Study of the Morphology and Optical Properties of Propylene/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

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 materials 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 birefringence. 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 thickness 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 polymer 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 controlled 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

viii 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

◦ 4.32 Morphology and HV SALS pattern of PE7.0 cooled at 1 C/min...... 95

◦ 4.33 Morphology and HV SALS pattern of PE12.8 cooled at 1 C/min...... 95

◦ 4.34 Morphology and HV SALS pattern of PE16.6 cooled at 1 C/min...... 95

◦ 4.35 Morphology and HV SALS pattern of PE0.0 cooled at 10 C/min...... 96

◦ 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

4.80 AFM height image of cast ﬁlm 43-4. RMS roughness = 7.8 nm...... 144

4.81 AFM height image of cast ﬁlm 43-6. RMS roughness = 9.9 nm...... 145

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.2 Morphology and HV SALS pattern of PE3.3 cooled at 1 C/min...... 183

◦ B.3 Morphology and HV SALS pattern of PE5.4 cooled at 1 C/min...... 183

◦ B.4 Morphology and HV SALS pattern of PE6.7 cooled at 1 C/min...... 184

◦ B.5 Morphology and HV SALS pattern of PE12.3 cooled at 1 C/min...... 184

◦ B.6 Morphology and HV SALS pattern of PE16.6 cooled at 1 C/min...... 184

◦ B.7 Morphology and HV SALS pattern of PE0.0 cooled at 10 C/min...... 185

◦ B.8 Morphology and HV SALS pattern of PE3.3 cooled at 10 C/min...... 185

◦ B.9 Morphology and HV SALS pattern of PE5.4 cooled at 10 C/min...... 185

◦ B.10 Morphology and HV SALS pattern of PE6.7 cooled at 10 C/min...... 186

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

◦ B.12 Morphology and HV SALS pattern of PE0.0 cooled at 90 C/min...... 186

◦ B.13 Morphology and HV SALS pattern of PE3.3 cooled at 90 C/min...... 187

◦ B.14 Morphology and HV SALS pattern of PE5.4 cooled at 90 C/min...... 187

◦ B.15 Morphology and HV SALS pattern of PE6.7 cooled at 90 C/min...... 187

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

◦ B.17 Morphology and HV SALS pattern of ZN8.3 cooled at 1 C/min...... 188

◦ B.18 Morphology and HV SALS pattern of ZN4.4 cooled at 10 C/min...... 188

◦ B.19 Morphology and HV SALS pattern of ZN8.3 cooled at 10 C/min...... 189

◦ B.20 Morphology and HV SALS pattern of ZN4.4 cooled at 90 C/min...... 189

xvi ◦ B.21 Morphology and HV SALS pattern of ZN8.3 cooled at 90 C/min...... 189

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

◦ B.23 Morphology and HV SALS pattern of MET6.5 cooled at 1 C/min...... 190

◦ B.24 Morphology and HV SALS pattern of MET11.1 cooled at 1 C/min...... 190

◦ B.25 Morphology and HV SALS pattern of MET13.5 cooled at 1 C/min...... 191

◦ B.26 Morphology and HV SALS pattern of MET5.2 cooled at 10 C/min...... 191

◦ B.27 Morphology and HV SALS pattern of MET6.5 cooled at 10 C/min...... 191

◦ 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

◦ B.30 Morphology and HV SALS pattern of MET5.2 cooled at 90 C/min...... 192

◦ B.31 Morphology and HV SALS pattern of MET6.5 cooled at 90 C/min...... 193

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 packaging 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 rubber (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 molecular 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 measurement 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 characterization techniques routinely used by Dow Chemical scientists were unable to distinguish between 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 several 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, respectively. 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 symmetric 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 experimentally 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 crystallization 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 appearance 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 amorphous interlamellar regions.10, 11

Polymer spherulites display interesting optical properties due to their symmetry and internal structure. 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 condition 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 difference 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 birefringent 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 0 0 the undercooling, deﬁned as Tm − T, where Tm 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 undercooling 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 deposition 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.

