle-like morphology in an i-PP

with regio- and stereodefects.116 The positive or near zero (mixed) spherulite birefringence seen by

Hosier et al. and in this work is consistent with spherulites composed of α-α and/or α-γ branched

crystals.48, 58 The impact of the morphology on the bulk optical properties is discussed further in

the following sections.

98

4.2.3 Lamellar Morphology

In this and other work, the Dow Chemical copolymers were found to produce a morphology some-

what different than expected from a typical metallocene-type propylene/ethylene copolymer due

to the unique defect and comonomer distribution imparted by the Dow Chemical catalyst.3, 53, 134

Although the larger crystalline aggregates were the primary source of light scattering from the

bulk of these films, the morphology was also examined at the lamellar level to elucidate the fine

structure of the spherulites and crystalline bundles.

Both AFM and SEM techniques were used to view the crystalline morphology on the nanometer

scale. The copolymers were found to be sensitive to charging and damage from the SEM electron

beam, even when coated with approximately 4 nm of gold and using accelerating voltages as low

as 2 kV, which made acquisition of high-quality images difficult. Therefore, some of this work was

conducted with tapping mode AFM under ambient conditions.

Samples crystallized from the melt by cooling at 1◦C/min were expected to form the most well-

developed and thickest crystal lamellae due to the extended time spent at high temperature. As

was seen previously by WAXD analysis, these conditions also lead to the greatest proportion of

γ-phase crystals in the copolymers.

SEM images of PE0.0, PE8.2, and PE13.3, all crystallized from the melt at 1◦C/min, are shown in

Figures 4.39 through 4.41. These materials show a crosshatched morphology characteristic of α-

phase i-PP crystallization. Some small crystals in Figure 4.40 branched at the 40◦ angle indicative

of α-γ branching. This sample was known to be composed of approximately 80% γ-phase crystals

from WAXD analysis. The small granular crystals enclosed by α-α crosshatched branches were

likely γ-phase.

All slowly cooled PE copolymers displayed evidence of a crosshatched morphology, but a different

arrangement of densely packed lamellae was also visible in many of the copolymers (Figure 4.42).

At times this morphology was coexistent with the typical crosshatched one as seen in Figure 4.43

for PE8.2 and Figure 4.44 for PE12.8. Since these domains were only seen in materials with

99

Figure 4.39: SEM image of PE0.0 crystallized at 1◦C/min. The crosshatched morphology is clearly visible.

high γ/α ratios and showed no crosshatching, they were likely composed of γ-phase crystals. A

similar morphology was observed in i-PP copolymers with high γ-phase contents by Hosier et al.48

The birefringence model previously discussed for crosshatched i-PP would not be applicable to a

spherulite or crystalline bundle composed primarily of this densely packed morphology.58

Recalling the discussion of Section 2.1.5, the proportion of parent/daughter lamellae directly in-

fluenced the spherulite birefringence. A recent review by Lotz discussed how the crosshatched

morphology produced spherulites with mixed birefringence.162 The tangential (daughter) lamellae

always had their chain axes oriented in the spherulite’s radial direction and contributed to positive

birefringence. The birefringence contribution from the radial (parent) lamellae varied from near

zero to negative depending on whether their basal plane was normal or parallel, respectively, to

the light beam used for observation. Because the orientation of the parent lamellae was fixed over

domains in the spherulite, each domain would have its own value of birefringence, producing a

mixed spherulite.

As the γ/α ratio increased, the amount of crosshatching decreased and the densely packed lamellar

morphology appeared, leading to structures with lamellae predominantly oriented in one direction.

100

Figure 4.40: SEM image of PE8.2 crystallized at 1◦C/min. Arrows indicate locations of α-γ crystallographic

branching. This image was printed at a large scale to show fine detail.

Although the γ-phase lamellar crystals in these domains were oriented along a common direction

and displayed no branching, the domains would still exhibit a low total birefringence due to the

alternating bilayer structure of the i-PP helices in each lamella. The observation of spherulites

with mixed birefringence containing γ-phase crystals was therefore consistent with the lamellar

morphology described above, with domains of crosshatched lamellae that exhibited a variable but

generally positive birefringence intermixed with domains of commonly oriented γ-phase lamellae

with low birefringence.

In summary, the Dow Chemical PE copolymers always produced morphologies with either posi-

tive or mixed birefringence, even when crystallized under conditions that primarily produced the

γ-phase. In many cases, an underlying α-phase crystal network on which the γ-phase crystals

101

Figure 4.41: SEM image of PE13.3 crystallized at 1◦C/min and subjected to permanganic etching. Note

the crosshatched morphology.

Figure 4.42: SEM image of PE8.2 crystallized at 1◦C/min and subjected to permanganic etching. Densely

packed lamellar morphology.

102

Figure 4.43: SEM image of PE8.2 crystallized at 1◦C/min and subjected to permanganic etching. Arrows

indicate domains of crosshatched morphology coexistent with densely packed lamellae. This image was

printed at a large scale to show fine detail.

nucleated and grew was observed. Morphologies composed of domains of crosshatched and uni-

directionally oriented lamellae were also seen in some copolymers. All structures resulted in mor-

phologies of low and mixed birefringence and suggested that the α- and γ-phase crystals nucleated

and grew at or near the same time. This view was supported by previous work by Uan-Zo-li and

Alamo et al.33, 53 The low birefringence of the mixed spherulites caused them to be less effective

scatterers of light than a fully positive or negative spherulite would have been. This argument

assumes that the contribution to the degradation in optical properties from light scattering due to

fluctuations in density was relatively small and constant among the samples (see Section 4.3.2

103

Figure 4.44: AFM image of PE12.8 crystallized at 1◦C/min. Primarily composed of short densely packed

γ-phase lamellae, but some long α-phase lamellae are visible (arrows).

for supporting evidence). Thus, considering the assumptions stated above, the mixed morphology

contributed to the generally good optical properties of these materials.

104

4.3 Control of Optics by Variation of Bulk Morphology

The cooling rates for the preparation of PE films of several comonomer contents were chosen to

produce a wide array of bulk morphologies. In cases where the morphology was spherulitic, the

spherulite superstructure determined the angular range and intensity of the light scattered from the

bulk of the film according to the model of Stein and Rhodes.69 The work described in this section

attempted to correlate the light scattering from the bulk morphology to the bulk haze, clarity, and

transparency of the films.

The model of Stein and Rhodes was developed for a spherically symmetric array of crystallites

with different indexes of refraction along the radial and tangential directions. The structure was

surrounded by a medium of uniform refractive index similar to the radial and tangential refrac-

tive indexes of the array.69 Although the basic version of the theory did not account for several

experimentally observed features such as spherulite impingement, interference between different

spherulites in the illuminated area, or internal spherulite disorder, it has been successfully used to

predict the optical and morphological behavior of many polymer systems.

The morphologies developed in the compression molded films used in this work displayed the

typical deviations from ideal spherulitic behavior as described above, but presented additional

problems. In many cases, the spherulites did not display clear overall birefringence, but rather a

mixed morphology that contained domains of varied birefringence throughout the spherulite. At

higher ethylene content and faster cooling rates complete spherulites did not form; the morphology

was primarily composed of sheaf-like crystalline bundles.

The HV SALS patterns collected from most of these samples still displayed the basic four-leaf

clover pattern characteristic of spherulitic scattering. The effects of spherulite disorder, impinge-

ment, and incompleteness were seen in the patterns as a nonzero intensity at θ = 0 and often a

more monotonic decrease in scattered intensity along µ = 45◦ than expected and no distinct max-

imum. Several extensions to the basic SALS theory have been made to address these issues, but

the improvement in accuracy has come at the expense of the convenience of the basic theory due

105

to the complex mathematics required.71, 73–75, 77, 78

The SALS technique has other limitations for use in comparing angular scattering from spherulites

to optical properties. SALS experiments use monochromatic polarized light to produce scattering

patterns, while the haze, clarity, and transparency meters all utilize unpolarized white light for bet-

ter comparison to human perception under everyday illumination conditions. After consideration

of these issues, the HV basic SALS theory and technique was still found to be useful for this work

in a semi-quantitative role.

Spherulite (or sheaf-like crystal aggregate) sizes were estimated from HV patterns using Equation

2.17. Despite the limitations mentioned above, the R0 values calculated using this expression for

well-formed spherulitic morphologies correlated well with estimates from optical micrographs as

seen in Table 4.2 and Figure 4.45.

For much of the analysis in this section, the technique of HV pattern averaging was used. The

fourfold symmetry of the patterns was exploited to increase the signal-to-noise ratio of the patterns

by the calculation of a quadrant average. A radial intensity profile was measured along the µ = 45◦

line for the estimation of R0 using Equation 2.17. The results of this procedure are shown in Figure

4.46.

The intensity profiles measured in this manner were complicated by significant noise due to speckle

and the pixellation of the CCD camera. The quadrant averaging procedure reduced this somewhat,

but data smoothing procedures were also used to clearly reveal the trends in the intensity profiles.

Table 4.2: Estimates of R0 by HV SALS and POM for PE5.4.

Cooling Rate R0 by HV SALS, µm R0 by POM, µm

Quench 4.1±0.1 4.0±0.1

10◦/min 19±1 22±5

1◦/min 39±10 37±5

106

Figure 4.45: HV SALS patterns and POM micrographs for PE5.4. Left: quenched. Center: cooled at

10◦/min. Right: cooled at 1◦/min. See Table 4.2 for estimates of R0.

Figure 4.46: HV SALS quadrant average for PE5.4 quench.

107

Several techniques were explored for smoothing the profile data, including moving averages and

exponential smoothing over various intervals, without a satisfactory result.

Smoothing of the entire pattern had the advantage of including intensity data from the second

dimension before reduction to a one-dimensional intensity profile. The Gaussian blur filter of

the ImageJ image manipulation software package was used to smooth the SALS pattern before

profiling as shown in Figure 4.47.141 The best results were generally obtained using a Gaussian

blur of radius 10, which provided enough smoothing to clearly view the intensity profile without

significant muddling of the data (Figure 4.48). This procedure was analogous to the placement of

a frosted glass screen in front of the film plate as had been done historically in SALS experiments.

