Effect of Loading and Process Conditions on the Mechanical

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2-2009 Effect of Loading and Process Conditions on the Mechanical Behavior in SEBS Thermoplastic Elastomers (TPEs) Mohit Mamodia University of Massachusetts Amherst, [email protected]

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EFFECT OF LOADING AND PROCESS CONDITIONS ON THE MECHANICAL BEHAVIOR IN SEBS THERMOPLASTIC ELASTOMERS (TPEs)

A Dissertation Presented

MOHIT MAMODIA

Submitted to the Graduate School of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

February 2009

Polymer Science and Engineering

EFFECT OF LOADING AND PROCESS CONDITIONS ON THE MECHANICAL BEHAVIOR IN SEBS THERMOPLASTIC ELASTOMERS (TPEs)

A Dissertation Presented

MOHIT MAMODIA

Approved as to style and content by:

______Alan J. Lesser, Chair

______Samuel P. Gido, Member

______Henning H. Winter, Member

______Shaw L. Hsu, Department Head

DEDICATION

Aditi, Mummy & Papa

ACKNOWLEDGMENTS

I would like to thank Prof. Alan Lesser for being a great adviser. He was instrumental not only as an advisor but as a true mentor and infact a guru. It was because of his guidance that helped me in growing as a research scientist. He taught me the importance of being responsible for my own research work in the lab. I enjoyed immensely the freedom he gave me in trying out various things in the lab. This greatly enhanced my knowledge of application of the basic principles of science for solving material science problems. I am also extremely grateful to him for all the opportunities he provided me in presenting my work at various places. He taught me very patiently the importance of communicating ideas simply and effectively.

My sincere thanks to Prof. Henning H. Winter and Prof. Samuel P. Gido for serving on my committee. They provided me numerous suggestions during my work that greatly improved the quality of this thesis. I consider it a great privilege for me to have such accomplished scientists on my committee. I am extremely grateful to Prof.

Wim De Jeu for his help, insight and guidance with x-ray scattering work. I truly cherish the great discussions I had with him.

I would like to thank past members of the Lesser group Kishore, Peter, Dr.

Xianbo Hu, Kevin, Melissa and Jian for all their help in the lab. Kishore helped me a lot in my first year when I was totally new to research. He also taught me deformation calorimetry which is unique device by itself. Discussions with Peter were really helpful.

He also taught me the art of building devices. His expertise was really helpful in building the high strain-rate tensile testing device. His suggestions and help are greatly appreciated. The present Lesser group Donna, Joonsung, Scott, Andrew, Jared, Sinan,

v Kate, Naveen, Dave and Michael are a cool bunch and we all had so much fun together both inside and outside the lab.

My acknowledgements to MRSEC, CUMIRP and KRATON Polymers for all the funding support through the years. Many thanks to Evgenia, Sekar, Lou Raboin and

John Domian for all the help through the years. The graduate life became simpler with the support of the PS&E office group-Vivien, Greg, Sophie, Ann, Katera and others.

There are numerous friends Malvika, Vikram, Priyanka and Ruchir who have made my stay at UMass very pleasant. I would especially like to thank Malvika who was a very good friend. She really helped me in preparing for my first conference and her suggestions really helped me in improving my presentation skills.

I would also like to thank few people who not only were great friends, but they created a family away from home. I call them my US-family. First of all Naveen, with whom I have shared room for almost entire of my stay in Amherst. Only my wife Aditi could replace him. He is like a brother to me and was always there in my good and bad times. Divya (gudiya) she was closest to me in first year, but then went to University of

Wisconsin Madison. Rachit and Ila were almost like local guardians to me. I would always cherish the moments when we used to spend in their house almost every weekend. Rishi and madhura were also great friends. Rishi was always there to help and

I would miss his sense of humor. I would also like to thank Gaurav and Somya for being such nice friends.

I would also like to thank my parents in law for their love, trust and support.

Their blessings were always there with me. I would like to thank Abhinav, Arti bhabhi and Shonna for their wishes.

vi I would like to thank my sisters Sakshi and Richa for their material and emotional support. They always wanted the best out of me and were always proud of their brother. I know how happy they are always for all of my accomplishments. I also thank my brother in law Ritesh (jiju) and my nephew Kush for all their constant love and support.

For their constant love and support, I would like to thank my dad and mother. I guess the word ‘thank’ appears too small for them. Whatever I am today is all because of them. I always wonder about my dad’s farsightedness. I still remember how my mother used to sit with me and my sisters during our school times and teach all the subjects.

Finally for her endless love I would like to thank my wife Aditi. Although she has been in my life for past one and a half years, but she was my strength all this time.

She has done and sacrificed so much for me. She makes my life complete. Whatever I have achieved so far, and would like to in future, will be for her. I absolutely cannot imagine this without you.

vii ABSTRACT

EFFECT OF LOADING AND PROCESS CONDITIONS ON THE MECHANICAL

BEHAVIOR IN SEBS THERMOPLASTIC ELASTOMERS (TPEs)

FEBRUARY 2009

MOHIT MAMODIA, B.TECH., INDIAN INTSTITUTE OF TECHNOLOGY

BOMBAY

M.S., UNIVERSITY OF MASSACHUSETTS AMHERST

Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST

Directed by: Professor ALAN J. LESSER

Styrenic block copolymer thermoplastic elastomers are one of the most widely used thermoplastic elastomers (TPEs) today. The focus of this research is to fundamentally understand the structure-processs-property relationships in these materials. Deformation behavior of the block copolymers with cylindrical and lamellar morphologies has been investigated in detail using unique techniques like deformation calorimetry, transmission electron microscopy (TEM), combined in-situ small angle x- ray and wide angle x-ray scattering (SAXS/WAXS). The research involves the study of structural changes that occur at different length scales along with the energetics involved upon deformation. The structural changes in the morphology of these systems on deformation have been investigated using combined SAXS/WAXS setup. Small angle x-ray scattering probed the changes at the nano-scale of polystyrene (PS) cylinders, while wide angle x-ray scattering probed the changes at molecular length

viii scales of the amorphous/crystalline domains of the elastomeric mid-block in these systems. TEM analysis of the crosslinked elastomers (by UV curing) further confirms the interpretation of structural details as obtained from SAXS upon deformation. New structural features at both these length scales have been observed and incorporated into the overall deformation mechanisms of the material.

Characteristic structural parameters have been correlated to differences in their mechanical response in the commercially relevant cylindrical block copolymers. Effect of various process conditions and thermal treatments has been investigated. The process conditions affect the structure at both micro-scopic (grain size) and nano-scopic

(domain size) length scales. A correlation has been obtained between a mechanical property (elastic modulus) and an easily measurable structural parameter (d-spacing).

Effect of various phase transitions such as order-to-order transition has been studied. Selective solvents can preferentially swell one phase of the block copolymer relative to other and thus bring a change in morphology. Such kinetically trapped structures when annealed at higher temperature try to achieve their thermodynamic equilibrium state. Such changes in morphology significantly affect their tensile and hysteretic response. In another work it has been shown that by carefully compounding these styrenic block copolymers having different morphologies, it is possible to completely disrupt the local scale order and remove the grain boundaries present in these materials.

Finally, a new test technique has been developed, by modifying an existing

Charpy device to test polymeric films at a high strain rate. A custom designed load-cell is used for force measurements which imposes harmonic oscillations on a monotonic

ix loading signal. The data obtained from this device can be used to analyze visco-elastic response of polymeric films at frequencies much higher than the conventional dynamic mechanical analyzer (DMA).

x TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS ...... v

ABSTRACT...... viii

LIST OF TABLES...... xiv

LIST OF FIGURES ...... xv

CHAPTERS ...... 1

1. INTRODUCTION ...... 1

1.1 Structure Property Relationships of SEBS Thermoplastic Elastomers ...... 1 1.2 Dissertation Overview ...... 3

2. DEFORMATION BEHAVIOR OF BLOCK COPOLYMER THEMOPLASTIC

ELASTOMERS ...... 6

2.1 Introduction...... 6 2.2 Experimental...... 8 2.2.1 Materials and Sample Preparation ...... 8 2.2.2.1. Simultaneous SAXS/WAXS...... 9 2.2.2.2. Mechanical Testing and Thermal Analysis ...... 10 2.2.2.3. Deformation Calorimetry...... 10 2.3. Results and Discussion ...... 11 2.3.1 Deformation behavior of lamellar block copolymers ...... 11 2.3.1.1 Un-stretched state and small deformations (strain ≤ 30%)...... 11 2.3.1.2 Deformation at intermediate strains (strain ≈ 50%)...... 16 2.3.1.3 Lamellar systems: deformation at higher strains (strain % > 50) ...... 20 2.3.2 Deformation behavior of cylindrical block copolymers ...... 24 2.3.2.1 Un-stretched state and deformation at small strains ...... 24 2.3.2.2 Deformation at intermediate strains (strains ~ 50%)...... 27 2.3.2.3 Deformation at high strains (strain > 50%) ...... 29 2.3.3 Wavelength of micro-buckling ...... 34 2.4 Conclusions...... 36

xi 3. THREE DIMENSIONAL INVESTIGATION OF DEFORMATION

BEHAVIOR IN LAMELLAR BLOCK COPOLYMER SYSTEMS...... 37

3.1 Introduction...... 37 3.2. Experimental...... 39 3.2.1. Materials and Sample Preparation ...... 39 3.2.2. Morphological Characterization ...... 39 3.3 Results and Discussion ...... 40 3.4 Conclusions...... 55