∗ −U −Kg G = G0 exp exp (2.1) R(T − T∞) T∆T

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

∗ A key factor in polymer crystal growth is the dependence of the initial lamellar thickness, lg on ∗ −1 crystallization temperature. Hoffman showed that lg is proportional to (∆T) ; 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 annealing.

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 properties 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 solution 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 23 i-PP 31 helix. 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 transformed 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 24 displayed a surprising non-parallel arrangement of 31 i-PP helices. 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 permit 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 crystallization 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 formation 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 incorporated 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 common, 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 temperature than Type II, had a small but positive birefringence.12 Type II spherulites had a slightly negative 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 crosshatched 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 composed 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 crystal 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 structure 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 commonly 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 illumination 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 parameter 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:

2 n − 1 NAρα 2 = (2.5) n + 2 3Mε0 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 reflection, 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) = îE0x cos(kz − ωt) (2.6) where E0x is the maximum amplitude of the field, î 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)

th where a is the spacing between lines on the grating, θm is the angle that the m 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:

4πhcosθ ∆φ = (2.10) λ

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:

λ h < (2.11) 8cosθ

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 approximations are employed depending on the magnitude of the refractive index ﬂuctuations in the material 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 patterns 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 multiple 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 polarizer 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:

2 2 3 2 IVV = Aζ V0 (3/U ) {(αt − αs)(2sinU −U cosU − SiU) 2 +(αr − αs)(SiU − sinU) + (αr − αt)[cos (θ/2)/cosθ] ×cos2 µ(4sinU −U cosU − 3SiU)}2 (2.12)

2 2 3 2 2 IHV = Aζ V0 (3/U ) {(αr − αt)[cos (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 polarizability 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:

q ζ = cosθ cos2 θ + sin2 θcos2 µ (2.14)

SiU is the sine integral given by: 27

Z U sinx SiU = dx (2.15) 0 x and is solved using a series expansion. U is the shape factor for a sphere, and is given by:

4πR U = 0 sin(θ/2) (2.16) λ

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

2 The VV mode patterns generally show anisotropy along the polarization axis due to the cos 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 scattering 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:

4.1λ R0 = (2.17) 4πsin(θmax/2)

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 increase 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:

6 2 I ∝ R0 (∆n) (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 respect 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 milkiness 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 quantify 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:

(Φ )90 haze = s 2.5 × 100% (2.19) Φt + (Φs) f

90 ◦ where (Φs)2.5 is the light scattered between 2.5 and 90 , Φt is the intensity of the undeviated transmitted 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 scattered 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 materials 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

I T = × 100% (2.20) I0 where I is the transmitted light intensity with the specimen in the beam path and I0 is the transmitted 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 heterogeneities 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 application 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 specified 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 intermediate 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:

 2 2 p 2 2 ! 2 p 2 2 ! Ir 1 cosi − n − sin θ n cosi − n − sin θ Rs = =  p + p  (2.21) I0 2 cosi + n2 − sin2 θ n2 cosi + n2 − sin2 θ

68 where Ir is the intensity of the specularly reﬂected beam. 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:

" # 4πσcosθ2 R = R exp − (2.22) r s λ

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 increased 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 development 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 optical 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 roughness 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:

1 N Ra = ∑ |Zi− < Z >| (2.23) N i=1

s N 1 2 σ = ∑ (Zi− < Z >) (2.24) N i=1

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 ∑ (Zi− < Z >) = 0 (2.25) i=1

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 parameter 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 micrometers 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 included 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 characterization, 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 consideration. 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 roughness 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 principles 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 distribution, 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 materials 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 different 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 prepared 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 recrystallized 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 copolymer 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 recrystallized 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 transmission 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 frequency 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 incandescent 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 described 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 following, 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.

PM Tube (Detector) Electronic Baffled from Entrance Port Shutter

Sample Holder Light Trap

He/Ne Laser λλλ = 633 nm

Neutral Density 6-inch Integrating Filter; OD = 2 Sphere

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 measured 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

3 VT Haziness, a.u.

0 0 1 2 3 4 5 6 7

Dow Chemical Haze, %

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

25 Total

Bulk

Haziness, a.u. Haziness, 10

0 0 1 2 3 4 5 6 Number of layers

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

2 VT Haziness/mil, a.u.

0 0 1 2 3 Dow Chemical Haze/mil, %/mil

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

4 Total Bulk

2 Haziness/mil, a.u.

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Cast Film Number

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 determinations 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 optics 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 birefringence, 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 microscope hotstage or a DSC.