In many cases, the morphologies developed in the PE copolymers in this work were composed of

bundle or sheaf-like crystalline aggregates. Therefore, the spherulitic light scattering model could

not be used. Picot et al. developed a model for scattering from anisotropic sheaves which predicted

more scattering at high and low angles than would be expected for a spherulite.71 The HV patterns

observed in this study were consistent with this model.

The scattered intensity profiles along the µ = 45◦ line generally showed a monotonic decrease in in-

tensity with an increased scattering angle for the non-spherulitic morphologies. For these samples,

the intensity of scattering decreased as the sheaf size decreased with an increase in comonomer

content as shown in Figure 4.49. This decrease in scattered intensity was consistent with the de-

crease in haze seen with increasing ethylene content for the quenched samples (Figure 4.13).

108

Figure 4.47: HV SALS pattern smoothing with Gaussian blur. Left: pattern as imaged. Right: smoothed

with Gaussian blur r = 10. Sample is MET13.5 cooled at 1◦/min. The faint arcs seen in the upper left and

right corners of each image are artifacts from the experimental apparatus and should be disregarded.

0

10000

20000

30000

40000

0 2 4 6 8

Scattering Angle, degrees

Intensity, a.u.

Raw data

Gaussian blur r = 5

Gaussian blur r = 10

Figure 4.48: µ = 45◦ intensity profile for MET13.5 cooled at 1◦/min.

109

0

5

10

15

20

25

0 1 2 3 4 5 6

Scattering Angle, degrees

Scattered Intensity, a.u.

PE00

PE33

PE54

PE67

Figure 4.49: µ = 45◦ intensity profiles for PE films cooled at 90◦/min.

110

4.3.1 Spherulite Size

According to the model of Stein and Rhodes, the angular location of the maximum scattered inten-

sity in HV mode was a function of spherulite size (Equation 2.17), while the intensity at the maxi-

mum was a function of the sixth power of the radius and the square of the spherulite birefringence

(Equation 2.18).69 Therefore, films composed of small spherulites with near zero birefringence

are expected to scatter light poorly and exhibit good optical properties. The predictions made by

these relationships are utilized in the following sections to correlate the light scattering from the

bulk morphology of the PE copolymer films to their observed optical properties.

As discussed above, in many cases a well-developed spherulitic morphology did not form in these

films, which prevented the direct quantitative application of the SALS theory. Materials with low-

to mid-range ethylene contents cooled at 1◦C/min or 10◦C/min typically displayed a mixed mor-

phology of poorly organized spherulies and sheaf-like crystals. The disorder, mixed birefringence,

and the presence of the bundle-like crystals prevented the estimation of spherulite size using Equa-

tion 2.17. However, the general prediction of the SALS model that the scattered intensity increases

rapidly with spherulite radius should still apply.

Because well-ordered HV SALS patterns were not available in most cases, spherulite radii were

estimated from optical micrographs of thin film samples. The distribution of spherulite sizes was

typically broad. The trend of increased haze with increasing spherulite size is clearly seen in

Figure 4.50. The specific processing conditions were found to be less important than the resultant

spherulite size in correlations with measured bulk haze.

Large spherulites are predicted by the SALS model to scatter primarily at small angles.69 Scatter-

ing in the 3.2–4.0◦ range should diminish clarity, while scattering at very low angles would reduce

transparency. Therefore, small spherulites, which scatter at large angles and with lower intensity,

should lead to better clarity and transparency values. The results of this analysis are presented in

Figures 4.51 and 4.52. Despite the uncertainty in spherulite size, the clarity and transparency were

both seen to decrease with increasing spherulite size, as predicted by the SALS theory.

111

0

2

4

6

8

10

0 20 40 60 80

Spherulite Radius, µµµµm

Bulk Haze/mil

1K/min

10K/min

Figure 4.50: Haze/mil as a function of spherulite radius. The trendline includes all data points. Error

bars for haze/mil are ±0.5 haze/mil units and those for R0 are one standard deviation as calculated from

measured data.

Recall that the copolymers crystallized at 1◦C/min and 10◦C/min were shown to have generally

similar optical properties. These materials formed morphologies of approximately the same size

when cooled at either rate, which explains their similar optical properties. Although more rapid

cooling from the melt was expected to produce a morphology composed of crystalline aggregates

of small characteristic dimensions (subsequently referred to as small scale morphologies), it ap-

peared that the PE copolymers could form relatively large spherulites and/or sheaves when cooled

at either 1 or 10◦C/min. Very rapid cooling at 90◦C/min or upon ice/water quenching did produce

disorganized morphologies with a finer texture and correspondingly better optical properties than

those formed at slower cooling rates. The light intensity scattered from small scale morphologies

was generally less than that scattered from large scale morphologies. The smaller scale morpholo-

gies therefore displayed better optical properties.

112

90

92

94

96

98

100

0 20 40 60 80

Spherulite radius, µµµµm

No

rmali

zed

Bu

lk C

lari

ty,

%

1K/min

10K/min

Figure 4.51: Normalized clarity as a function of spherulite radius. The trendline includes all data points.

Error bars for normalized clarity are ±1% and those for R0 are one standard deviation as calculated from

measured data.

4.3.2 Spherulite Birefringence

The influence of the second factor in the model for scattered intensity from a spherulite, ∆n, was

also investigated. Following Equation 2.18, the intensity at θmax should vary as the square of the

spherulite birefringence. The impact of the spherulite radius is clearly larger than that of ∆n, but a

low or near zero birefringence, as seen in the Dow Chemical polymers, may reduce the scattered

intensity significantly.

To avoid ambiguous results from samples with variable spherulite radii, the variation of ∆n was

attempted by annealing samples composed of space-filling impinged spherulites. Annealing close

to the spherulite melting point could change the birefringence through partial melting of thinner

crystals and recrystallization as thicker lamellae, crystal perfectioning, or thickening of the existing

lamellar crystals.163–168 These effects could change the spherulite birefringence if the relative

113

70

75

80

85

90

95

100

0 20 40 60 80

Spherulite radius, µµµµm

Norm

alized Bulk Transparency, %

1K/min

10K/min

Figure 4.52: Normalized transparency as a function of spherulite radius. The trendline includes all data

points. Error bars for normalized clarity are ±2% and those for R0 are one standard deviation as calculated

from measured data.

proportion of radial and tangential lamellae and/or Xγ were altered.

Large spherulites were desired to provide for easy observation of birefringence changes and for

their moderately poor optical properties for which improvements or degradation could easily be

measured. Through trial and error, PE0.0 cooled at 1◦C/min was chosen for the annealing study

for the reasons described above. Compression molded and thin films were annealed in parallel to

provide samples for macro- and microscopic examination. Large films were annealed in a Lindberg

Blue convection oven, while thin films were annealed in a Linkam THM600 hotstage equipped

with a TP91 controller. A nitrogen atmosphere was used in both cases to prevent oxidation of the

polymer during long residence times at the elevated annealing temperature.

The PE0.0 spherulites formed during cooling from the melt at 1◦C/min were observed to melt at

150◦C. The annealing temperature was correspondingly selected at 140◦C. Samples were annealed

for specified periods of time, removed from the oven and allowed to cool to room temperature, and

114

measured for haze, clarity, and transparency using the Haze Gard Plus and CL–100 transparency

meter. Several samples were cut from the edges of the film for subsequent density analysis before

further annealing of the film in the oven.

The density/crystallinity of the films increased linearly with the logarithm of annealing time up to

48 hours as shown in Figure 4.53. Crystallinity increased by approximately 3% after 48 hours at

140◦C.

0.906

0.907

0.908

0.909

0.910

1 10 100 1000 10000

Annealing Time, min

Density, g/cm3

80

82

84

86

Crystallinity, wt%

Density

Crystallinity

Figure 4.53: Density and crystallinity of PE0.0 crystallized at 1◦C/min and subsequently annealed at 140◦C.

The error bars on density are ±0.0002 g/cm3 and those for crystallinity are ±0.5 wt%.

Optical microscopy revealed no discernible change in the size or birefringence of the spherulites

after annealing for 18 hours (Figure 4.54). HV SALS patterns showed no significant change in

shape after annealing, which confirmed that the average spherulite dimensions were not affected

by the annealing treatment. Therefore, it was speculated that the reduction in film optical quality

was the result of a small birefringence change that resulted in an increase in the intensity of light

scattered from the spherulites.

To confirm this hypothesis, the thin film annealing experiment was repeated in a specially con-

115

Figure 4.54: POM images of PE0.0 crystallized at 1◦C/min before (Left) and after (Right) annealing at

140◦C for 18 hours.

structed apparatus that allowed the HV scattering intensity to be measured in real-time. A sample

prepared identically to the one used above was melted and recrystallized by cooling at 1◦C/min in

a Linkam hotstage to form the initial morphology. Microscopic observations were used to locate a

region of the film that contained well-formed spherulites and that was free of any visually observ-

able voids or other defects. This region was centered in the hotstage window and care was taken

to avoid any further adjustments of the hotstage.

The SALS setup was modified to accommodate the hotstage and to align the laser beam with

the hotstage window, which illuminated the previously selected region of the sample film. The

analyzer was positioned very close to the upper hotstage window. A six inch diameter integrating

sphere was mounted to center the entrance port directly above the analyzer. The exit port of the

sphere was fitted with a diffusing plug. A photomultiplier (PM) tube and electromechanical shutter

were mounted on the side port of the sphere. The PM tube was operated at a bias of −500 V and

was found to produce an extremely stable signal after an initial warm up period.

The sample was heated in the hotstage under a nitrogen atmosphere to the annealing temperature

of 140◦C and the scattered intensity was measured using the PM tube as a function of annealing

time. The measured values were corrected for the dark current signal, which varied by less than

116

5% during the experiment. Figure 4.55 shows the results of this experiment along with the optical

properties of a large PE0.0 film annealed in parallel.

0

10

20

30

40

50

60

70

1 10 100 1000 10000

Annealing Time, min

Haze,

Cla

rity

, T

ran

sp

are

ncy,

%

0

5

10

15

20

HV

In

ten

sit

y,

a.u

.