4. EFFECT OF MICRO-DOMAIN STRUCTURE AND PROCESS

CONDITIONS ON THE MECHANICAL BEHAVIOR OF CYLINDRICAL

BLOCK COPOLYMER SYSTEMS ...... 56

4.1 Introduction...... 56 4.2. Experimental...... 58 4.2.1. Materials and Sample Preparation ...... 58 4.2.2. Characterization and Testing ...... 60 4.2.2.1. Morphological Characterization ...... 60 4.2.2.2. Mechanical Testing and Thermal Analysis ...... 61 4.2.2.3. Deformation Calorimetry...... 61 4.3 Results and Discussion ...... 62 4.3.1 Deformation Calorimetry...... 62 4.3.2 Melt Processed Films: Effect of Cooling Rate ...... 63 4.3.3 Solution Cast Films: Effect of Annealing...... 69 4.3.4 Effect of Temperature and Cooling Rate on d-spacing ...... 74 4.3.5 Correlating Grain-Size and/or d-spacing to Elastic-Modulus ...... 77 4.3.6 Cyclic Behavior ...... 84 4.3.7 Single Grain Systems...... 85 4.4. Conclusions...... 87

5. MORPHOLOGICAL TRANSITIONS IN BLOCK COPOLYMERS AND

THEIR CORRESPONDING MECHANICAL BEHAVIOR...... 88

5.1 Introduction...... 88 5.2 Experimental...... 90 5.2.1 Materials and Sample Preparation ...... 90 5.2.2 Characterization...... 91 5.3 Results and Discussion ...... 92 5.4. Conclusions...... 105

xii 6. CHARACTERIZATION OF HYBRID BLOCK COPOLYMERS

DEVELOPED THROUGH BLENDING ...... 106

6.1 Introduction...... 106 6.2 Experimental...... 107 6.2.1 Materials and Sample Preparation ...... 107 6.2.2 Characterization and Testing ...... 109 6.3 Results and Discussion ...... 109 6.4 Conclusions...... 115

7. HIGH STRAIN-RATE TENSILE TESTING OF POLYMERIC FILMS...... 117

7.1 Introduction...... 117 7.2 Materials and Devices...... 118 7.3 Device Setup ...... 118 7.4 Working Principle...... 123 7.5 Results and Discussion ...... 128 7.6 Conclusions...... 133

8. FINAL COMMENTS AND FUTURE WORK...... 134

BIBLOGRAPHY…….…...... …..137

xiii LIST OF TABLES

Table Page

Table 2.1 WAXS data before and after deformation ...... 16

Table 2.2 SAXS data at various levels of deformation...... 22

Table 4.1 Change in d-spacing due to different sample preparation methods and thermal histories and corresponding changes in elastic modulus...... 68

Table 5.1 The d-spacing and stiffness (C1) of heptane cast and toluene cast samples before and after annealing at 120°C & 160°C...... 101

Table 6.1 Compositional details ...... 108

Table 7.1 Natural frequency (theoretical and measured) response of various loadcells…………...... 124

Table 7.2 Damping ratio values obtained using instrumented charpy device and a conventional DMA ...... 132

xiv LIST OF FIGURES

Figure Page

2.1 Geometry of the experiment ...... 12

2.2 2-D SAXS patterns for SEBS-30-lam at small strains ...... 13

2.3 1-DSAXS plots for SEBS-30-lam and tensile test result...... 14

2.4 WAXS results for SEBS-30-lam in unstretched state ...... 15

2.5 SAXS result for SEBS-30-lam at 50% strain ...... 17

2.6 1-D SAXS plots for SEBS-30-lam along the cross axes at different strains………………...... 17

2.7 2-D SAXS pattern for SEBS-30-lam with x-ray beam incident through the thickness of the film in the unstretched state...... 20

2.8 Combined 2-D SAXS/WAXS patterns for SEBS-30-lam at different strains………...... 21

2.9 1-D WAXS intensity plot of SEBS-30-lam at 200% strain obtained by sector integration over an opening angle of 20° along equatorial axis ...... 22

2.10 Deformation calorimetry on SEBS-30-lam ...... 24

2.11 2-D SAXS patterns for SEBS-30-cyl at small strains...... 25

2.12 1-DSAXS plots for SEBS-30-cyl and tensile test result...... 25

2.13 2-D WAXS patterns of SEBS-30-cyl for the un-stretched state and 50, 200 & 400% strain…...... 27

2.14 2-D WAXS patterns for SEBS-30-cyl at 50% strain...... 28

2.15 1-D SAXS intensity plots for SEBS-30-cyl obtained by integration over 20° along the cross axes for (from bottom to top) the unstretched state and 50, 100, and 200% strain ……...... 29

2.16 2-D SAXS patterns of SEBS-30-cyl at 100, 200, 300 & 400% strains ...... 30

2.17 1-D SAXS intensity plots of SEBS-30-cyl obtained by integration over 20° along the equatorial axis at various strain levels …… ...... 31

xv 2.18 Deformation calorimetry of SEBS-30-cyl ...... 32

2.19 Angle of cross-pattern (as obtained from 2-D SAXS patterns) at various strain levels…………...... 33

2.20 Internal energy change in SEBS-30-lam and SEBS-30-cyl as obtained from deformation calorimetry...... 34

3.1 (a) Schematic of unstretched SEBS-30-lam with a transversely isotropic structure; (b) corresponding 2-D SAXS pattern ...... 41

3.2 TEM micrograph of SEBS-30-lam across thickness in the unstretched state…………...... 42

3.3 Geometry of the experiment ...... 43

3.4 2-D SAXS patterns for SEBS-30-lam with x-ray beam incident through the thickness at 50% strain ...... 43

3.5 Schematic representation of Fig. 3.4 ...... 44

3.6 2-D SAXS patterns of SEBS-30-lam with x-ray beam incident through the thickness at 100, 200 and 350% strain...... …..44

3.7 (a) 1-D SAXS plots of SEBS-30-lam at various strains with normal incidence of the x-ray beam; (b) corresponding 2-D SAXS pattern at 100% strain 46

3.8 TEM micrographs ((a) & (b)) of SEBS-30-lam UV-cured at 100% strain with sections taken parallel to the film-plane ...... 48

3.9 TEM micrograph of SEBS-30-lam UV-cured at 100% strain with sections taken across the thickness and parallel to SD...... 50

3.10 Schematic description of deformation of a solution cast lamellar BC and corresponding 2-D SAXS patterns in two orthogonal directions ...... 52

3.11 Illustration of the TEM projection of a deformed lamellar structure where increased lamellar spacing is observed due to lamellar rotation ...... 53

3.12 TEM micrograph of UV-cured SEBS-30-lam at 100% strain viewed through the thickness and along the SD...... 54

3.13 Schematic diagram describing possible orientation of buckled lamellar sheets when observed along the SD using TEM...... 55

4.1 Chemical structure of SEBS tri-block copolymer ...... 59

xvi 4.2 Energetics of deformation of SEBS-18-cyl ...... 62

4.3 TEM images of melt processed samples at different cooling rates ...... 64

4.4 1-D SAXS plots of the cylindrical system prepared by: (i) melt processing, prepared at different cooling rates (un-filled symbols), (ii) solution cast method and then annealed at 80ºC, 120ºC and 160ºC for 24hrs (filled symbols)...... 65

4.5 Tensile behavior of melt pressed samples prepared at different cooling rates…………………...... 67

4.6 Change in d-spacing with cooling rate of the samples prepared by melt processing…………...... 69

4.7 TEM image, showing the cylindrical morphology in the SEBS triblock copolymer prepared by solution cast method ...... 70

4.8 Change in d-spacing with annealing temperature of solution cast samples………...... 71

4.9 (a) Stress Vs extension ratio curves (tensile behavior) for solution cast films before and after annealing, (b) Average elastic modulus values at two different annealing temperatures ...... 72