To determine the linearity of the press cooling profiles in the 140–30◦C range, a 0.005 inch diameter 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

250

Run 1

Run 2 200

150 140°C

100 Sample Temperature, °C Temperature, Sample

30°C

0 0 6000 12000 18000 24000 Elapsed Time, s

Figure 4.6: Sample temperature proﬁle for slow cool.

250

Run 1

Run 2 200

150 140°C

100 Sample Temperature, °C Temperature, Sample

50 30°C

0 0 1500 3000 4500 6000 7500 Elapsed Time, s

Figure 4.7: Sample temperature proﬁle for bench top cool. 66

250

Slope from 198.4 to 22.4°C is 5000°C/min R2 = 0.988

200

150

100 Sample Temperature, °C Temperature, Sample

0 0 20 40 60 80 100 120 Elapsed Time, s

Figure 4.8: Sample temperature proﬁle for ice/water quench.

250

Slope from 140 to 30°C is 1°C/min Run 1 R2 = 0.998 Run 2

200 Run 3

150 140°C

100 Sample Temperature, °C Temperature, Sample

30°C

0 0 1500 3000 4500 6000 7500 9000 Elapsed Time, s

Figure 4.9: Sample temperature proﬁle for cooling at 1◦C/min. 67

250

Slope from 140 to 30°C is 9°C/min Run 1 R2 = 1.000 Run 2 200 Run 3

Run 4

150 140°C Run 5

100 Sample Temperature, °C Temperature, Sample

50 30°C

0 0 300 600 900 1200 1500 Elapsed Time, s

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 conducted. 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 values 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.

8 Quenched

4 Film mil Thickness,

0 100 150 200 250 300 350

MW, kg/mol

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

Total

Bulk 40

30 Haze, % Haze, 20

0 0 5 10 15 20 25 Cumulative Film Thickness, mil

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

10 1K/min

10K/min

8 Quenched

6 Haze/mil 4

0 0 3 6 9 12 15 Comonomer Content, mol %

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

1K/min - total

1K/min - bulk

8 10K/min - total

10K/min - bulk

Quenched - total 6 Quenched - bulk Haze/mil 4

0 0 3 6 9 12 15

Comonomer Content, mol %

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 measurements. In contrast to the nonuniform cast film samples provided by Dow Chemical, the compression 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 measurement 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 described 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:

100% − clarity Normalized Clarity = 100% − (4.1) thickness

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

100

90 Clarity, % Clarity,

Total

Bulk

70 0 5 10 15 20 25

Cumulative Film Thickness, mil

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

100

1K/min - total 94 1K/min - bulk Normalized Clarity, % Clarity, Normalized 10K/min - total

92 10K/min - bulk Quenched - total

Quenched - bulk 90 0 3 6 9 12 15

Comonomer Content, mol %

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:

I − I Clarity = center ring × 100% (4.2) Icenter + Iring 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◦, detected 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 instrument. 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.

100

60 Total

Bulk

40 Transparency, % Transparency,

0 0 5 10 15 20 Cumulative Film Thickness, mil

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.

100 15

80 12

1K/min - total 1K/min - bulk 10K/min - total 60 10K/min - bulk 9 Quenched - total Quenched - bulk Average film thickness 40 6 Transparency, % Transparency, Film mil Thickness,

20 3

0 0 0 3 6 9 12 15 Comonomer Content, mol %

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

100

1K/min Normalized Bulk Transparency, % Bulk Normalized Transparency, 10K/min

Quenched

70 0 3 6 9 12 15 Comonomer Content, mol %

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 content. The quenched samples all exhibited high transparency.

All three optical measurement techniques studied thus far established similar trends for the compression 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%.