Haze

Clarity

Transparency

Hv Intensity

Figure 4.55: Haze, clarity, transparency, and HV intensity of PE0.0 crystallized at 1◦C/min and subsequently

annealed at 140◦C. The error bars for each sample represent one standard deviation as calculated from

measured data.

The HV intensity increased and the degradation in the optical properties followed a linear de-

pendence on the logarithm of annealing time. After 48 hours of annealing at 140◦C, haze had

decreased 32%, clarity by 15%, and transparency by nearly 60% compared to their starting val-

ues. Because the spherulite radii were constant, the spherulite birefringence must have increased

(become more positive) with longer annealing time to cause the increased scattered HV intensity.69

The increased scattering resulted in the reduction in optical quality.

The annealing process significantly affected the light scattering properties of the PE0.0 films, but

no change was observed by optical microscopy even after long residence times at 140◦C. There-

fore, additional investigations were conducted to identify the morphological origin of the increased

scattering after annealing.

117

The lamellar morphology was examined for any changes using tapping mode AFM. Images of

samples taken before and after an 18 hour annealing treatment are shown in Figures 4.56 and 4.57.

The characteristic α–α crosshatched morphology is clearly visible in both samples. Although this

sample was crystallized under quiescent conditions, the dense and profuse crosshatched branching

causes the lamellae to possibly have an oriented appearance. The parent and daughter lamellae

have thickened after 18 hours at 140◦C.

Figure 4.56: AFM images of PE0.0 crystallized at 1◦C/min (before annealing).

The fraction of γ-phase crystallinity in the samples was estimated using WAXD analysis as de-

scribed previously. A plaque of PE0.0 was crystallized from the melt by cooling at 1◦C/min and

the WAXD pattern recorded. The sample was then annealed at 140◦C for 19 hours and the WAXD

pattern remeasured (Figure 4.58). The total crystallinity increased approximately 4% (recall Fig-

ure 4.53) while the α-phase fraction of the total crystallinity increased from 65% to 80% after the

annealing treatment.

The different orientations of the i-PP helices in the α- and γ-phase crystals are presumed to prohibit

118

Figure 4.57: AFM images of PE0.0 crystallized at 1◦C/min (after annealing at 140◦C for 18 hours).

0

1000

2000

3000

17 18 19 20 21

Scattering Angle (2Θ),Θ),Θ),Θ), degrees

Norm

alized Inte

nsity, cps

As prepared

Annealed 19h

(130)αααα

(117)γγγγ

Figure 4.58: WAXD patterns of PE0.0 crystallized at 1◦C/min and annealed at 140◦C for 19 hours.

119

a direct solid phase γ to α transition in the absence of deformation.25 Therefore, the loss of γ-phase

crystals must be due to melting with subsequent recrystallization in the α-phase.

To observe this process, the annealing experiment was repeated in a Perkin-Elmer Pyris 1 DSC

using an ice/water bath as a heat sink. The temperature scale of the DSC was calibrated using an

indium standard sandwiched between two sheets of i-PP to account for thermal lag in the sample.

A small portion of PE0.0 film was sealed into an aluminum DSC pan, held at 200◦C for 5 min to

erase any previous thermal history, and recrystallized by cooling from the melt at 1◦C/min. The

melting thermogram of this sample was recorded by heating from 30◦C to 200◦C at 10◦C/min.

The sample was then recrystallized as before, subjected to an annealing treatment at 140◦C for

20 min, and then cooled to 30◦C. The melting thermogram was recorded at 10◦C/min as described

previously. The experiment was repeated with an annealing time of 12 h. All three melting traces

are shown in Figure 4.59.

20

25

30

35

40

80 100 120 140 160 180


Heat Flow, mW

As Prepared

Annealed 20 min

Annealed 720 min

Figure 4.59: DSC melting traces recorded at 10◦C/min for PE0.0 crystallized at 1◦C/min and annealed at

140◦C for 20 and 720 minutes.

The thermograms show a decrease in the area of the low-temperature endotherm and an increase in

120

area and peak melting temperature for the high-temperature endotherm with increased annealing

time. Previous studies of defect-containing i-PP have shown that the low-temperature endotherm

arises primarily from the melting of γ-phase crystals, while the high-temperature endotherm re-

sults from the melting of α-phase crystals.33, 53 These results support the conclusions reached

through analysis of the WAXD data, that some of the γ-phase crystals melt during annealing and

that α-phase crystals form in their place, resulting in a higher fraction of α-phase crystallinity. Ad-

ditionally, the α-phase crystals undergo a degree of perfectioning and lamellar thickening, which

may be a less important mechanism for the copolymers because the comonomer units may disrupt

the thickening process, resulting in a higher peak melting temperature than in the pre-annealed

condition.

The α-phase melting peak also gained a high temperature shoulder that increased in size with

increased annealing time. This behavior is entirely consistent with the domain III annealing regime

described by Fillon et al. for i-PP.164 In this regime no significant change to the microscopically

observed bulk spherulitic morphology was seen, as was the case in the present work.

The annealing studies were repeated using PE3.3 to confirm the generality of the behavior seen

in the PE0.0 samples. For each material, an annealing temperature 6◦C below the peak melting

temperature, as determined by DSC analysis, for a sample crystallized at 1◦C/min was used. There-

fore, PE0.0 was annealed at 140◦C, as described above, and PE3.3 was annealed at a temperature

of 130◦C. With the exception of the annealing temperature, the sample preparation and evaluation

procedures used for the analysis of PE3.3 were identical in all respects to those used for PE0.0.

The results of the studies of both materials were similar, as shown in Figures 4.60–4.62.

Prior to the annealing treatment, the PE0.0 specimen was composed primarily of α-phase crystals,

while the PE3.3 sample was primarily composed of γ-phase crystals. Upon annealing, both mate-

rials showed an increase in the fraction of α-phase crystals, with the PE0.0 sample increasing from

65% to 80% α-phase, and the PE3.3 sample increasing from 37% to 51%. The relative changes in

α-phase content, 23% for PE0.0 and 38% for PE3.3, correlate with the observed relative change in

haze of 31% and 109%, respectively. This data supports the conclusion that an increase in α-phase

121

0

20

40

60

80

100

1 10 100 1000 10000

Annealing Time, min

Haze, Clarity, Transparency, %

0

1

2

3

4

HV Intensity, a.u.

Haze

Clarity

Transparency

Hv Intensity

Figure 4.60: Haze, clarity, transparency, and HV intensity of PE3.3 crystallized at 1◦C/min and subsequently

annealed at 130◦C. The error bars for each sample represent one standard deviation as calculated from

measured data.

content leads to a degredation of optical properties.

Since the radial lamellae of the spherulites were well established during primary crystallization, the

new α-phase crystals formed during annealing would likely nucleate epitaxially from existing α-

phase lamellae and form crosshatched daughter lamellae. Employing the model of Binsbergen and

De Lange (recall Equation 2.4), the development of the majority of these new lamellae in directions

tangential to the spherulite radius would cause the initially slightly positive ∆n to become more

positive, and therefore cause the increased HV intensity observed experimentally.58

The model of Binsbergen and De Lange was extended to consider the effect of γ-α branching on

the spherulite birefringence. The derivation of this model is given in Appendix C. The model

predicts that the γ-phase daughter crystals are less effective at increasing (making more positive)

the spherulite birefringence as shown by:

122

0

1000

2000

3000

17 18 19 20 21

Scattering Angle, 2(ΘΘΘΘ)

Norm

alized Intensity, cps

As prepared

Annealed 20min

Annealed 1060min

(117)γγγγ(130)αααα

Figure 4.61: WAXD patterns of PE3.3 crystallized at 1◦C/min and annealed at 130◦C for 20 min and 18 h.

20

25

30

35

80 100 120 140 160 180


Heat Flow, mW

As Prepared

Annealed 20 min

Annealed 120 min

Annealed 720 min

Figure 4.62: DSC melting traces recorded at 10◦C/min for PE3.3 crystallized at 1◦C/min and annealed at

130◦C for 20, 120, and 720 min.

123

∆n = (n′c−n′a)(t/4− r/2) (4.8)

where n′c is the index of refraction along the helix axis and n′a is the index of refraction perpen-

dicular to the iPP helix axis; these quantities are identical to nc and na, respectively, used in the

derivation of Equation 2.4.58 The conclusions of this model are consistent with the experimental

observations of the current study.

The arguments presented in this section correlate the increase of total scattering intensity mea-

sured by HV SALS, which employs polarized monochromatic light, to the degradation in optical

properties, which are determined using unpolarized white light. Although VV SALS studies were

not performed on these materials, the contribution from VV scattering should be significant.69 To

confirm the validity of the comparison of SALS data to the optical test results, the Haze Gard Plus

was modified to allow for measurements under HV and VV polarization conditions.

The Haze Gard employs an integrating sphere to allow for the measurement of the total intensity

of light scattered at angles up to 90◦. The evaluation of total scattering intensity under HV and

VV polarization conditions has been studied previously.169–171 Following the discussion of Li and

Akpalu, the total integrated scattering intensity under HV and VV conditions can be approximated

by the relative invariants QHV and QVV , respectively.169 For space filling spherulites:

QHV =< δ2 >= K(δ0

crxCSP2)2 (4.9)

where < δ2 > is the mean square fluctuation in the anisotropy (orientation) of the crystalline ag-

gregate, K is a constant dependent on the geometry of the scattering object(s) and wavelength of

light used in the experiment, δ0cr is the intrinsic anisotropy of a pure crystal of the material, xCS is

the volume fraction of crystals in the spherulite, and P2 is a Hermans-type orientation function that

describes the orientation of the crystals with respect to the spherulite radius.169

For VV scattering:

124

QVV = K2 < η2 > +K3QHV (4.10)

where K2 and K3 are constant factors dependent on geometry and experimental conditions, and

< η2 > is the mean square fluctuation in the average polarizability (density) of the crystalline

aggregate.169

Thus, in the general case QVV > QHV due to the addition of the < η2 > term, which may be large

if inclusions with densities very different than the polymer matrix (e.g. voids, air bubbles, or dirt

particles) are present. The results of HV and VV haze measurements are shown in Figure 4.63.