4.10 Stress vs extension ratio curves of solution cast films annealed for 8 days……...... 73

4.11 Linear fit showing a correlation of elastic-modulus (represented by the Mooney-Rivlin constant C1) and d-spacing ...... 74

4.12 (a) Temperature resolved SAXS of the solution cast sample, (b) following changes in d-spacing with temperature...... 76

4.13 TEM micrographs of fast-cool sample annealed at: (a) 120ºC for 1 hour, (b) 120ºC for 24 hours, (c) 180ºC for 1 hour, and (d) 180ºC for 24hours…...... 79

4.14 Change in d-spacing with annealing temperature and time, (a) fast-cool sample at and (b) slow-cool sample...... 81

4.15 Tensile behavior of fast-cool samples on annealing: (a) at 120ºC for 1 and 24 hours, (b) at 120 ºC and 180 ºC for 24 hours...... 83

4.16 Tensile behavior of slow-cool sample, on annealing at 120ºC and 160ºC for 24 hours…………...... 84

xvii 4.17 Cyclic behaviors of melt pressed samples prepared at four different cooling rates, (a) slow-cool, (b) medium-cool, (c) quenched, and (d) fast-cool ………….. 85

4.18 Changes in d-spacing of extruded samples on annealing at higher temperatures…………...... 86

5.1 SAXS patterns of samples before (un-filled symbols) and after annealing (filled symbols)...... 93

5.2 TEM micrographs of the sample solution cast in heptane and toluene...... 93

5.3 Energetics of deformation of the cylindrical block copolymer ...... 95

5.4 Tensile behavior of spherical (heptane cast) and cylindrical (toluene cast) samples…………...... 96

5.5 Cyclic behavior expressed in terms of the extent of Mullins effect……..…98

5.6 Change in d-spacing (as calculated from temperature resolved SAXS experiment) with temperature for heptane cast and toluene cast samples ………... 99

5.7 Tensile behavior of samples, (a) heptane cast before and after annealing at 120°C, (b) heptane cast and toluene cast samples after annealing at 120°C……. . 101

5.8 Tensile behavior of samples, (a) heptane cast before and after annealing at 160°C, (b) heptane cast and toluene cast samples after annealing at 160°C…….. 102

5.9 Variation of stiffness (C1) with changes in d-spacing of the sample under different process conditions and thermal histories ...... 103

6.1 AFM images showing the mixing of spherical and lamellar block copolymers in non-equilibrium state ...... 110

6.2 TEM micrograph showing mixing of spherical (SEBS-S13) and lamellar (SEP-L37) block copolymers in equilibrium state ...... 111

6.3 Rheological measurements showing ODT measurements of SEBS-C18 and SEBS-S12……… ...... 112

6.4 TEM micrographs showing mixing behavior of SEBS-C18 and SEBS-S12 in melt process conditions...... 113

6.5 Tensile response upon mixing of SEBS-S12 and SEBS-C18: (a) solution cast mixing, (b) melt mixing (melt mix and extruded mix ...... 114

xviii 6.6 Cyclic behavior of SEBS-C18, SEBS-S12 and their mixed state in melt processed state (extruded mix and melt mix) ...... 115

7.1 Schematic representation of the modified Charpy device with a load-cell setup…………………...... 119

7.2 Schematic of the movable and fixed clamps...... 120

7.3 Schematic representation of the custom designed load-cell ...... 121

7.4 Calibrations curves for the: (a) cantilever beam load cell, (b) rotatory indicative position sensor (RIPS) ...... 122

7.5 A typical response of an elastomeric material (SEBS-18-cyl) using this device……………… ...... 125

7.6 Spring-mass system with damping ...... 126

7.7 Free-vibration response of under-damped system...... 128

7.8 Tensile response of spherical and cylindrical block copolymers: (a) using instrumented Charpy device, (b) conventional Instron machine ...... 128

7.9 High speed tensile response of SEBS-18-cyl ...... 129

7.10 Oscillatory response of SEBS-18-cyl obtained from Figure 7.9 after subtracting the monotonic loading signal ...... 130

7.11 Sine-Damp function fit to the data in Figure 7.10 ...... 131

7.12 Sine-Damp function fit to the data in Figure 7.9 after sample-failure...... 132

xix

CHAPTER 1

INTRODUCTION

1.1 Structure Property Relationships of SEBS Thermoplastic Elastomers

Styrenic block copolymer thermoplastic elastomers are one of the most widely used thermoplastic elastomers (TPEs) today. As thermoplastic elastomers (TPEs), they are elastomeric at service temperatures, but can be easily processed as thermoplastics at elevated temperatures. This ease of processing and recyclability are major advantages

TPEs possess over conventional chemically cross-linked elastomers [1].

Since their introduction six decades ago, various aspects[2-23] of styrene- butadiene-styrene (SBS) and styrene-isoprene-styrene (SIS) block copolymers TPEs have been extensively studied. These studies identify several important deformation mechanisms. A four-point zigzag pattern in small angle x-ray scattering (SAXS) has been observed in all of these systems at moderate strains. This has been attributed to the microbuckling of polystyrene (PS) cylinders that occurs, as they are stretched perpendicular to their orientation direction. In addition, it has been observed in some studies[11, 14, 16, 19] that these cylindrical rods when deformed parallel to the stretching direction, break into smaller rods. Theoretical[21] and experimental[22, 23] studies relating the observed structural changes in morphology to uniaxial tensile tests show that this buckling instability can be related to a sharp turnover in the stress-strain curve observed for these block copolymers.

Though the structure property relationships of un-hydrogenated SBS, SIS block copolymers have been studied by several authors [9, 12, 14, 20, 24-28], very few

studies have been devoted to commercially important SEBS block copolymers. SEBS

systems are obtained by hydrogenation of butadiene segment of the SBS block

copolymers and have ethylene-butylene (E/B) mid-blocks which resemble branched

polyethylene chains (with ethyl branches)[4]. Increasing or decreasing the number of

branches can make the E/B phase of SEBS system slightly more crystalline or

completely amorphous[4, 29, 30]. It can be expected that this ability to crystallize can

have significant influence on their mechanical properties.

These SEBS systems develop a structural hierarchy which occurs at three length

scales (at the molecular length scales of crystallites, at the nanometer length scale of

cylinders/spheres and at micrometer length scale of grains and accompanying grain

boundaries). There are no detailed studies investigating the structural changes in

morphology that occur upon deformation of SEBS systems at these length scales.

Process conditions can also have significant impact on the structures at different length

scales (such as grain and domain size). However no detailed investigations have been

undertaken on whether grain size or domain size have any influence on the mechanical

properties. This thesis looks at a wide range of structure-process-property relationships of SEBS systems. In-situ simultaneous SAXS and wide-angle x-ray scattering (WAXS) studies combined with transmission electron microscopy (TEM) studies on deformed samples are conducted to understand the deformation behavior of these materials. These studies help in establishing the fundamentals of mechanisms of deformation in these technologically important materials.

1.2 Dissertation Overview

In chapter 2 we report on the deformation behavior of commercially relevant

lamellar and cylindrical tri-block copolymers poly (styrene-b-ethylene-co-butylene-b- styrene) (SEBS) with same composition. The structural changes that occur at various length scales have been studied using a simultaneous small- and wide-angle x-ray scattering (SAXS/WAXS) during uni-axial tensile deformation of the polygrain samples. SAXS provides information about changes that occur upon deforming the glassy cylindrical or lamellar PS domains. WAXS, on the other hand, is sensitive to the crystallographic structure of the rubbery mid-block. Deformation calorimetry has been used to determine the energetics involved. The combined results from the various techniques indicate that the deformation takes place in three stages. First, at small strains, dilation occurs in the rubbery phase. At intermediate strains, the hard lamellar or cylindrical domains undergo micro-buckling, which is associated with a downturn in the stress-strain curve. Finally, we interpret that at higher strains, the bent lamellar/cylindrical domains rotate in the stretching direction resulting in a significant shear on the rubbery mid-block. This in turn leads to strain-induced crystallization in these materials. Although we could not prove it by WAXS, deformation calorimetry

(which is more sensitive than the WAXS) was utilized to show its presence.

Chapter 3 presents a detailed investigation of deformation in solution cast lamellar system as discussed in chapter 2. SAXS and TEM performed on deformed samples in orthogonal directions give a three-dimensional overview of how domains and grains undergo deformation. We also consider a possible model to describe the deformation mechanism.