100

60 1:1 Correspondence Clarity, % Clarity, 40 1K/min - total 1K/min - bulk 10K/min - total 20 10K/min - bulk Quenched - total Quenched - bulk

0 0 20 40 60 80 100

Transparency, %

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 correlation 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 measurement 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 properties 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 significant 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 fluctuations 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 optical 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

100

80 Gloss-45

1K/min

10K/min

Quenched

40 0 3 6 9 12 15 Comonomer Content, mol %

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 samples 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 (according 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 temperature, 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,

0.90

0.89

3 0.88

PE4.4 - quenched PE7.8a - quenched PE8.2 - quenched

Density, g/cm Density, 0.87 PE12.4 - quenched PE7.8 - slow cooled PE8.2 - slow cooled 0.86 PE12.4 - slow cooled PE13.6 - slow cooled PE15.0 - slow cooled PE19.4 - slow cooled 0.85 0 50 100 150 200 Elapsed Time, hours

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.

PE0.0 PE7.0 Haze, % Haze, 8 PE7.8

0 0 50 100 150 200 250 Elapsed Time, hours

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 fundamental 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

PE0.0 PE7.0 PE7.8 93

92 Clarity, % Clarity,

90 0 50 100 150 200 250 Elapsed Time, hours

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

0.90

0.89 3

0.88 Density, g/cm Density,

0.87

0.86 1.480 1.484 1.488 1.492 1.496

Index of Refraction

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 Normalized Intensity,Normalized a.u.

(130)ααα (117)γγγ

17 18 19 20 21 Scattering Angle, degrees (2ΘΘΘ)

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:

Aγ Xγ = (4.3) Aα + Aγ 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

0.8

PE Slow Cool 0.6 PE 1K/min PE 10K/min γ γ γ γ

X PE Quench

0.4

0.2

0 0 3 6 9 12 15 Comonomer Content, mol %

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:

ρ − ρA XVC = (4.5) ρC − ρA

Crystalline fraction by mass, which was more desirable for comparison to thermal data, is deﬁned as:

mC XmC = (4.6) mC + mA 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:

ρ − ρA ρC XC = XmC × 100% = × 100% (4.7) ρC − ρA ρ

The choice of density values was also discussed by Uan-Zo-li.53 Following the discussion of Uan- 3 Zo-li, an amorphous density of ρA = 0.854 g/cm 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 containing 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 appropriate 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 crystallization. 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

0.92

1K/min 10K/min 0.91 90K/min Quenched

0.90 3

0.89 Density, g/cm Density, 0.88

0.87

0.86 0 4 8 12 16 20

Comonomer Content, mol%

Figure 4.29: Density of P/E copolymers at 23◦C. Errors are within the data points.

100

1K/min 10K/min 90K/min 80 Quenched

60 Crystallinity, Crystallinity, wt%

20 0 4 8 12 16 20

Comonomer Content, mol%

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 propylene/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 transparency. 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 provided 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 primarily 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

◦ Figure 4.32: Morphology and HV SALS pattern of PE7.0 cooled at 1 C/min.

◦ Figure 4.33: Morphology and HV SALS pattern of PE12.8 cooled at 1 C/min.

◦ Figure 4.34: Morphology and HV SALS pattern of PE16.6 cooled at 1 C/min. 96

◦ Figure 4.35: Morphology and HV SALS pattern of PE0.0 cooled at 10 C/min.

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

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 increasing 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 somewhat 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 positive 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 morphologies 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 refractive 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, impingement, 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 maximum. 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 better 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 71 more scattering at high and low angles than would be expected for a spherulite. 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 intensity 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 decrease 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.

40000

Raw data

Gaussian blur r = 5

Gaussian blur r = 10 30000

20000 Intensity, a.u.

10000

0 0 2 4 6 8 Scattering Angle, degrees

Figure 4.48: µ = 45◦ intensity proﬁle for MET13.5 cooled at 1◦/min. 109

PE00 PE33 PE54 20 PE67

10 Scattered Intensity, a.u. ScatteredIntensity,

0 0 1 2 3 4 5 6 Scattering Angle, degrees

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 maximum 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 morphology 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

1K/min

10K/min 8

Bulk Bulk Haze/mil 4

0 0 20 40 60 80 Spherulite Radius, µµµm

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 appeared 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 morphologies therefore displayed better optical properties. 112

100

94 Normalized Bulk % Normalized Clarity,

92 1K/min

10K/min

90 0 20 40 60 80 Spherulite radius, µµµm

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

100

80 Normalized Bulk Transparency, % Bulk Normalized Transparency,

75 1K/min

10K/min

70 0 20 40 60 80 Spherulite radius, µµµm

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.