0

10

20

30

40

50

60

70

1 10 100 1000 10000

Annealing Time, min

Polarized Haze, %

-10

0

10

20

30

40

50

60

Relative Change in Polarized Haze, %

Total Hv

Bulk Hv

Total Vv

Bulk Vv

Relative change - total Hv

Relative change - total Vv

Figure 4.63: Polarized haze of PE0.0 crystallized at 1◦C/min and annealed at 140◦C.

Both the HV and VV haze increased with annealing time, in a manner similar to the unpolarized

haze as shown in Figure 4.55. As expected from the discussion presented above, the VV haze

increase was larger than the HV increase. The relatively small contribution from the < η2 > term

(see Equation 4.10) indicates that the density fluctuations present in the spherulites did not change

significantly during annealing. Therefore, the change in total scattering intensity could be well

125

described by following the increase in HV scattering intensity. The total and bulk HV and VV

haze values were similar, indicating that the surface scattering contribution to total haze was small.

Therefore, the increase in total haze values as a function of annealing time represents increased

light scattering intensity resulting from changes in the the bulk morphology of the films.

Equation 4.9 shows that the total HV scattering intensity of impinged spherulites increases with

the square of the crystallinity and orientation or the spherulite. Although a small increase in crys-

tallinity was observed during annealing, the relatively large change in the α-phase crystal content

leads to a significant reordering of iPP helices from a tangential to a radial orientation, resulting in

an increase in P2 and, consequently, the spherulite birefringence.

The larger relative increase in haze seen in the PE3.3 annealing experiment (versus the PE0.0 ex-

periment) supports the speculation that the increased crystallite orientation is the major contributor

to the increased scattering intensity because the increase in crystallinity and degree of lamellar

thickening should be less in the PE3.3 copolymer than for the homopolymer due to the necessity

of including the comonomer units in the α-phase iPP crystal lattice. Therefore, the larger relative

increase in α-phase content in the PE3.3 sample (versus the PE0.0 sample) lead to a larger rela-

tive increase in crystallite orientation, which resulted in a relatively larger increase in scattering

intensity and haze.

In conclusion, this investigation revealed that in addition to the size of the bulk morphology and

the surface roughness, a third parameter, ∆n, makes an important contribution to the optical quality

of i-PP films. Variations in ∆n too small to be easily detected by POM were shown to have sig-

nificant impacts on film optics. Although most commercial processes for the manufacture of i-PP

films involve orientation significant enough to prevent the development of spherulites, examples of

spherulitic morphologies in commercial films do exist, as discussed in Section 4.6. In such cases

the spherulite birefringence and γ-phase content should not be overlooked as material parameters

during investigations of optical properties.

126

4.4 Control of Optics by Variation of Surface Roughness

4.4.1 Introduction and Sample Preparation

The previous sections showed that the surfaces of the copolymer films have a significant influence

on the optical properties. This effect is due to the reflection, refraction, and scattering of light at

the air/polymer interface as a result of roughness.

The optical properties of polymer films are often greatly affected by surface roughness, which is

well documented in the literature.85–96, 106, 107, 172, 173 In the cited studies, the surface roughness

of the films was typically varied through the use of different resins and/or processing conditions.

What follows is a different approach, designed to alter surface roughness without changing other

variables.

Surface roughness was varied by compression molding one surface of the PE films in contact with

different substrates. Typical examples of substrate materials include smooth glass plates, ground

glass plates, KaptonTM films (where each side of the film was found to have a different roughness),

or TeflonTM films, all of which displayed a different surface roughness. Additionally, some films

were remelted and crystallized with no top substrate (free surface). In all cases, the second surface

of the PE films was crystallized in contact with the smooth surface of KaptonTM film. As an

example of a similar procedure, Stone et al. produced smooth and flat films of polyetherimide by

compression molding with smooth plates of float glass as the substrate.117 In the current study,

RMS roughness values were calculated from tapping mode AFM height images under ambient

conditions.

Sampling issues were of primary concern during this work. The film areas probed for haze, clarity,

and transparency measurements were approximately 2 cm diameter circular regions. However, the

largest images gathered by AFM were 100× 100 µm2 squares. Therefore, several images were

taken to determine a representative average roughness for the whole film. Figure 4.64 showed

that the average scatter in the roughness for measurements on three replicate films was large and

127

increased with image size. Larger images were more likely to contain random contamination or

defects that could influence the roughness measurements. Also, if the image size approached

a transition in correlation length scales, different sampled areas could have large differences in

measured roughness. The results of this investigation showed that ±30% of the average measured

value was a representative error estimate for AFM roughness measurements.

0

10

20

30

40

0 10 20 30 40 50

Image size, µµµµm

RMS Roughness, nm

Figure 4.64: Repeatability of RMS roughness measurements for three films of PE4.8. Error bars represent

±30% of the average measured value.

As discussed above, the roughness values measured by AFM often vary with image size due to the

sampling of longer correlation lengths at larger image size. Figure 4.64 shows that higher RMS

roughness values were measured at larger image sizes, as expected.

Although replication of the substrate surface roughness during the fabrication process was not

expected, some characteristics of the substrate roughness would be transferred to the copolymer

film. The difference between substrate and film roughness is shown in Figure 4.65 for a PE4.8 film

and the Kapton film used as its substrate. The PE film displayed a larger roughness value than the

substrate, which was the typical result of this fabrication process.

128

0

10

20

30

40

50

60

70

0 10 20 30 40 50

Image size, µµµµm

RMS Roughness, nm

Kapton film

PE4.8

Figure 4.65: Roughness of Kapton film and of PE4.8 film using Kapton substrate. Error bars represent


Different compression molding substrates produced films with different roughnesses as seen in

Figure 4.66 for PE4.8 and PE13.3. The RMS roughness of PE copolymer films also increased with

image size. For comparison of measured roughness with optical properties, the RMS roughness

values had to be selected from a fixed image size. Ideally this value would have been selected from

the plateau region as discussed in Section 2.3, but images of this size were not always attainable

with the samples and equipment used in this study. Therefore, the roughness values were obtained

from the largest available high quality images across a film series; these were normally the 20×20

or 40×40 µm2 images.

4.4.2 Correlation of Surface Roughness with Optical Properties

The surface roughness of the films was an extremely important parameter in the determination of

their optical characteristics. Many studies cited previously showed that haze improved significantly

129

0

10

20

30

40

50

60

0 10 20 30 40 50

Image Size, µµµµm

RM

S R

oughness, nm

PE4.8 Kapton film

PE13.3 Pyrex plate

PE13.3 cover glass

Figure 4.66: RMS roughness of PE4.8 and PE13.3 vs. image size and substrate type. Error bars represent


when polymer films were immersed in an oil of matching refractive index due to the elimination

of surface scattering. In particular, Patel et al. recently showed a linear dependence of surface haze

on roughness measured by AFM.96 Other work on polymeric and metallic surfaces has shown a

decrease in gloss with increased roughness.109–111

By fabricating several films using different substrates, but the same resin and processing condi-

tions, a series of samples could be produced that were similar in most respects except for local

random fluctuations in film characteristics and their surface roughness. Films of PE13.3 were used

for this investigation for two reasons: quenched films of this material exhibited low bulk scatter-

ing, so the source of poor haze and clarity would be almost entirely due to surface scattering; and

this film tended to stick somewhat to the KaptonTM substrate, which allowed for the removal of

one KaptonTM film without the introduction of air between the PE film and second substrate film.

Air trapped between the PE and substrate films often resulted in a bubble-filled PE film upon re-

processing to produce a freely crystallized surface. The visual appearance of these films varied

130

greatly; the freely crystallized film was optically clear while the film molded against the ground

glass plate was opaque. The optical properties and surface roughness measured from 40×40 µm2

AFM images were measured and the results are shown in Figure 4.67.

0

20

40

60

80

100

1 10 100 1000

RMS Roughness, nm

Haze/Clarity/Gloss-45

Haze

Clarity

Gloss-45

Free

Surface

Smooth

Glass

Dull

Kapton

Ground

Glass

Figure 4.67: Haze, clarity, and Gloss-45 of PE13.3 films with different surface roughness.

The RMS surface roughness was varied from a few nanometers to nearly one micrometer through

the use of different substrates during compression molding. The optical properties were relatively

unchanged until the roughness exceeded 50 nm. Use of the Rayleigh criterion and Equation 2.11

for the mean wavelength of white light, 550 nm, showed that the transition from rough to smooth

surface for a 45◦ incident angle (the same angle used for gloss-45 measurements) occurs at a

roughness of about 100 nm, which is consistent with our findings.

Recall that the only desired effect of processing with different substrates was the physical transfer

of some of the surface roughness characteristics of the substrate to the PE film. Previous work

has shown that some potential substrate materials, such as polytetrafluoroethylene (TeflonTM) and

poly(ethylene terephthalate) (MylarTM) films, can induce nucleation of i-PP at the contact surfaces

during melt crystallization.174 To confirm that the substrates used in the present work did not sig-

131

nificantly influence the bulk optical properties of the PE films, the haze and clarity of the PE13.3

films were remeasured with the films immersed in oil of matching refractive index (Figure 4.68).

The results showed that the bulk morphology was not significantly affected by the surface rough-

ness, and demonstrated the effectiveness of the oil immersion technique for optically removing

surface roughness contributions over two orders of magnitude in length scale.

0

0.2

0.4

0.6

0.8

1

1 10 100 1000

RMS Roughness, nm

Haze/mil

90

92

94

96

98

100

ClarityBulk haze/mil

Bulk clarity

Free

Surface

Smooth

Glass

Dull

Kapton

Ground

Glass

Figure 4.68: Bulk haze and clarity of PE13.3 films of different roughness.

It was shown that the surface roughness of polymer films significantly affects the optical properties

when the RMS roughness exceeds approximately 50 nm due to the effective scattering of visible

light beyond this length scale. The control of surface roughness during film fabrication, indepen-

dent of other variables, was demonstrated and shown to be a useful tool for the investigation of

film optical properties. Finally, the removal of surface scattering by immersion of the films into an

oil of matching refractive index was shown to be effective even for films with very rough surfaces.