Chapter 4 describes the effect that process conditions have on the structural

characteristics and mechanical response of a cylindrically phase-separated poly(styrene-

ethylene-co-butylene-styrene) (SEBS) triblock copolymer system. SAXS and TEM

have been used (on undeformed samples) to study the microdomain and grain structure,

respectively. It is observed that the structural changes that occur with different process

conditions and thermal treatment alter the mechanical behavior in both monotonic

tensile and cyclic tests. Results show that the d-spacing decreases with increasing

temperature and increasing cooling rate from the melt state. These subtle changes in d- spacing are correlated with the elastic modulus. Such variations in domain spacing and size depend on the segregation power (χ) of the system. Grain size changes

significantly with cooling rate and upon annealing fine-grain structures but has no

significant effect on the material’s modulus.

Chapter 5 presents the effect of morphological transitions on the mechanical

behavior of SEBS TPEs. Effect of selective solvents has been described. It is shown

that a morphology change occurs from cylindrical to spherical when a preferential

solvent (for ethylene/butylene phase) is used. This kinetically trapped spherical system,

when annealed above the glass transition of polystyrene, is expected to undergo an

irreversible morphological transition. However, this transition is incomplete when

annealed even 50 °C above the glass transition. It has been shown that the mechanical

response of these materials is much more sensitive to the structural changes than SAXS.

In chapter 6 we develop some hybrid systems by blending block copolymers

with different morphologies. By mixing these materials in non-equilibrium state, it is

possible to disrupt the local order in cylindrical and lamellar systems.

In chapter 7 we present a high strain-rate tensile testing device, which we have built by instrumenting an existing charpy device. Here we have developed an economical method to provide tensile data on films at high strain-rates and also at higher strains. A custom designed loadcell, with simple cantilever beam geometry, is used for force measurements. The loadcell imposes harmonic oscillations on a monotonic loading signal. Such a response can be used to analyze dynamic visco-elastic response on films at high strain rates.

CHAPTER 2

DEFORMATION BEHAVIOR OF BLOCK COPOLYMER THEMOPLASTIC

ELASTOMERS

2.1 Introduction

A well-known class of Thermoplastic Elastomers (TPEs) consists of tri-block

copolymers with glassy domains of atactic polystyrene (aPS) within an elastomeric

matrix[1]. Depending on the composition, these materials microphase separate into

nano-structures of spheres, cylinders or lamellae. In addition a structural hierarchy

develops because they nucleate and grow into randomly oriented grains of micron size

when cooled from melt or cast from a solution. The morphology and deformation

behavior of these materials have been widely studied[31-44]. Significant work on deformation behavior has been done on both highly oriented ‘single-crystal’ specimens[31-36, 40, 42-44] as well as on polygrain structures[37, 41, 45, 46]. Highly oriented poly (styrene-b-butadiene-b-styrene) (SBS) TPEs were studied by Keller and coworkers for their deformation behavior at low to moderate strains using SAXS, transmission electron microscopy (TEM) and Birefringence[44]. These studies revealed several important structural features that occur at small to moderate deformations. The deformation behavior at large strains was studied by Godovsky and coworkers[47] using SAXS and deformation calorimetry.

For oriented lamellar and cylindrical microstructures deformation orthogonal to the orientation is accompanied by a transformation into a ‘zig-zag’ structure in real space. Longitudinal deformation, on the other hand, results in the breakdown of the

cylindrical and lamellar domains. Macroscopically isotropic TPE’s which contain random distribution of grains consisting of oriented block domains indicate the formation of a chevron pattern at high strains[37, 41]. However, most of these studies are restricted to two dimensions (2-D) and do not elucidate the full 3-D deformation.

The ‘zig-zag’ and chevron patterns have been modeled by Read et al[48]. These studies show that orthogonal deformation of multi-layered structures causes initially a sinusoidal buckling of cylinder/layers, which at higher strains develops into a chevron texture. In addition, the buckling instability corresponds to the sharp turn over in the stress-strain curves. Thomas and coworkers[33] have observed dilation of the rubbery phase, at small strains, along the stretching direction (SD) in oriented cylindrical systems. However, such an effect was not seen for perpendicular deformation of oriented lamellar systems[42]. Most studies have focused on the structural changes occurring in the hard PS domains and less attention has been given to the soft rubbery matrix.

The majority of research so far has been on SBS or styrene-isoprene-styrene

(SIS) systems, both of which have non-hydrogenated elastomeric mid-blocks. However, commercial interest is mainly in the hydrogenated versions i.e. SEBS and styrene-b- ethylene-propylene-b-styrene (SEPS) because of their improved resistance to degradation. Increasing or decreasing the number of ethyl or propyl branches can make the mid-block completely amorphous or more crystallizable, respectively[30, 49]. In the case of crystallization another length scale (of the crystallites) comes into play in addition to the length scale of cylinder and lamellar domains. The objective of this paper is to investigate and compare the structural changes that occur at the different

length scales, upon deformation of two commercial SEBS tri-block copolymers that

phase separate into lamellar or cylindrical morphology and a polygrain structure. The

difference in morphology will be related to the changes in the uniaxial tensile response

and behavior in deformation calorimetry.

2.2 Experimental

2.2.1 Materials and Sample Preparation

The material used for most part of this study is a SEBS triblock copolymer provided by Kraton Polymers, U. S. LLC, commercially known as KP16, but will be referred as SEBS-30 throughout the chapter. The number ‘30’ refers to the weight fraction of atactic PS at the end blocks (15% PS on each block). The number-average molecular weight (Mn) as determined by GPC is 94 kg/mol with a poly-dispersity index

(Mw/Mn) of 1.08. Thick films (0.5 to 1 mm) for mechanical and morphological

characterization were prepared by solution casting in a petri-dish. The block copolymer

was first dissolved in toluene to obtain a 5-weight % by volume solution. Solvent

evaporation occurred over a period of 8-10 days at room temperature. The film was then

dried at 45ºC for 6 hours to remove the excess solvent. The SEBS-30 system formed a

lamellar morphology, and will be referred to as SEBS-30-lam throughout the paper. The

SEBS-30 system was also cast in cyclohexane, in which case it formed a different

morphology, cylindrical (SEBS-30-cyl). Another material used is also a SEBS triblock

copolymer commercially known as G6926 and is referred as SEBS-20-cyl in this work.

Again the number’20’ refers to the weight fraction of atactic PS at the end blocks and it

forms an equilibrium state cylindrical morphology.

2.2.2 Characterization and Testing

2.2.2.1. Simultaneous SAXS/WAXS

SAXS and WAXS were done using an in-house setup from Molecular

Metrology Inc. It uses a 30 W microsource (Bede) with a 30×30 µm2 spot size matched to a Maxflux® optical system (Osmic) leading to an almost parallel beam of monochromatic CuKα radiation (wavelength λ=0.154 nm). After passing beam-defining and guard pinholes the beam with a diameter of about 0.5 mm enters the sample chamber. The SAXS intensity is collected by a two-dimensional gas-filled wire detector

(mesh size 120 µm) at a distance of 120 cm. A beam-stop of diameter 0.7 mm in front of the detector has in its center a photodiode allowing monitoring the intensity of the direct beam. WAXS is performed using an image plate with a hole in its center positioned in the sample chamber at the desired distance from the sample (usually about

13 cm). The whole system is evacuated. The angular range for SAXS (determined by the beamstop and the size of the detector) covers a wave vector range 0.09

been determined from the local maxima in the linear scale. We have checked that the

background does not influence the peak position.

2.2.2.2. Mechanical Testing and Thermal Analysis

Monotonic tensile tests were performed at room temperature on an Instron 5800

tensile testing machine using the ASTM D1708 test geometry (gauge length = 22 mm)

at a strain-rate of 0.45 mm/mm/min. The strain is expressed in percentage values (i.e.

strain% = (L/Lo) x 100). To determine the degradation temperature of the block

copolymers thermo-gravimetric analysis (TGA) was performed using a TGA2950 (TA

Instruments®) for samples of 7-8 mg at a heating rate of 10ºC/min. Differential scanning calorimetry (DSC) was performed using a DSC Q1000 (TA Instruments ®) at a scan rate

of 5 ºC/min.

2.2.2.3. Deformation Calorimetry

To investigate the enthalpic versus entropic nature of deformation and to

determine any strain-induced crystallization, deformation calorimetry was carried out.

In this method the incremental work (dW), absorbed heat (dQ) and hence the internal

energy changes (dU) are measured during deformation as described elsewhere[30, 50,

51]. The calorimeter has been used previously to study the heat and internal energy

changes in strain-crystallizing natural rubber[52, 53] and thermoplastic elastomers[30].

We used ASTM D1708 test geometry at a strain rate of 1.08 mm/mm/min at a

temperature of about 25 °C. The internal energy was recorded after two stress-strain

cycles.