0.910 86

Density Crystallinity

0.909

84 3

0.908 Density, g/cm Density, 82 Crystallinity, wt%

0.907

0.906 80 1 10 100 1000 10000

Annealing Time, min

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.

70 20

15 50

40 10 30 HV Intensity,HV a.u. Haze 20

Haze, Clarity, Transparency, % Transparency, Clarity, Haze, Clarity 5

Transparency 10 Hv Intensity

0 0 1 10 100 1000 10000

Annealing Time, min

◦ 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 dependence 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 values. Because the spherulite radii were constant, the spherulite birefringence must have increased 69 (become more positive) with longer annealing time to cause the increased scattered HV intensity. 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 described 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).

3000

As prepared

Annealed 19h

2000

(117)γγγ

1000 Normalized Intensity,Normalized cps

(130)ααα

0 17 18 19 20 21

Scattering Angle (2Θ), degrees

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.

40 As Prepared Annealed 20 min Annealed 720 min

30 Heat Flow,Heat mW

20 80 100 120 140 160 180 Sample Temperature, °C

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 results 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 materials 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

100 4

80 Haze 3 Clarity

Transparency 60 Hv Intensity

40 HV Intensity,HV a.u.

Haze, Clarity, Transparency, % Transparency, Clarity, Haze, 1 20

0 0 1 10 100 1000 10000

Annealing Time, min

◦ 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 58 positive, and therefore cause the increased HV intensity observed experimentally.

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

3000

As prepared

Annealed 20min

Annealed 1060min

2000

1000 Normalized Intensity,Normalized cps

(130)ααα (117)γγγ 0 17 18 19 20 21

Scattering Angle, 2(ΘΘΘ)

Figure 4.61: WAXD patterns of PE3.3 crystallized at 1◦C/min and annealed at 130◦C for 20 min and 18 h.

35 As Prepared Annealed 20 min Annealed 120 min Annealed 720 min

30 Heat Flow,Heat mW 25

20 80 100 120 140 160 180 Sample Temperature, °C

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

0 0 ∆n = (nc − na)(t/4 − r/2) (4.8)

0 0 where nc is the index of refraction along the helix axis and na is the index of refraction perpendicular 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 measured 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 69 not performed on these materials, the contribution from VV scattering should be signiﬁcant. 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 169–171 VV polarization conditions has been studied previously. Following the discussion of Li and

Akpalu, the total integrated scattering intensity under HV and VV conditions can be approximated 169 by the relative invariants QHV and QVV , respectively. For space ﬁlling spherulites:

2 0 2 QHV =< δ >= K(δcrxCSP2) (4.9)

where < δ2 > is the mean square ﬂuctuation in the anisotropy (orientation) of the crystalline aggregate, K is a constant dependent on the geometry of the scattering object(s) and wavelength of 0 light used in the experiment, δcr 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

2 QVV = K2 < η > +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

2 Thus, in the general case QVV > QHV due to the addition of the < η > 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.

70 60

60 50

50 40

40 30

30 20 Polarized Haze, % Polarized Haze,

20 Total Hv 10 Bulk Hv

Total Vv Change in Relative % Polarized Haze, 10 Bulk Vv 0 Relative change - total Hv Relative change - total Vv 0 -10 1 10 100 1000 10000

Annealing Time, min

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 2 increase was larger than the HV increase. The relatively small contribution from the < η > 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 crystallinity 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 experiment) 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 relative 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 significant 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.

20 RMS Roughness, nm RMSRoughness,

0 0 10 20 30 40 50 Image size, µµµm

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

30 RMS Roughness, nm RMSRoughness, 20

Kapton film 10 PE4.8

0 0 10 20 30 40 50 Image size, µµµm

Figure 4.65: Roughness of Kapton ﬁlm and of PE4.8 ﬁlm using Kapton substrate. Error bars represent ±30% of the average measured value.