132

4.5 Comparison of Dow Chemical P/E copolymers to Ziegler-

Natta and Metallocene P/E copolymers

Previous work had shown that the distribution and type of regio- and stereoerrors and incorpora-

tion of comonomers in the Dow Chemical copolymers induced unique crystallization behavior and

morphological character.3, 4, 53, 134, 175 This part of the current investigation focused on the mor-

phology and optical properties of propylene/ethylene copolymers prepared by different catalyst

systems.

Several propylene/ethylene copolymers synthesized using Ziegler-Natta and metallocene catalysts

were provided by Dow Chemical for comparison to the new PEX.X copolymers. The character-

istics of these materials were presented in Table 3.4. Films of these materials were prepared in

a manner identical to that of the Dow Chemical copolymers and were evaluated using the same

techniques.

The defect and comonomer distribution in the Dow Chemical copolymers was found to be more

effective at disrupting crystallization than that in the Ziegler-Natta or metallocene copolymers,

leading to lower crystallization and melting temperatures.53 Stephens et al. reported a less ordered

morphology composed of axialites rather than spherulites for the Dow Chemical copolymers with

high ethylene content.134 The differences reported by Stephens et al. between the morphology of

the Dow Chemical copolymers and traditional metallocene copolymers increased with comonomer

content. These reports are consistent with the results from the present work.

The density-based crystallinity of samples from the different catalyst systems is shown in Figure

4.69. The ZN copolymers displayed the highest crystallinity, the MET intermediate, and the Dow

Chemical PE copolymers the lowest.

The segregation of defects by the ZN catalyst into defective chains allowed long defect-free chains

to crystallize at high temperature and for these materials to achieve the highest crystallinity, as

expected. Metallocene catalysts tend to randomly distribute defects and comonomer units along

133

20

40

60

80

100

0 4 8 12 16 20


Crystallinity, wt%

PE 1K/min

PE 10K/min

PE 90K/min

ZN 1K/min

ZN 10K/min

ZN 90K/min

MET 1K/min

MET 10K/min

MET 90K/min

Figure 4.69: Crystallinity of PE, ZN, and MET films versus cooling rate. Error bars are ±1% crystallinity.

the chains, which results in a steadily decreasing defect-free propylene sequence length as the

comonomer content increases. This distribution caused the materials to crystallize at a lower tem-

perature and develop lower crystallinity than the ZN materials. The Dow Chemical copolymer

defect distribution was even more effective than that in the metallocene copolymers at reducing

total crystallinity.

Analysis of the polymorphism of these materials revealed further differences between copolymers

produced by different catalyst systems as shown in Figure 4.70. The ZN copolymer crystallized

primarily in the α-phase, even when crystallized slowly, due to the presence of long crystallizable

propylene sequences.33 Conversely, the MET materials showed a preference to crystallize in the

γ-phase. The random defect distribution left primarily short crystallizable propylene sequences,

which favor the formation of the γ-phase.33 Each data point in Figure 4.70 was calculated from

a single sample run. Statistical errors were not determined for this data, but it is clear that the

estimates of Xγ for samples with very high or low γ-phase content will be somewhat uncertain due

to error in the calculation of the small area of the minority component peak.

134

0

0.2

0.4

0.6

0.8

1

0 3 6 9 12 15


Xγγ γγ

PE 1K/min

PE 10K/min

ZN 1K/min

ZN 10K/min

MET 1K/min

MET 10K/min

Figure 4.70: Xγ of PE, ZN, and MET films crystallized at 1 and 10◦C/min. See text for a discussion of the

error in Xγ.

The somewhat blocky distribution of defects in the Dow Chemical PE materials produced a mor-

phology with an intermediate γ/α crystal ratio. As shown by Uan-Zo-li, the PE copolymers con-

tained a fraction composed of highly crystallizable sequences.53 These sequences were likely the

origin of the α-phase crosshatched network seen even at ethylene contents over 20 mol% as shown

in the present study and reported by Stephens et al.134 Thus, the high crystalline fraction was

responsible for the relatively high α-phase content of the Dow Chemical copolymers.

These differences in chain architecture led to widely different bulk morphologies during crys-

tallization from the melt, which are shown in Figures 4.71 – 4.73. Copolymer ZN4.4 formed a

morphology of large impinged spherulites at the two slower cooling rates, with somewhat smaller

spherulites at 10◦C/min than at 1◦C/min, and under 90◦C/min cooling displayed a less ordered

morphology with a finer texture. MET5.2 exhibited a sheaf-like morphology that decreased in size

as the cooling rate was increased. The PE5.4 sample developed a poorly formed spherulitic mor-

phology during 1◦C/min cooling, a mixture of spherulites and sheaves when cooled at 10◦C/min,

135

and an array of small spherulites and bundle-like crystals under 90◦C/min cooling. The longer

crystallizable sequences in the ZN and, to a lesser extent, the PE copolymers could crystallize at

higher temperatures and form longer lamellar structures, which led to larger and better-ordered

bulk morphologies.

Figure 4.71: Bulk morphology of ZN4.4 versus cooling rate from the melt.

136

Figure 4.72: Bulk morphology of MET5.2 versus cooling rate from the melt.

137

Figure 4.73: Bulk morphology of PE5.4 versus cooling rate from the melt.

138

The optical properties of the three copolymers of similar ethylene content made with different

catalyst systems were also studied. The bulk haze, clarity, and transparency data for films of

PE5.4, ZN4.4, and MET5.2 are shown as a function of cooling rate in Figures 4.74, 4.75, and 4.76,

respectively. Only the bulk values are reported because the present study focused on the effect of

the bulk morphology on optical properties.

0

2

4

6

8

Cooling Rate

Bulk Haze/m

il

PE5.4

ZN4.4

MET5.2

10°C/min Quenched1°C/min

Figure 4.74: Bulk haze/mil of PE, ZN, and MET films versus cooling rate. Error bars are ±0.5% haze/mil

units. The trendlines are present only to guide the eye.

All films showed similarly poor optical properties at the two lowest cooling rates and improved

optics when quenched. The two lowest cooling rates were not different enough to produce sig-

nificantly different morphologies in these films. Generally, ZN4.4 displayed the worst optical

properties while the MET5.2 and PE5.4 were similar. The results were consistent with the bulk

morphologies discussed above, with ZN4.4 having formed large spherulites at low cooling rates

and coarse sheaf-like texture after quench, PE5.4 composed of a mixture of smaller spherulites and

bundles, and MET5.2 displaying a morphology composed primarily of sheaf-like crystals. The op-

tical properties generally improved as the scale of the crystalline morphology decreased, as shown

139

85

88

91

94

97

100

Cooling Rate

No

rmali

zed

Bu

lk C

lari

ty,

%

PE5.4

ZN4.4

MET5.2


Figure 4.75: Normalized bulk clarity of PE, ZN, and MET films versus cooling rate. Error bars are ±1%

clarity. The trendlines are present only to guide the eye.

previously in Section 4.3.1.

While the optical properties of the ZN and MET copolymers exhibited a monotonic improve-

ment in optical properties with increasing cooling rate, the PE5.4 sample displayed unusual be-

havior, with the sample cooled at 10◦C/min showing poorer optical properties than the 1◦C/min

or quenched samples. Throughout the current work it has been difficult to distinguish between

the morphology and optical properties of the PE materials cooled at 1◦C/min and 10◦C/min. The

results shown in Figures 4.74 – 4.76, however prompted a reexamination of the trends seen in these

figures and in the haze, clarity, and transparency data presented in Section 4.1.

Although the error bars in Figures 4.14, 4.16, and 4.20 sometimes overlap, the PE copolymers

with 3–8%E often displayed better optical properties when cooled at 1◦C/min than when cooled at

10◦C/min. The haze and clarity data may be expected to follow similar trends, since it was shown

in Section 4.1.2.4 that the two measurements measure light scattered through similar angles. How-

ever, the independent transparency measurement also shows the unexpected behavior in materials

140

70

75

80

85

90

95

100

Cooling Rate

Normalized Bulk Transparency, %

PE5.4

ZN4.4

MET5.2


Figure 4.76: Normalized bulk transparency of PE, ZN, and MET films versus cooling rate. Error bars are

±2% transparency. The trendlines are present only to guide the eye.

with moderate levels of ethylene comonomer (Figures 4.20 and 4.76).

In this moderate range of comonomer content the fraction of γ-phase crystals in the PE copolymers

changes markedly, from approximately 70% to 20% when cooled at 1◦C/min and 10◦C/min, re-

spectively (Figure 4.70). The same figure shows that a less significant decrease in Xγ occurs when

the ZN and MET copolymers are cooled at 10◦C/min. The annealing study reported in Section

4.3.2 showed that optical properties degraded as annealing time increased, and that the γ-phase

content also decreased during this period. Upon consideration of the evidence discussed here, it

was speculated that the decrease in γ-phase crystal content may be responsible for the unusual

behavior seen in the PE copolymers with 3–8%E cooled at 1◦C/min and 10◦C/min.

As shown in Equation 2.4, the birefringence of a crosshatched i-PP spherulite depends on the

relative magnitude of nc and na.58 If α-γ branching is present, then the effective value of nc should

decrease due to the nonparallel orientation of helices in the γ-phase unit cell. This reduction in

nc would lead to a decrease in the birefringence (becoming less positive) of the spherulite. The

141

lower birefringence would scatter less light and lead to better optical properties, consistent with

the experimental observations of the present work.

The Dow Chemical PE copolymers generally resemble the metallocene-based resins more closely

than the ZN materials. However, the presence of some long crystallizable propylene sequences in

the PE materials gives them some of the qualities of a more heterogeneous ZN-type copolymer,

such as crystallization at higher temperature. This conclusion was also reached by Uan-Zo-li based

on thermal analysis of the three classes of material.53

The unique comonomer and defect distribution present in the PE copolymers results in several

desirable characteristics. The defects are effective at lowering the crystallinity of the PE materials

below that of either the ZN or MET resins, which should lead to improved toughness. The optical

properties of the PE materials are typically better, all else being equal, than those of the ZN mate-

rials which suggests an application in packaging films. Additionally, the PE copolymers exhibit a

broad melting peak and contain a highly crystalline fraction more reminiscent of a traditional ZN

material than a homogeneous metallocene-made resin. This distribution of crystallizable propylene

lengths should provide for good processability in fiber and blown film applications.4 In conclusion,

the Dow Chemical PE materials possess a defect and comonomer distribution that shows charac-

teristics typical of both Ziegler-Natta and metallocene based polymers, which lead to mechanical

and optical properties that may be better suited to many applications than either of the traditional

materials.