2.3. Results and Discussion

2.3.1 Deformation behavior of lamellar block copolymers

2.3.1.1 Un-stretched state and small deformations (strain ≤ 30%)

SAXS was performed in the geometry illustrated in Figure 2.1. The un-stretched

SEBS-30-lam system (Figure 2.2a) shows an isotropic diffraction pattern with a series of rings of decreasing intensity at increasing q-values. This pattern suggests a random distribution of the internally oriented grains. Figure 2.2b and c show the shape of the first-order diffraction maximum with a schematic of a grain. These can be compared with Figure 2.2d, e, f for 10% strain. Figure 2.3a shows 1-D SAXS plots obtained by a full circular integration of Figure 2.2a. The plot indicates positions of the diffraction peaks in a ratio of 1:2:3, which illustrates the lamellar morphology. However, from the composition we expect the equilibrium morphology of the SEBS-30 system to be cylindrical. Cylindrical morphology was also seen when prepared from melt state. The lamellar structure observed here is attributed to toluene used for solution-casting, which acts as a selective solvent for styrene. It preferentially swells the styrene domain which changes the morphology from thermodynamic equilibrium to a kinetically-trapped lamellar morphology. Such changes in morphology have been observed before[38]. The equilibrium cylindrical morphology is obtained for solution casting from cyclohexane only.

X-rays Stretching Direction (SD)

5 mm

0.5 mm

Figure 2.1 Geometry of the experiment

Unstretched 10 % (a) (d)

-0.66 -0.33 0 0.33 0.66 -0.66 -0.33 0 0.33 0.66 q (nm-1) q (nm-1) (b) (e) d = 37.6 nm d` = 41.8 nm

d d = 36.6 nm d` d (c) (f)

Figure 2.2 2-D SAXS patterns for SEBS-30-lam at small strains. SAXS, shape of the first-order diffraction maximum and schematic representation of a grain, in un-stretched state (a, b, c) and at 10% strain (d, e, f)

Figure 2.3 1-DSAXS plots for SEBS-30-lam and tensile test result. (a) 1-D SAXS intensity plots for (from bottom to top) the unstretched state and perpendicular and parallel to the SD at 20% strain (curves are obtained by an integration over 20° along a required direction and are shifted over two decades for clarity), (b) Stress versus extension ratio plot showing the small strain regime

At 5-10% strain a noticeable anisotropy is seen in the SAXS. The first-order maximum transforms from circular to elliptical (compare Figure 2.2a and 2.2d). The scattering along the meridian axis shift to smaller scattering angles, while there is hardly a change in the peak positions along the equatorial axis. The variation in the shape of the diffraction pattern is illustrated in Figure 2.2b and 2.2e. The shift is associated with an increase in the period of the lamellar structures (about 11% dilation) aligned perpendicular to the SD. The region below 5% strain falls in the initial linear elastic region of the stress-extension ratio plot (Figure 2.3b). Hence we attribute the deformation in the elastic region initially to stretching of the soft segments (compare 2.

2c and 2.2f). At 10% strain, there is a sharp drop in the stiffness. The extent of dilation along the SD further increases to ~18% at a macroscopic strain of 20%.

Figure 2.3a includes 1-D SAXS plots for the sample stretched at 20% strain in the direction parallel and perpendicular to the SD. The ratio between the position of the first-order and second-order scattering peaks remains close to 1:2 both parallel and perpendicular to the SD. This indicates that the lamellar packing is preserved.

WAXS pattern in the unstretched state (Figure 2.4a) reveals a broad diffuse scattering centered at q = 14.6 nm-1. The large full-width at half maximum (FWHM), see Table 2.1, indicates typically short range order only without any indication of crystallinity. However, differential scanning calorimetry shows a melting point at 29°C and an exotherm of about 16J/g (~ 5% crystallinity) on 2nd heating run from below room temperature. No change was observed in the WAXS pattern at small strains

(strain ≤ 50%).

Unstretched

0.3

0.2

0.1 Intensity (arb. units) (arb. Intensity

0.0 5 101520 q (nm-1) -25 -15 0 15 25 q (nm-1) (a) (b)

Figure 2.4 WAXS results for SEBS-30-lam in unstretched state. (a) WAXS pattern, (b) 1-D WAXS plot (obtained by full circular integration of the 2-D pattern in ‘a’), in the un-stretched state

Table 2.1 WAXS data before and after deformation Sample d-spacing (Å) FWHM (nm-1) Correlation length (Å)

SEBS-30-lam: unstretched 4.26 4.57 13.7 SEBS-30-lam: 200% strain 4.18 4.1 15.3 SEBS-30-cyl: unstretched 4.54 4.6 13.7 SEBS-30-cyl: 200% strain 4.48 4.1 15.3

2.3.1.2 Deformation at intermediate strains (strain ≈ 50%)

At intermediate strains of about 50% the 2-D SAXS pattern (Figure 2.5a) shows a fundamental change. First the elliptical shape changes to a four-point cross. In addition, two strong diffraction spots are seen along the meridian axis. The position of the SAXS measurements on the stress-extension ratio curve is indicated in Figure 2.3b.

By integrating the 2-D figure over 20° around the cross axes, we obtain the 1-D SAXS intensities shown in Figure 2.6 for various strain levels. Note the second-order peaks along the cross axes, which are barely visible in Figure 2.5b, can be clearly distinguished in the 1-D plot. A schematic representation of this scattering pattern is given in Figure 2.5b. We attribute the cross pattern to the formation of a herringbone/chevron structure by the lamellar sheets. Such structures have been interpreted[48] as a consequence of a micro-buckling instability that occurs in the glassy PS sheets. Following Thomas’s work[42] a schematic picture of such a deformation is given in Figure 2.5c. Alternatively the lamellar sheets could undergo fragmentation (at small strains) and subsequent rotation (at intermediate to high strains) leading chevron pattern in real space, and thus to a cross pattern in reciprocal space.

50 %

-0.66 -0.33 00.330.66 q (nm-1)

(a) (b) (c)

Figure 2.5 SAXS result for SEBS-30-lam at 50% strain. (a) 2-D SAXS pattern, (b) schematic representation of ‘a’ and (c) schematic representation of micro-buckling of glassy lamellar sheets

q L 2q L 100% q L 2q L 50% q L 2q L 20% 3q L

Intensity (arb. units) Intensity Unstretched

0.0 0.2 0.4 0.6 0.8 q (nm-1)

Figure 2.6 1-D SAXS plots for SEBS-30-lam along the cross axes at different strains. Plots are obtained by integration over 20° along the cross axes for (from bottom to top) the unstretched state and 20, 50, and 100% strain. For 20% strain integration is done along the axis same as that of 50% strain

The 1-D SAXS plot along the cross axes in Figure 2.6 shows that at 50% strain the ratio of first and second order peak position is still 1:2. Evidently the lamellar packing is preserved even after micro-buckling suggesting that buckling occurs in a cooperative fashion (i.e. the lamellar sheets in a single grain buckle simultaneously). At a certain critical load (Figure 2.3b) the buckling instability is responsible for a sudden drop in the stiffness near 5% strain (apparent yield like behavior). However, there is no way that we can directly monitor this instability with x-ray scattering. Stress relaxation tests were performed both before and after this sudden change in stiffness. Most of the relaxation occurs in first few minutes, i.e. well before the x-ray exposure and very little change is expected during the x-ray measurements. Comparisons are made in the stable regimes that occur before and after the sudden change in stiffness. It is the interpretation of the morphologies, which occur in these regimes, we have used to understand the micro-mechanics of deformation. Note that such real-time studies, feasible with sub-second time-resolved SAXS/WAXS at synchrotron x-ray sources, could shed further light on the issue. There is still no significant change in the WAXS pattern in this intermediate strain regime.

The strong meridonal peaks deserve special attention. In reference 13, meridonal streaks were reported at these positions during the perpendicular deformation of oriented lamellar systems. These were attributed to thin hinged regions where the layers are in a plane perpendicular to the SD with an increased lamellar spacing (compare

Figure 2.5c). This interpretation cannot be expected to apply in full to our results on polygrain lamellar systems in which the meridonal peaks are strong.

We conclude that our results so far on the deformation behavior in lamellar

systems only qualitatively tend to agree with the findings of other authors2-4,13,14 on SIS and SBS systems as well as with the model of micro-buckling. This regards especially the strong lamellar peaks along the meridonal axis. Figure 2.7 shows a 2-D SAXS pattern of SEBS-30-lam with the x-ray beam incident along the plane of the film. A significant anisotropy is observed which we associate with alignment of lamellar sheets as they are stratified in the plane of the as-cast film. Any other possibility would disrupt the isotropy observed when the x-ray beam is along the film normal (Figure 2.2a).