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

60 PE4.8 Kapton film

PE13.3 Pyrex plate 50 PE13.3 cover glass

RMS Roughness, nm RMSRoughness, 20

0 0 10 20 30 40 50 Image Size, µµµm

Figure 4.66: RMS roughness of PE4.8 and PE13.3 vs. image size and substrate type. Error bars represent ±30% of the average measured value.

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 conditions, 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 scattering, 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.

100 Ground Glass

60 Haze Clarity

Gloss-45 40 Haze/Clarity/Gloss-45

20 Dull Kapton Free Smooth Surface Glass

0 1 10 100 1000 RMS Roughness, nm

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 roughness, and demonstrated the effectiveness of the oil immersion technique for optically removing surface roughness contributions over two orders of magnitude in length scale.

1 100

0.8 98

0.6 96 Bulk haze/mil

Bulk clarity Clarity Haze/mil 0.4 94

0.2 92

Free Smooth Dull Ground Surface Glass Kapton Glass 0 90 1 10 100 1000 RMS Roughness, nm

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, independent 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 incorporation 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 morphology 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 characteristics 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

100 PE 1K/min PE 10K/min PE 90K/min ZN 1K/min 80 ZN 10K/min ZN 90K/min MET 1K/min MET 10K/min MET 90K/min

60 Crystallinity, Crystallinity, wt%

20 0 4 8 12 16 20

Comonomer Content, mol%

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 temperature 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

0.8

PE 1K/min PE 10K/min 0.6 ZN 1K/min ZN 10K/min γ γ γ γ

X MET 1K/min MET 10K/min 0.4

0.2

0 0 3 6 9 12 15 Comonomer Content, mol %

◦ 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 morphology with an intermediate γ/α crystal ratio. As shown by Uan-Zo-li, the PE copolymers contained 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 crystallization 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 morphology 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.

PE5.4 ZN4.4 MET5.2 6

4 Bulk Bulk Haze/mil

0 1°C/min 10°C/min Quenched Cooling Rate

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 significantly 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 optical properties generally improved as the scale of the crystalline morphology decreased, as shown 139

100

91 Normalized Bulk % Normalized Clarity,

88 PE5.4 ZN4.4

MET5.2

85 1°C/min 10°C/min Quenched Cooling Rate

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 improvement in optical properties with increasing cooling rate, the PE5.4 sample displayed unusual behavior, 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

100

80 Normalized Bulk Transparency, % Bulk Normalized Transparency, PE5.4 75 ZN4.4

MET5.2 70 1°C/min 10°C/min Quenched Cooling Rate

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, respectively (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 58 relative magnitude of nc and na. 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 materials 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 characteristics 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 crystallization 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, cannot be made without reliable, consistent, and representative metrics. Scientists from Dow Chemical had communicated that the existing haze, clarity, and gloss measurement techniques were sometimes 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 morphology 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.

Figure 4.80: AFM height image of cast ﬁlm 43-4. RMS roughness = 7.8 nm. 145

Figure 4.81: AFM height image of cast ﬁlm 43-6. RMS roughness = 9.9 nm.

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 scattering 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 matching 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.

3 VT total

VT bulk

Dow Chemical total

2 Haze, % Haze,

0 43-2 43-4 43-6

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

100

80 Gloss-45

Dow Chemical

60 43-2 43-4 43-6

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 immersion 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 scattering. 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

100 10

99 8

98 VT total clarity 6 VT bulk clarity

Dow Chemical total clarity

Clarity, % Clarity, Dow Chemical thickness 97 4 VT thickness Film mil thickness,

96 2

95 0 43-2 43-4 43-6

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 differentiate. 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

100 4

80 3

40 Transparency, % Transparency, Film mil thickness,

1 Total transparency 20 Bulk transparency Dow Chemical thickness VT thickness 0 0 43-2 43-4 43-6

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 propylene/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 copolymer films. High temperature annealing was used to vary the fraction of γ-phase crystals in impinged 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 scattering 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 different 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 resemble 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 crystallinity 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 decreased with increasing comonomer content and with faster cooling rates.