The MET13.5 sample displayed unusual behavior worth discussion. This material crystallized as

small well-formed spherulites during slow cooling despite its high comonomer content (Figure

4.77). These spherulites were the only negatively birefringent spherulites seen during this study.

Isotactic polypropylene spherulites with negative birefringence are known to form at high crys-

tallization temperatures where the radial lamellae dominate the spherulitic structure.12, 55–59 This

material, however, was found to be approximately 96% γ-phase by WAXD. AFM analysis of the

lamellar structure revealed densely packed lamellae with no indication of crosshatching (Figure

4.78). It is possible that these spherulites were composed of almost entirely γ-phase crystals. Lotz

142

et al. predicted that a spherulite composed exclusively of γ-phase lamellae would likely exhibit

negative birefringence, but noted that no example was known.20 It is possible that this material

developed such a structure during cooling at 1◦C/min.

Figure 4.77: POM micrographs and HV SALS patterns of MET13.5 cooled from the melt at 1◦C/min and

10◦C/min.

Figure 4.78: AFM height and phase images of MET13.5 cooled from the melt at 1◦C/min.

143

4.6 Cast Films Revisited — Optical Characterization

The development of a more complete understanding of the optical characterization of polymer films

in the commercial setting is one of the primary goals of the current research project. Meaningful

comparisons of film properties, which are required for research and quality control purposes, can-

not be made without reliable, consistent, and representative metrics. Scientists from Dow Chemical

had communicated that the existing haze, clarity, and gloss measurement techniques were some-

times unable to distinguish between films of different visual appearance. Such a set of films was

evaluated and the findings are discussed below.

Of the sixteen cast films provided by Dow Chemical, three were given as specific examples of the

inadequacy of the standard haze, clarity, and gloss measurements. These films, index numbers 14–

16 or samples 43-2, 43-4, and 43-6 from Table 3.3, were of similar thickness and displayed similar

values of haze, clarity, and gloss-45 but, according to Dow Chemical scientists, looked different

to the naked eye. Visual observation of these films confirmed the subjective differences in film

optical quality.

Because the optical properties of polymer films were well known to be highly dependent on surface

properties, and the cast films received from Dow Chemical typically exhibited poor surface quality,

the roughness of these films was measured using AFM. AFM height images captured at 20×

20 µm2 are shown in figures 4.79 – 4.81, and a higher resolution image of film 43-6 in Figure 4.82.

The RMS roughness of all three films was similar.

Surprisingly, these films displayed an unoriented spherulitic surface morphology. Little was known

about the resins used to manufacture these films, but clearly the chain architecture and processing

conditions allowed the melt to relax after extrusion but before crystallization. This observed mor-

phology is consistent with processing in the crystallization haze regime described by Sukhadia et

al. for blown polyethylene films.95

Since the surfaces of the film would be subjected to the highest cooling rates in the extrusion

casting process, the polymer chains near the surface would have the least time to undergo relaxation

144

Figure 4.79: AFM height image of cast film 43-2. RMS roughness = 7.4 nm.


145


Figure 4.82: 5×5 µm2 AFM height image of cast film 43-6.

146

before solidification. The well-developed spherulitic morphology visible on the surface of the films

indicated that the polymer was able to relax enough to crystallize without significant influence

from orientation. If chains at the surface were able to relax, then the material subjected to lower

cooling rates in the bulk of the films would also able to attain a reasonably unoriented state before

crystallization. Therefore, it was assumed that the spherulitic morphology persisted throughout the

bulk of the films.

HV SALS patterns were collected from these films, but the characteristic four-leaf spherulitic scat-

tering pattern was not observed. Instead, HV patterns were dominated by intense streaks whose

orientation varied with the film position (Figure 4.83). The application of refractive index match-

ing oil to the film surfaces did not significantly diminish the intensity of the streaks, suggesting

that the heterogeneities responsible for the scattering are located in the bulk of the film. Close

inspection of the AFM images presented in Figures 4.81 and 4.82 revealed row structures along

the NW-SE direction. These structures (or similar structures within the bulk of the films) may

be responsible for the streaked HV SALS patterns, but the intensity and variability of the streaks

suggest that reflections or artifacts are more likely the cause.

Since the scattering angle associated with the maximum intensity of the spherulitic scattering pat-

tern could not be measured directly from the HV patterns, the spherulite radius was estimated from

the AFM images. The scattering angle giving the maximum intensity for 550 nm light, the mean

of visible light, was calculated using Equation 2.17. Corrections were made for the wavelength of

light in the film with a refractive index of 1.49. The results of these calculations are listed, along

with the RMS roughness of the films, in Table 4.3.

While the scattering angle calculations stretched considerably the applicable range of ‘small angle’

scattering theory, it was clear that this morphology would scatter light primarily at large angles

and therefore the bulk morphology would make a finite contribution to haze. Conversely, the small

fraction of light scattered through small angles would result in films with high bulk clarity.

The small particles on the surface of these films, especially visible in Figure 4.80, may have made

a significant contribution to the total scattering due to their micrometer-scale spacing and heights

147

Figure 4.83: HV SALS patterns from cast film 43-4 with oiled surfaces. Upper left: MD horizontal with

respect to the image. Upper right: MD vertical. Lower: MD at 45◦.

Table 4.3: Estimated scattering angles and RMS roughness for cast films.

Sample RMS Roughness, nm R0,µm θmax,◦

43-2 7.4 0.6 23

43-4 7.8 0.3 50

43-6 9.9 0.6 23

148

of 20–50 nm (Figure 4.84). AFM images showed that the presence of the particles was somewhat

sporadic, with regions of high and low particle density across the films. These particles are possibly

residue from a processing additive but their identity remains unknown.142

Figure 4.84: AFM section through 25 nm high particle on cast film 43-4.

The optics of these films were examined with the complete set of commercial optical measurement

equipment in the VT lab to determine if any test could resolve the differences in appearance. Wher-

ever possible, this information was compared with data provided by Dow Chemical to confirm that

the testing results from VT were consistent with those obtained by Dow Chemical personnel. Test-

ing was done with and without the oil cell to separate the bulk and surface scattering contribution.

Five samples were carefully cut from each of the film rolls to minimize the inclusion of dirt,

defects, spots, or wrinkles that could affect the optical testing, and to match the thickness values

reported by Dow Chemical. The center of each sample was marked and all testing was carried out

in this region. Five or six replicate measurements were performed on each sample film, for a total

of 25–30 measurements for each of the three cast film samples.

149

The haze and gloss-45 data is presented in Figures 4.85 and 4.86, respectively. For this study

total haze was used rather than haze/mil because the primary parameter of interest was human

perception of film quality and films were all of similar thickness.

0

1

2

3

Haze, %

VT total

VT bulk

Dow Chemical total

43-643-2 43-4

Figure 4.85: Total and bulk haze of cast films 43-2, 43-4, and 43-6. Error bars on Dow Chemical data are

reported variations; those on VT data are ± one standard deviation as calculated from measured data. The

trendlines are present only to guide the eye.

Reported Dow Chemical haze was similar for all samples, and clustered around 1 haze unit, while

the VT results showed higher total haze for films 43-2 and 43-6. About half of the total haze was

contributed by bulk scattering which followed the same trend as VT total haze. The significant bulk

haze contribution was likely due to light scattered at large angles from the spherulitic morphology

discussed above.

The films displayed similar values for the gloss-45 measurements, where all samples exhibited

high gloss surfaces (over 80 gloss units). Dow Chemical gloss values were consistently higher

than VT data, which could have been due to differences in testing apparatus and procedure since

gloss measurements are very sensitive to local surface properties and sample preparation details.

150

60

70

80

90

100

Gloss-45

VT

Dow Chemical

43-643-2 43-4

Figure 4.86: Gloss-45 of cast films 43-2, 43-4, and 43-6. Error bars on Dow Chemical data are reported

variations; those on VT data are ± one standard deviation as calculated from measured data. The trendlines

are present only to guide the eye.

Clarity and film thickness results obtained at VT were similar to those reported by Dow Chemical

and are shown in Figure 4.87. Clarity values of all three films were in excess of 98%, with film 43-6

slightly worse than the others. The oil immersion technique revealed that most of the loss of clarity

was due to surface scattering. The similar values of clarity for all of the films was consistent with

the previously discussed arguments regarding the relative insensitivity of the clarity measurement.

The effect of surface scattering was more dramatic in the transparency data (Figure 4.88). Total

transparency of the films was moderate, with film 43-2 ranking the highest at 40%. Upon immer-

sion in the oil cell, all films displayed a dramatic improvement to nearly 100% transparency. It was

concluded that the loss of transparency in these films was almost entirely due to surface scatter-

ing. The relatively high bulk transparency values were consistent with a bulk morphology of small

spherulites that scattered little of the incident light.

In summary, a significant difference between the optical test results of these cast films was seen

151

95

96

97

98

99

100

Clarity, %

0

2

4

6

8

10

Film thickness, mil

VT total clarity

VT bulk clarity

Dow Chemical total clarity

Dow Chemical thickness

VT thickness

43-643-2 43-4

Figure 4.87: Thickness and total and bulk clarity of cast films 43-2, 43-4, and 43-6. Error bars on Dow

Chemical data are reported variations; those on VT data are ± one standard deviation as calculated from

measured data. The trendlines are present only to guide the eye.

only in the VT haze and transparency data. Dow Chemical haze results showed that all films had

approximately 1% haze. The source of the discrepancy between the Dow Chemical and VT total

haze data is not clear, as the same instruments and similar operational procedures were used. This

effect may have been another consequence of the inconsistent nature of the film quality. The total

transparency values for these films ranged from 24–40% while the total clarity values all measured

higher than 98%. Bulk clarity and transparency were nearly 100% as a result of the bulk spherulitic

morphology that scattered light at high angles and with low intensity.