Given the extension of the arc in Figure 2.7, the lamellar sheets can be expected to have a preferred plane of alignment, with a fraction of sheets somewhat tilted out of the plane. Such morphology raises questions with regard to the mechanisms of deformation.

It is difficult to accept that micro-buckling followed by plastic-hinge formation is the prevalent mechanism when the majority of the sheets are still aligned along the loading direction. Other possibilities should be considered like fragmentation and subsequent rotation of the glassy domains. Further experiments are required to solve this problem and are the subject of future work.

Unstretched

x-rays

-0.66 -0.33 0 0.33 0.66 -1 q (nm )

Figure 2.7 2-D SAXS pattern for SEBS-30-lam with x-ray beam incident through the thickness of the film in the unstretched state

2.3.1.3 Lamellar systems: deformation at higher strains (strain % > 50)

At high levels of strain the 2-D SAXS patterns (Figure 2.8a) still show the cross pattern clearly. The opening angle of the cross increases from 141° at 100% strain to

148° at 400% strain. We attribute this increase to a rotation of the bent lamellar sheets in the SD, as illustrated in Figure 2.8b. Note that upon going from the unstretched state to 100% strain, the first-order peak positions (along the cross axes) first remain unchanged at smaller q-values (from 0 to 20% strain) to finish at slightly larger ones

(see Figure 2.6 and Table 2.2). This suggests that after micro-buckling the lamellar distance decreases even while the rubbery chains are stretched – this is theoretically conceivable when lamellar stacks rotate/tilt and rubbery chains are “sheared” to form shallow angles with the glassy lamellar plane. Also note that up to the highest strains the meridonal peaks remain strong. The WAXS patterns at high strains of Figure 2.8d show that the relative intensity along the equatorial axis increases at the expense of the original diffraction ring. We associate this asymmetry with orientation of rubbery chains. As the glassy lamellar PS sheets rotate, they put a significant shear on the

PE/PB matrix; see the schematic in Figure 2.8c. The shear imposed deformation leads to elongation of the PE/PB chains along the SD. If the mid-block is able to crystallize, such a significant deformation could cause strain-induced crystallization. However, the present WAXS patterns provide no evidence for such an effect. 1-D WAXS intensity plot obtained from the 2-D pattern along the equatorial axis at 200% strain (Figure 2.9) also fails to show any crystallization peak. The large FWHM (Table 2.1) again indicates a short range order.

100 % 200 % 300 % 400 %

141° 148°

(a)

-0.66 -0.33 0 0.33 0.66 -0.66 -0.33 0 0.33 0.66 -0.66 -0.33 0 0.33 0.66 -0.66 -0.33 0 0.33 0.66 q (nm-1) q (nm-1) q (nm-1) q (nm-1)

(b) (c)

100 % 200 % 300 % 400 %

(d)

-25 -15 0 15 25 -25 -15 0 15 25 -25 -15 0 15 25 -25 -15 0 15 25 q (nm-1) q (nm-1) q (nm-1) q (nm-1)

Figure 2.8 Combined 2-D SAXS/WAXS patterns for SEBS-30-lam at different strains. (a) 2-D SAXS patterns at 100, 200, 300 & 400% strain (The angle was measured by first creating 2-D SAXS patterns with linear intensity scaling and manually measuring the angle between two sharp spots w.r.t. the center), (b) schematic representation showing rotation of bent PS-sheets, (c) schematic representation showing imposed shear deformation in rubbery phase due to the rotation of PS-domains, (d) corresponding WAXS patterns

Table 2.2 SAXS data at various levels of deformation SEBS-30-Lam

-1 -1 Strain % qL (nm ) d-spacing (Å) 2qL (nm ) 0 0.167 376.0 0.337 20 0.167 376.0 0.333 50 0.181 347.0 0.344 100 0.178 352.8 - SEBS-30-Cyl

-1 -1 Strain % qL (nm ) d-spacing (Å) 2qL (nm ) 0 0.235 267.2 0.384 50 0.198 317.2 0.326 100 0.186 337.6 - 200 0.174 360.9 - 20 (⊥ to SD) 0.243 258.4 - 20 (║ to SD) 0.178 352.8 0.292

1.2

1.0

0.8

0.6

0.4

0.2 Intensity (arb. units) Intensity 0.0 0 5 10 15 20 q (nm-1)

Figure 2.9 1-D WAXS intensity plot of SEBS-30-lam at 200% strain obtained by sector integration over an opening angle of 20° along equatorial axis

As a further check of possible strain-induced crystallization, deformation

calorimetry was employed which is more sensitive than the present WAXS and has an

error margin of 0.1 Joule/gm. It measures the energy changes upon deformation and

hence provides a valuable tool for studying non-linear changes in the internal energy of

elastomers/rubbery solids. It has been used effectively to study strain-induced

crystallization in natural rubber[52, 53] and polyurethanes[54]. Indukuri and Lesser[30]

have performed deformation calorimetry on similar SEBS tri-block copolymers that

shows strain-crystallization when in the mid-block the number of ethylene segments

exceeds that of the butylene segments. Figure 2.10 shows the changes in internal energy

(∆U), along with work exerted on (∆W) and heat released by the system (∆Q). For reference the figure also displays the stress-extension ratio plot. The internal energy measurement indicates that as ∆W increases initially, ∆U also increases. However, at about 130% strain the ∆U starts to drop. Such a decrease in ∆U between intermediate and large strains indicates strain-induced crystallization[30, 52]. The internal energy decreases steadily till about 250% strain, after which it again increases. The latter increase in ∆U above 250% strain may be due to the distortion or breaking apart of crystallites at high stress levels (stress-induced de-crystallization). This behavior was observed[52] for natural rubber at strains close to it’s failure (i.e. strain > 650%).

6 20 ∆W 5 10 4

0 3

2 Joules/gm -10 ∆U Stress (MPa) 1 -20 ∆Q 0 50 100 150 200 250 300 350

Strain%

Figure 2.10 Deformation calorimetry on SEBS-30-lam.

2.3.2 Deformation behavior of cylindrical block copolymers

2.3.2.1 Un-stretched state and deformation at small strains

The 2-D SAXS pattern of an un-stretched SEBS-30-cyl system (Figure 2.11a) shows a circularly symmetric diffraction pattern with a series of rings of decreasing intensity at increasing q-values. The 1-D SAXS plot corresponding to this pattern shown in Figure 2.12a is obtained by full circular integration. The diffraction peak positions have a ratio of 1:√3:√7 indicating a hexagonal packing (cylindrical PS domains in a PE/PB matrix). In addition, the √7 peak is superimposed on a broad diffraction ring at q = 0.69 nm-1. No peak is seen at √4, most probably indicating a close

form-factor zero. The 2-D SAXS data support a model of localized regions of parallel

PS cylinders packed in a planar hexagonal lattice. These regions are in turn distributed randomly in the plane of the film.

(a) Unstretched (c) 20 %

-0.66 -0.33 0 0.33 0.66 -0.66 -0.33 0 0.33 0.66 q (nm-1) q (nm-1) (b) (d) d = 26.5 nm d` = 35.1 nm

d d`` = 25.9 nm

Figure 2.11 2-D SAXS patterns for SEBS-30-cyl at small strains. SAXS and shape of the first-order diffraction maximum in un-stretched state (a & b) and at 20% strain (c & d)

qL √3q L 8 qL ⊥ SD (20%) √3qL 6 50% || SD (20%) qL √3q L 4 20% √7qL 2 Stress (MPa) Intensity (arb. units) Unstretched 0 0.0 0.3 0.6 0.9 0 100 200 300 400 Strain % q (nm−1) (a) (b)

Figure 2.12 1-DSAXS plots for SEBS-30-cyl and tensile test result. (a) 1-D SAXS intensity plots for (from bottom to top) the unstretched state and perpendicular and parallel to the SD at 20% strain, (b) Stress versus extension ratio plot showing the small and intermediate strain regime

At 20% strain, the first-order maximum of the 2-D SAXS pattern (Figure 2.11c) shows a transition from a circle to an ellipse indicating an increase in the periodicity of cylinders aligned perpendicular to the SD. The dilation is about 30%, appreciably larger than for the lamellar system (18%) at the same level of macroscopic strain. In the cylindrical systems, the glassy PS-cylinders are embedded in rubbery matrix which is fully continuous. As a result the system can be easier and further deformed than the lamellar one, in which the rubbery layers are all connected to and separated by glassy

PS layers. Transverse loading of relatively stiff PS-sheets will impose a tri-axial state of stress on the rubbery phase. This indicates that the rubbery chains are rather constrained in the lamellar system compared to the cylindrical situation. The state of 20% strain falls in the initial linear elastic region of the stress-extension ratio plot in Figure 2.12b.