Microscopic investigations revealed that slowly cooled copolymers of low ethylene content crystallized in a spherulitic morphology. These spherulites were of slightly positive or mixed birefringence, 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 crosshatching present in all of the PE copolymers, which developed from long crystallizable propylene sequences present in these materials even at high ethylene concentrations.

The optical microscopy and small-angle light scattering techniques were used to estimate the intensity 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 crystallinity, 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 propylene/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 metallocene 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 materials 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 techniques, 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 substrates 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 reproducible fashion, the directional roughness found in commercial cast roll ﬁlms. 160

The evaluation of light scattering from non-randomly rough surfaces could beneﬁt from investigations 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 temperature 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 methods 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 characterization 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 suggested 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. Bibliography

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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 *** 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.

◦ Figure B.2: Morphology and HV SALS pattern of PE3.3 cooled at 1 C/min.

◦ Figure B.3: Morphology and HV SALS pattern of PE5.4 cooled at 1 C/min. 184

◦ Figure B.4: Morphology and HV SALS pattern of PE6.7 cooled at 1 C/min.

◦ Figure B.5: Morphology and HV SALS pattern of PE12.3 cooled at 1 C/min.

◦ Figure B.6: Morphology and HV SALS pattern of PE16.6 cooled at 1 C/min. 185

◦ Figure B.7: Morphology and HV SALS pattern of PE0.0 cooled at 10 C/min.

◦ Figure B.8: Morphology and HV SALS pattern of PE3.3 cooled at 10 C/min.

◦ Figure B.9: Morphology and HV SALS pattern of PE5.4 cooled at 10 C/min. 186

◦ Figure B.10: Morphology and HV SALS pattern of PE6.7 cooled at 10 C/min.

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

◦ Figure B.12: Morphology and HV SALS pattern of PE0.0 cooled at 90 C/min. 187

◦ Figure B.13: Morphology and HV SALS pattern of PE3.3 cooled at 90 C/min.

◦ Figure B.14: Morphology and HV SALS pattern of PE5.4 cooled at 90 C/min.

◦ Figure B.15: Morphology and HV SALS pattern of PE6.7 cooled at 90 C/min. 188

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

◦ Figure B.17: Morphology and HV SALS pattern of ZN8.3 cooled at 1 C/min.

◦ Figure B.18: Morphology and HV SALS pattern of ZN4.4 cooled at 10 C/min. 189

◦ Figure B.19: Morphology and HV SALS pattern of ZN8.3 cooled at 10 C/min.

◦ Figure B.20: Morphology and HV SALS pattern of ZN4.4 cooled at 90 C/min.

◦ Figure B.21: Morphology and HV SALS pattern of ZN8.3 cooled at 90 C/min. 190

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

◦ Figure B.23: Morphology and HV SALS pattern of MET6.5 cooled at 1 C/min.

◦ Figure B.24: Morphology and HV SALS pattern of MET11.1 cooled at 1 C/min. 191

◦ Figure B.25: Morphology and HV SALS pattern of MET13.5 cooled at 1 C/min.

◦ Figure B.26: Morphology and HV SALS pattern of MET5.2 cooled at 10 C/min.

◦ Figure B.27: Morphology and HV SALS pattern of MET6.5 cooled at 10 C/min. 192

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

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

◦ Figure B.30: Morphology and HV SALS pattern of MET5.2 cooled at 90 C/min. 193

◦ Figure B.31: Morphology and HV SALS pattern of MET6.5 cooled at 90 C/min. 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 tangentially 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 oriented 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 0 0 lamellae, respectively, and t + r = 1. The constants nc and na 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

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0 0 0 nr = (t/2)nc + (t/2)na + rna (C.1)

The index of refraction in the tangential direction is:

n0 + n0 n0 + n0 n = (t/2)n0 + (t/2) c a + r c a (C.2) t a 2 2

Therefore, the total spherulite birefringence, ∆n = nr − nt, is:

0 0 ∆n = (nc − na)(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.

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