The superior sensitivity of the total transparency measurement was found to confirm the reported

variation in visual appearance of the cast films which the clarity and gloss techniques could not dif-

ferentiate. The limitations of the clarity technique became evident when trying to differentiate films

with relatively good optical properties. The Haze Gard Plus reported total clarity values of 98%

or higher for all of the films even though significant differences were noted in their transparency

152

0

20

40

60

80

100

Transparency, %

0

1

2

3

4

Film thickness, mil

Total transparency

Bulk transparency

Dow Chemical thickness

VT thickness

43-643-2 43-4

Figure 4.88: Thickness and total and bulk transparency of cast films 43-2, 43-4, and 43-6. Error bars on

Dow Chemical data are reported variations; those on VT data are ± one standard deviation as calculated

from measured data. The trendlines are present only to guide the eye.

(see also Figure 4.21) and observed visually. Therefore, comparisons of films of subjectively good

optical quality should be carried out using a transparency measuring instrument compliant with

ASTM D 1746 or an equivalent standard, for which several studies have confirmed the correlation

between test results and human perception.97, 99–101, 103 Most importantly, the term ‘clarity’ should

be qualified in any context to avoid confusion between the very different metrics of Haze Gard

Plus clarity and transparency.

The sequence of worst to best optics was different if haze, clarity, or transparency data was used

(Table 4.4). This emphasized the need to understand the physical meaning of each metric and its

applicability to the desired application. Transparency data would be less important than haze in a

packaging application, for instance, due to the proximity of the film and target object. Conversely,

the transparency of a plastic sheet would be vital for use in a window or windscreen application

due to the need to resolve details of distant objects viewed through the sheet. It is clear that there

153

can be no ‘universal’ metric for the evaluation of the optical quality of polymer films.

Table 4.4: Cast films ranked using VT haze, clarity, and transparency.

Ranked by Ranked by Ranked by

bulk haze bulk clarity bulk transparency

Haze Film Clarity Film Transparency Film

2.4 43-6 98.30 43-6 24.3 43-4

2.2 43-2 99.36 43-4 28.6 43-6

0.9 43-4 99.40 43-2 40.2 43-2

154

4.7 Conclusions

This work examined the correlations between the optical properties and morphology of propy-

lene/ethylene copolymer films, with a focus on understanding the origins of light scattering from

the films and the tools used for their characterization. Dow Chemical reports of discrepancies

between haze, clarity, and gloss results and visually perceived film quality were investigated and

explained.

The γ-phase content was shown to have a significant effect on the optical properties of the copoly-

mer films. High temperature annealing was used to vary the fraction of γ-phase crystals in im-

pinged spherulites in PE0.0 and PE3.3 films. Haze, clarity, and transparency degraded and total

HV scattering intensity increased linearly with the logarithm of annealing time. Through AFM,

WAXD, and DSC analysis, these changes in optics and scattering behavior were shown to arise

from a partial melting of γ-phase crystals and subsequent recrystallization into thicker and higher

melting α-phase lamellae, with an inferred increase in spherulite birefringence.

The important role played by the γ to α crystal phase ratio was also suggested by the unusual

behavior of the PE copolymers of 3–8%E cooled at 1◦C/min and 10◦C/min. In many of these

cases, the 10◦C/min samples displayed poorer optical properties than the 1◦C/min materials. These

copolymers exhibited similar bulk morphologies at both cooling rates but underwent a transition

from primarily γ-phase crystals when cooled at 1◦C/min to primarily α-phase crystals when cooled

at 10◦C/min. These results suggest that the fraction of γ-phase crystals present in the PE copolymer

films may have a significant influence on the observed optical properties.

The contributions of film surface roughness to the degradation of polymer film optics were well

known and confirmed in this work. A new method of varying surface roughness by compression

molding the copolymer films in contact with various substrates was used to produce films with

surface roughness as the only variable. Films were characterized optically by haze, clarity, and

gloss and the surface roughness of the films was estimated using AFM. The results showed that a

significant increase in haze and decrease in clarity and gloss occurred at a RMS surface roughness

155

of approximately 50 nm, in agreement with the transition from a smooth to rough surface for

visible wavelengths of light.

Initial studies of cast films provided by Dow Chemical employed a custom made haziness meter

to evaluate the film quality. Total and bulk haziness was found to be proportional to thickness, and

a normalized haze/mil metric was developed to allow comparison of films of unequal thickness.

The majority of the scattering from these films originated at the air/film interfaces due to the

poor surface quality of the films. Inconsistencies in cast film quality prevented any systematic

investigations or meaningful correlations between the optical data and the copolymer composition

and related morphologies. The limitations of the VT haziness meter were recognized and the

decision to acquire a commercial hazemeter was made.

Copolymer films were compression molded and cooled under constant cooling rate conditions with

smooth surfaced substrates to improve film quality and to provide control of the crystallization

conditions. The laboratory press was modified to produce constant cooling rates of 1◦C/min and

10◦C/min. This fabrication process resulted in well defined films for optical characterization by

the haze, clarity, transparency, and gloss tests.

Haze and clarity were found to vary linearly with film thickness, whether total or bulk scatter-

ing was considered. Transparency measurements were found to be extremely sensitive to surface

variations and only the bulk transparency showed a linear dependence on thickness. Normalized

haze, clarity, and bulk transparency metrics were developed and utilized to compare films of dif-

ferent thickness. The cooling rates of 1◦C/min and 10◦C/min were found to produce films with

similar optical properties, while quenched films showed better optics (i.e., lower haze, and higher

gloss, clarity, and transparency). A general trend was found where optical properties improved as

comonomer content increased due to the development of morphologies with finer textures which

scattered less light.

Several significant differences were found between the clarity and transparency measurements.

The angular ranges of scattering measured by the two techniques were very different. In fact, the

clarity and transparency measurements were found to be based on entirely different principles. The

156

clarity measurement was shown to be insensitive to small variations in optical quality and to resem-

ble haze more than transparency. A good correlation between bulk clarity and bulk transparency

suggested that random inhomogeneities in bulk of the films influence the scattered light profile in

an unpredictable manner.

The Dow Chemical PE copolymers were found to contain significant fractions of γ-phase crys-

tallinity when slowly cooled, with higher Xγ at higher ethylene contents and slower cooling rates.

Quenched samples crystallized exclusively in the α-phase. The crystallinity of the materials de-

creased with increasing comonomer content and with faster cooling rates.

Microscopic investigations revealed that slowly cooled copolymers of low ethylene content crys-

tallized in a spherulitic morphology. These spherulites were of slightly positive or mixed bire-

fringence, indicative of a crosshatched lamellar morphology. This morphology was confirmed by

SEM and AFM investigations, which also showed that regions of densely packed lamellae were

present in copolymers of high γ-phase content. These domains were likely composed of γ-phase

crystals.

Films with higher comonomer content and/or those cooled more rapidly displayed disorganized

morphologies composed of sheaf-like crystal aggregates. SEM images revealed some crosshatch-

ing present in all of the PE copolymers, which developed from long crystallizable propylene se-

quences present in these materials even at high ethylene concentrations.

The optical microscopy and small-angle light scattering techniques were used to estimate the in-

tensity and angular range of scattering from the bulk morphology of the copolymer films. It was

shown that the film optical properties generally improved as spherulite size decreased, as expected

from the decrease in scattering intensity with decreasing spherulite size.

The Dow Chemical PE copolymers were compared to copolymers of similar ethylene content but

made with Ziegler-Natta or metallocene catalysts. The PE materials exhibited the lowest crys-

tallinity, optical properties similar to the metallocene resins, and Xγ intermediate between the other

two series. The data collected during this work, combined with the results of thermal analysis

investigations by Uan-Zo-li, established that the Dow Chemical catalyst produced PE copolymers

157

with mechanical and optical properties superior to those made with ZN and MET catalysts for

some film and fiber applications.53

The issue of inconsistent optical test results presented by the Dow Chemical scientists was also

investigated. Three cast films were provided by Dow Chemical as examples of films that displayed

similar total haze, clarity, and gloss values but differed in visual appearance. These materials

were evaluated in our laboratory and found to have similar total clarity values, as expected due

to the general insensitivity of the clarity measurement, but were distinguishable by total haze and

transparency. Discrepancies between Dow Chemical results and those obtained during this work

emphasized the importance of sample selection and film consistency.

These films were found to have a morphology composed of small well-formed spherulites. Using

the SALS model, the angular range of scattering was estimated and found to occur at very large

angles. The films were therefore expected to exhibit good bulk clarity and transparency, but show

a measurable bulk haze value. These predictions were confirmed by experimental data.

The compilation of all the investigations performed during the present work has, in addition to

the characterization of a novel series of propylene/ethylene copolymers, provided a new level of

understanding of the interplay between polymer film morphology and optical properties. Surface

roughness and imperfections contribute greatly to the overall optical quality of the films and efforts

should be undertaken to minimize these factors for nearly any application. The bulk morphology

can also make a significant contribution to the total optical properties of the film, and it was shown

that smaller spherulitic morphologies generally scatter less light and result in better film optics

than large scale morphologies.

Finally, it was shown that no single optical characterization technique is sufficient to describe the

optical quality of a polymer film. The proposed application of the film must be considered before

the relative importance of the haze, clarity, transparency, and gloss results can be determined.

Chapter 5

Future Work

The materials and techniques evaluated in the present studies have allowed for significant gains

in the understanding of the interplay between the morphology and optical properties of propy-

lene/ethylene copolymers. Additionally, the critical examination of commercial optical testing

equipment has revealed that different tests may be appropriate for the optical characterization of

polymer films depending on the desired application. Opportunities exist for further investigations

into these and other related areas as discussed below.

5.1 On the Dow Chemical P/E copolymers

The Dow Chemical copolymers possess a unique defect and comonomer distribution, which im-

parts mechanical and optical properties different than more traditional Ziegler-Natta and metal-

locene derived materials. The Series VII copolymer materials, for example, incorporate from

3.3%–21.2% ethylene yet still crystallize partially in the α-phase under the appropriate conditions.