Hence, both for the cylindrical and the lamellar system the deformation in the initial linear region of the stress-strain curve is due to the stretching of rubbery chains.

However, the linear elastic region extends further for the cylindrical system (till 20% strain compared to 5% for lamellar system).

Figure 2.12a includes 1-D SAXS plots for the sample at 20% strain in the direction parallel and perpendicular to the SD. The ratio between the positions of the first two diffraction peaks remains close to √3 both parallel and perpendicular to the SD

(see Table 2.2). Hexagonal packing of the cylindrical domains is preserved.

Figure 2.13 displays WAXS patterns for the SEBS-30-cyl system at various levels of strains. WAXS pattern of the un-stretched samples shows an amorphous halo,

corresponding to a dimension of 0.46 nm. As in the previous case no indication of crystallinity at room temperature is found.

Unstretched 50 % 200 % 400 %

-25 -15 0 15 25 -25 -15 0 15 25 -25 -15 0 15 25 -25 -15 0 15 25 q (nm-1) q (nm-1) q (nm-1) q (nm-1)

Figure 2.13 2-D WAXS patterns of SEBS-30-cyl for the un-stretched state and 50, 200 & 400% strain

2.3.2.2 Deformation at intermediate strains (strains ~ 50%)

At 50% strain (Figure 2.14a) the 2-D SAXS pattern transforms into a four-point cross, however now without meridonal peaks (see schematic in Figure 2.14b). The cross pattern indicates a micro-buckling instability in cylindrical domains. The position of the

SAXS measurements on the stress-extension ratio curve is indicated in Figure 2.12b.

Micro-buckling causes a drop in stiffness which we regard as ‘apparent’ yield like behavior, just as for the lamellar system. However, for the cylindrical system this drop is more gradual which is attributed to the continuous rubbery matrix where the rubbery chains are less constrained.

50 %

-0.66 -0.33 0 0.33 0.66 q (nm-1) (a) (b)

Figure 2.14 2-D WAXS patterns for SEBS-30-cyl at 50% strain. (a) 2-D SAXS pattern, (b) schematic representation of the diffraction pattern in ‘a’

The 1-D SAXS plots along the cross axes (Figure 2.15) reveals a ratio of first and second peak position ~1.64 (see Table 2.2). This is still close to √3 suggesting that the hexagonal packing is hardly disturbed. The broad diffraction ring at q=0.69 nm-1 in un-stretched state, has now transformed into a pair of arcs centered along the equator.

The arc length decreases with increasing strain. The origin of these diffraction arcs will be discussed below.

200% qL

√3qL 100% √4qL qL √3q L 50% √7qL

Intensity (arb. units) Intensity Unstretched

0.00.30.60.9 q (nm−1)

Figure 2.15 1-D SAXS intensity plots for SEBS-30-cyl obtained by integration over 20° along the cross axes for (from bottom to top) the unstretched state and 50, 100, and 200% strain

2.3.2.3 Deformation at high strains (strain > 50%)

At high strains the opening angle of the cross pattern (Figure 2.16) increases from 126° at 100% to 146° at 400% strain. We attribute this increase with the rotation of bent cylinders towards the SD. The 1-D SAXS plots at strains ≥50% (Figure 2.15) indicate a shift of the position of first-order maximum along the cross axes to smaller q- values with increasing strain (see Table 2.2). The periodicity of the (110) planes of the hexagonal lattice increases to 31.7 nm from the original value of 26.7 nm at 50% strain and continues to increase for higher strains even after micro-buckling. This behavior

differs from the situation in the lamellar system where the rubbery chains are highly

constrained and restrict dilation.

100 % 200 % 300 % 400 %

-0.66 -0.33 0 0.33 0.66 -0.66 -0.33 0 0.33 0.66 -0.66 -0.33 0 0.33 0.66 -0.66 -0.33 0 0.33 0.66 q (nm-1) q (nm-1) q (nm-1) q (nm-1)

Figure 2.16 2-D SAXS patterns of SEBS-30-cyl at 100, 200, 300 & 400% strains

At strains > 100%, the broad diffraction signal at q=0.69 nm-1 has changed into

a pair of vertical streaks. This diffraction signals are barely visible at small strain but are seen more clearly at 300 and 400% strain. The 1-D SAXS plot along the equatorial

axis in Figure 2.17 indicates that its position does not change with strain. This

diffraction can be attributed to the secondary maximum of the form-factor

scattering[55], i.e. the scattering from an individual cylindrical domain. The diameter of

PS cylinders (2R) can be calculated from the position of form-factor maxima using the

relationship:

4π ⎛ θ ⎞ sin ⎜ i ⎟ R = 4.98, 8.364, 11.46…. for cylinder; i = 1, 2, 3….. (1) λ ⎝ 2 ⎠

where, θi is the ith-order particle scattering peak. The diameter of the cylindrical

domains turns out to be 14 nm for SEBS-30-cyl. After micro-buckling, the bent

cylinders are oriented at some angle to the SD, which will vary from grain to grain.

Since the cylinders, oriented perpendicular to SD, have changed their direction, the

intensity of this signal diminishes along the meridonal axis. At high strains, most of the

cylindrical domains are at a small angle (which is a function of the angle of the kinked region) to the SD resulting in the formation of vertical streaks. The length of the streak can be expected to decrease with increasing orientation of the cylinder axis along the

SD.

400% 300%

200%

100%

50%

Intensity (arb. units) (arb. Intensity 20%

Unstretched

0.00.30.60.91.2 q (nm-1)

Figure 2.17 1-D SAXS intensity plots of SEBS-30-cyl obtained by integration over 20° along the equatorial axis at various strain levels

The rotation of glassy cylindrical domains imposes significant shear on the rubbery matrix orienting PE/PB chains along the SD. The WAXS patterns at high strains of Figure 2.13 show that the intensity along the equatorial axis increases at the expense of original diffraction ring, just like the lamellar system. Again, also for SEBS-

30-cyl the WAXS does not provide any evidence of strain-induced crystallization.

Deformation calorimetry (Figure 2.18) on this system reveals that the ∆U initially

increases till about 150% strain and then starts to decrease. This decrease indicates also

for SEBS-30-cyl strain-induced crystallization. However the ∆U does not show a

significant increase at strains > 300%, as observed for the lamellar system. This

indicates that decrystallization at high strain is absent in cylindrical system. These

results further substantiate that the rubbery chains are more constrained in lamellar

systems than in cylindrical systems.

20 4 ∆W 10 3

0 2 ∆U

Stress (MPa) -10 1 Stress (MPa)

∆Q -20 0 50 100 150 200 250 300 350 400

Strain % Figure 2.18 Deformation calorimetry of SEBS-30-cyl

We finish this discussion by a short summary of the similarities and differences of the cylindrical and lamellar system. In both cases the elliptical pattern in the SAXS pattern indicates dilation of the rubbery phase at small strains, while the four-point cross pattern indicates micro-buckling of the glassy PS-domain after a critical strain.

The lamellar system shows additional diffraction spots along the meridonal axis that

cannot be fully explained by plastic hinge formation. The cylindrical system, on the

other hand, shows equatorially placed vertical streaks indicating cylinder rotation at

higher strains. A comparison of the angle of cross-patterns (as obtained from 2-D SAXS

patterns) at various strains is shown in Figure 2.19. The angle increases sharply for

cylindrical as compared to the lamellar system. Increase in the angle is associated with

the rotation of bent/fragmented glassy PS domains which puts a significant shear on the

rubbery phase. Hence, a slow increase in lamellar system can be attributed to the high

level of constraint presented by rubbery phase which opposes the rotation. After about

200% strain, the angle reaches a plateau for both cylindrical and lamellar system.

160

150 Lamellar

140

130

Angle (degrees) Cylindrical 120

110 0 100 200 300 400 Strain %

Figure 2.19 Angle of cross-pattern (as obtained from 2-D SAXS patterns) at various strain levels

Figure 2.20 compares the ∆U changes in the SEBS-30-cyl and SEBS-30-lam systems. In both cases ∆U increases initially and starts to decrease after reaching a

maximum at ~ 150% strain. The decrease in ∆U corresponds to strain-induced crystallization in both morphologies. At higher strains (300% < strain < 400%) the ∆U

again shows a significant increase for the lamellar system. The ∆U reaches a minimum

for cylindrical system as well, but hardly increases. The sharp increase in the ∆U for

lamellar system tentatively attributed to stress-induced de-crystallization. The rubbery

chains in lamellar systems are more constrained and the crystals formed at high strain

can sustain distortions. The WAXS fails to show any strain-induced crystallization. It

might be because of weak signal on an amorphous halo from the amorphous phase.