Use of this set of copolymers would allow for the extension of the studies on the ethylene unit

partitioning coefficient done by Alamo, et al., whose work was limited to copolymers of relatively

low ethylene content.46 The examination of high comonomer materials would show whether the

158

159

partitioning coefficient remains constant at 42% at high comonomer concentration.

Similarly, the unit cell dilation of propylene/ethylene copolymers has been studied only for materi-

als with approximately 10% ethylene or less, for which the dilation is constant.43, 44, 156, 157 WAXD

investigations of the Dow Chemical Series VII copolymers could determine the unit cell expansion

in materials with more than 20% ethylene comonomer.

5.2 On the Surface Roughness

The present work has confirmed that surface roughness becomes a significant contributor to light

scattering when the RMS roughness, as measured by AFM, exceeds approximately 50 nm. AFM

is a powerful tool for surface characterization, but is limited to small sampling areas. Other tech-

niques, such as mechanical stylus or optical profilometry can sample larger areas of the film surface

and give a more representative view of the surface roughness at longer length scales.

Stylus profilometry has z-axis sensitivity comparable to AFM and scan lengths of up to 1 mm, but

the lateral resolution is typically much poorer due to the large radius of the stylus used. Care must

be taken to avoid excessive loading of the stylus to avoid damage to soft samples such as polymer

films. Finally, stylus profilometry measures only one-dimensional surface profiles, requiring many

runs to obtain an accurate representation of the surface roughness. Optical profilometry has the

advantage of providing an average roughness over the illuminated sample ares, but at the obvious

expense of spatial resolution. Each method has limitations but comprehensive investigations of

surface roughness using these complimentary approaches would provide a picture of the surface

topology from the nanometer to millimeter scale.

Finer control of the surface roughness during compression molding could be achieved using sub-

strates with designed surface features. Fused silica plates polished or ground to different degrees

could serve as reusable substrates with various randomly rough surfaces. Lithographic etching

techniques could be used to produce patterned substrates to simulate, in a controlled and repro-

ducible fashion, the directional roughness found in commercial cast roll films.

160

The evaluation of light scattering from non-randomly rough surfaces could benefit from investiga-

tions of metrics other than RMS roughness. In these cases, the correlation lengths of the surface

features would be an important parameter. Investigations of surface roughness in terms of fractal

dimension may also be useful. Films with repetitive surface features such as processing marks or

spherulitic surface morphologies would benefit most from these types of analysis.

Investigations of polymer film properties using the methods described in this section would lead to

increased understanding of the dependence of light scattering, and therefore optical properties, on

the surface roughness of polymer films.

5.3 On the Optical Properties

The present research project studied films crystallized under conditions that produced unoriented

morphologies of spherulites or sheaf-like crystal aggregates. In contrast, many industrial high

volume film manufacturing processes (e.g. extrusion casting, blow molding, or calendering) may

introduce significant orientation in the polymer melt and/or film and result in row nucleated or

shish-kebob type morphologies. The cooling of polymer films by chill rolls may introduce a tem-

perature gradient in the film resulting in a skin-core effect where the morphology varies from the

surface to the bulk of the film. Examination of high quality oriented polymer films using the meth-

ods employed in the present study could provide information on the morphology/optical property

relationships of industrially produced films, allowing for the optimization of processing conditions

to achieve the desired optical properties for a particular application.

In the current research, the angular dependence of light scattered from the bulk morphology was

measured using the polarized small-angle light scattering technique.69 The optical characteriza-

tion methods of haze, clarity, transparency, and gloss all employ unpolarized white light to better

approach typical environmental illumination conditions. Therefore, while the SALS technique

provides useful information regarding the morphology of polymer films, its use for the evaluation

of visually perceived film optical quality is not ideal.

161

To accurately map the intensity and angular dependence of white light scattered from a polymer

film requires the use of a photogoniometer, such as the instrument used by Webber in his initial

investigations of film transparency.97 The photogoniometer is somewhat similar in design to the

Zebedee CL–100 transparency meter, but with added provisions for monitoring the fluctuations in

incident beam intensity, precise positioning of the specimen, and most importantly the accurate

translation of the receiving aperture to allow the collection of scattered light at angles other than

0◦. An instrument of this type would most likely require custom manufacturing, but would provide

accurate maps of scattered intensity versus angle that could be directly correlated to haze, clarity,

and transparency measurements.

The results of the extensive evaluation of the optical properties of PE copolymer films has sug-

gested that the γ-phase crystal content may have a significant influence on the film optical quality.

Further investigations using materials such as PE5.4, which undergoes a large change in Xγ but only

a small change in crystallinity and bulk morphology with a change in cooling rate, could confirm

these speculations. More intensive study of the interesting crystallization behavior of the MET13.5

sample may also provide insight into the effect of the γ-polymorph on bulk optical properties as

this sample forms well defined negatively birefringent spherulites (the only example of spherulites

with negative ∆n seen in this study) which are composed almost entirely of γ-phase crystals.

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Appendix A

Temperature Controller BASIC Program

Listing

10 REM *** GWBASIC PROGRAM TO LOG TEMP DATA FROM OMEGA ***

20 REM *** iSERIES TEMPERATURE CONTROLLER ***

21 REM *** WRITTEN BY CHRIS FRATINI 2005 ***

30 REM

100 REM *** READ IN TIME INTERVAL VALUE ***

105 INPUT "ENTER THE LENGTH OF THE DATA RUN IN MINUTES";RUNLENM

110 INPUT "ENTER THE TIME INTERVAL BETWEEN READINGS IN SECONDS";INTERVAL

120 REM

130 REM *** SET UP COMMAND FOR TEMP CONTROLLER ***

140 REM *** FORMAT IS *, THEN COMMAND, THEN <CR> ***

145 REM *** X01 COMMAND REQUESTS TEMPERATURE FROM CONTROLLER ***

150 CMD$="*X01"+CHR$(13)

200 REM *** OPEN DATAFILE FOR OUTPUT ***

210 OPEN "FILENAME.TXT" FOR OUTPUT AS #1

215 PRINT #1, "DATA INTERVAL IS"INTERVAL"SECONDS"

180

181

220 REM

230 REM *** OPEN COM PORT AND SET UP ***

240 REM *** 9600 BAUD, ODD PARITY, 7 DATA BITS, ***

241 REM *** 1 STOP BIT, DISABLE FLOW CONTROL ***

250 OPEN "COM1:9600,O,7,1,RS,DS0" AS #2

260 REM

265 REM *** CONVERT MINUTES TO SECONDS ***

270 RUNLENS = 60*RUNLENM

275 REM *** BEGIN LOOP TO READ TEMPERATURES ***

280 I = INTERVAL

282 REM *** RESET TIMER ***

285 TIME$ = "0"

290 WHILE TIMER < RUNLENS

293 REM *** WAIT THE INTERVAL BEFORE SENDING COMMAND ***

295 WHILE TIMER < I

297 WEND

300 REM *** SEND COMMAND TO TEMP CONTROLLER AND STORE RESPONSE ***

320 PRINT #2, CMD$

330 INPUT #2, DAT$

335 REM *** PRINT TO SCREEN AND OUTPUT FILE ***

340 PRINT DAT$

350 PRINT #1, DAT$

360 I = I + INTERVAL

370 WEND

400 REM *** CLOSE DATAFILE AND COM PORT ***

410 CLOSE #1, #2

500 END

Appendix B

Morphology and HV SALS patterns of PE,

ZN, and MET copolymers

182

183

Figure B.1: Morphology and HV SALS pattern of PE0.0 cooled at 1◦C/min.



184




185




186




187




188

Figure B.16: Morphology and HV SALS pattern of ZN4.4 cooled at 1◦C/min.



189




190

Figure B.22: Morphology and HV SALS pattern of MET5.2 cooled at 1◦C/min.



191




192




193


Appendix C

Derivation of a Model for the Birefringence

of an iPP Spherulite with γ-α Branching

The model of Binsbergen and De Lange (see Section 2.1.5) predicts the birefringence of an iPP

spherulite composed of crosshatched α phase lamellae based on the fraction of radially and tangen-

tially oriented lamellae.58 The following derivation extends the model to predict the birefringence

of spherulites composed of some fraction of γ phase iPP lamellae grown epitaxially on radially ori-

ented α phase parent lamellae (see Figure 2.9 for a graphical representation of this arrangement).

In this model, t and r represent the fraction of daughter γ phase lamellae and parent α phase

lamellae, respectively, and t + r = 1. The constants n′c and n′a are the indexes of refraction parallel

and perpendicular to the iPP helix axis; these quantities are identical to nc and na, respectively,

used in the derivation of Equation 2.4.58 Recall that the γ phase lamellae nucleate and grow at a

crystallographically fixed 40◦ angle to the radially oriented parent α phase lamellae. The peculiar

arrangement of bilayers of non-parallel iPP helices oriented at 80◦ angles to one another in the γ

phase unit cell causes alternating bilayers to be oriented with their helix axes radial or tangential

in the spherulite. Thus, half of the total γ phase helices will be oriented radially and half will be

oriented tangential to the spherulite radius. Following the method of Binsbergen and De Lange,

the index of refraction of the spherulite in the radial direction is:58

194

195

nr = (t/2)n′c +(t/2)n′a + rn′a (C.1)

The index of refraction in the tangential direction is:

nt = (t/2)n′a +(t/2)(

n′c +n′a2

)+ r(

n′c +n′a2

)(C.2)

Therefore, the total spherulite birefringence, ∆n = nr −nt , is:

∆n = (n′c−n′a)(t/4− r/2) (C.3)

Vita

Christopher Fratini was born on July 20, 1976 and raised in Western Massachusetts. Chris attended

Worcester Polytechnic Institute where he received a BS in Chemistry in 1998. He worked as a

laboratory technician at Medeva/Armstrong Pharmaceuticals before accepting a Research Chemist

position with General Eastern Instruments in 1999. After a move to Blacksburg, Virginia and two

years of work at Alliant Techsystems, Chris began his PhD studies in Chemistry with Dr. Herve

Marand at Virginia Tech.

196

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