2 0 Lamellar -2 -4 -6 -8 Cylindrical -10

Energy (Joules/gm) -12 0 100 200 300 400 Strain %

Figure 2.20 Internal energy change in SEBS-30-lam and SEBS-30-cyl as obtained from deformation calorimetry

2.3.3 Wavelength of micro-buckling

The micro-buckling phenomenon has been studied extensively in systems like fiber-reinforced composites etc.[56-58] where there is a high modulus material embedded in a soft material. It was also observed that micro-buckling occurs as a

sinusoidal deformation in such fibers. The critical wavelength of such sinusoidal pattern has been predicted and simplified by the analyses of Darby, Kanellopoulos[59] and

Sadowsky et al. Baer and coworkers studied micro-buckling in model fiber reinforced composite systems with single fiber/matrix and multiple fiber/matrix samples[56, 58].

They studied interactive effects of multiple fibers embedded in a matrix to simulate a fiber reinforced composite and predicted co-operative micro-buckling modes in these systems under certain conditions. Since SEBS systems with cylindrical morphology behave similarly to a fiber-reinforced composite, some of the analyses described above describe the features of micro-buckling observed in SAXS patterns. Since the PS cylinders are chemically linked to each other through the rubbery matrix, a co-operative micro-buckling mode can be expected as opposed to an extensional mode of buckling.

Using the simplified analysis of Darby and Kanellopoulos[59], the buckling wavelength

λ, for cylindrical systems, is related to moduli of the two phases and to the diameter of the buckling phase with this (eq.2) simple relationship:

2 1/ 8 ⎡3Es ⎤ λ = πd ⎢ 2 ⎥ (2) ⎣8Em ⎦ where d is the diameter of PS cylinders, Es the modulus of PS cylinders and Em the modulus of the rubbery matrix. It can be seen from this relationship that the buckling wavelength strongly depends on the diameter of the PS cylinders and weakly on the ratio of moduli of the two phases. Composite theory is used on the oriented SEBS systems, prepared by extrusion process, to estimate Es ( =2.25 GPa) and Em ( =5.7

MPa). The diameter of PS cylinders is calculated from the position of form-factor maxima using the relationship (eq.3):

4π ⎛θ ⎞ sin⎜ i ⎟R = 4.98,8.364,11.46..... for cylinder; i = 1, 2, 3….. (3) λx−ray ⎝ 2 ⎠ where, λx-ray is the wavelength of x-rays and θi is the ith-order particle scattering peak.

The diameter was found be approximately 15nm for the SEBS-20-cyl system. The predicted buckling wavelength has been calculated (using eq. 2) to be approximately

200nm. This value also compares well with the buckling wavelength observed in TEM images of stretched SBS (un-hydrogenated) block copolymers by Thomas et al[32] using electron beam irradiation to preserve morphology in the stretched state.

2.4 Conclusions

We have compared the deformation behavior of a cylindrical and lamellar triblock copolymer at different length scales. The deformation behavior appears to occur in three stages. Dilation of rubbery phase occurs at small strains, followed by micro- buckling at intermediate strains and rotation of the bent cylindrical or lamellar domains in the SD at high strains. Details of the SAXS patterns reveal that the micro-buckling occurs in a cooperative fashion. The rotation at high strains puts significant shear on the rubbery mid-block and is responsible for strain-induced crystallization, as indicated by the internal energy measurement from deformation calorimetry. However, the

WAXS fails to show the crystallization. It might be because of a weak signal on an amorphous halo from the glassy PS and amorphous rubbery phase. In the lamellar block copolymers the rubbery chains are more constrained than in the cylindrical one, in which they form a continuum. This affects their deformation at both length scales.

CHAPTER 3

THREE DIMENSIONAL INVESTIGATION OF DEFORMATION BEHAVIOR

IN LAMELLAR BLOCK COPOLYMER SYSTEMS

3.1 Introduction

The response of a layered structure to external stresses has been a subject of consideration for more than two decades [31, 37, 42, 43, 48]. A number of studies[42,

43, 48] on the deformation behavior of near single-crystal lamellar block copolymer have shown that force applied parallel to the lamellar normal causes folding of the layers into a ‘chevron’ morphology. A common mechanism of layer folding, identified in many layered structures, is buckling of the layers due to an undulation instability, which occurs beyond a critical strain[48, 60-63]. Thomas and coworkers[42, 43] have indicated the possibility of an alternative mechanism, namely, nucleation and propagation of kink boundaries due to defects in the lamellar structure. The buckling behavior has been explained by the formation of a four-point cross pattern during in situ deformation studies using small angle x-ray scattering (SAXS). The deformation parallel to the lamellae results in the breakup of glassy PS layers and this may also lead to a macroscopic yielding [42].

Deformation studies on isotropic polygranular lamellar systems have shown that the prevalent mechanism is expected to be formation of new internal boundaries, parallel to the stretching direction (SD), by undulation or kinking [37, 42, 64]. The transformation of an initial isotropic ring of scattering in the undeformed state to a four- point cross pattern in SAXS suggests micro-buckling at intermediate strains. At large

deformations the lobes of the four-point pattern continues to rotate at fixed azimuthal angle, leading Seguela and Prud’homme[37] to conclude that intragrain shearing of lamellae is the most likely deformation mechanism. In most studies, solvent casting is used to prepare isotropic polygranular materials. However, due to the anisotropy of cylindrical and lamellar domains, it is extremely difficult to produce completely isotropic materials in films. This anisotropy can lead to preferential alignment of cylindrical and lamellar domains in solution cast samples [41]. However the effect of this alignment has not been considered in deformation studies.

In most of the deformation studies SAXS technique has been used where the changes in reciprocal space (i.e. 2-D scattering patterns) are used to describe the structural changes that occur in the real space. Attempts have also been made to directly image the deformed morphology of the thermoplastic elastomers via TEM [31, 32, 42,

65] and other techniques such as AFM [65]. Thomas and coworkers used a combination of SAXS and TEM to describe a 3-D deformation behavior of highly oriented cylindrical block copolymers. Present literature lack similar deformation studies on isotropic lamellar block copolymer systems. A variety of sample preparation techniques have been used for freezing the structure in the stretched state with varying degrees of success[32, 35, 66]. By crosslinking these TPEs in the stretched state it is possible to study the structural changes in various directions.

This chapter describes deformation behavior of solution cast lamellar block copolymers in detail. SAXS has been performed in orthogonal directions and corresponding TEM micrographs have been taken on deformed regions for direct

comparison to provide a three-dimensional description of the deformation behavior. A deformation mechanism based on these studies is then proposed.

3.2. Experimental

3.2.1. Materials and Sample Preparation

The material used in this work is SEBS-30-lam as described in chapter 2.

Samples for morphological characterization were prepared by solution cast method using toluene as a solvent. The cast films were further dried at 45° C for 6 hours to remove excess solvent.

In order to perform TEM analysis in the deformed state, the films were stretched at 100% strain and cross-linked by exposing them to UV-Vis spectrum radiation using a

Suntest CPS + weatherometer. The radiation source is a xenon lamp with a broad- spectrum filter that closely simulates the distribution of wavelengths and intensity found in natural sunlight. The UV-Vis exposure provides crosslinks due to radical formations. This locks the morphology in a particular deformed state for observation in the TEM.

3.2.2. Morphological Characterization

Sections with a 40-50nm thickness were obtained by cryo-microtoming the bulk films using a Leiica EM-FCS® microtome at -90ºC. These sections were then collected and stained with ruthenium tetroxide (RuO4) for approximately 20 min. TEM was performed using a JEOL 100 CX TEM operating at 100 kV.

SAXS measurements were performed on a Molecular Metrology ® SAXS instrument with a sealed-tube source. CuKα radiation with a wavelength of 0.154nm was used. A 3-pinhole columation system produced a spot size at sample of 700μm.

The raw data was calibrated for the peak position with the standard silver-behenate, which has peak position at scattering vector, q = 1.076 nm-1. The sample to detector distance was found to be ~ 1.2m using the above calibration. Each profile was recorded at room temperature over a period of 1h, unless a different temperature (or time) is mentioned. The intensity of the scattered beam is taken directly without any background subtraction. The profiles are represented as a function of magnitude of scattering vector, q, which is related to the scattering angle, θ. The Braggs d-spacing in lamellar block copolymer systems corresponds to the lamellar long period.

3.3 Results and Discussion

As described in chapter 2 a significant anisotropy is observed in the 2-D SAXS pattern of SEBS-30 when the x-ray beam is incident along the film-plane (Figure 2.7, chapter 2). We associate this anisotropy with alignment of lamellar sheets as they are stratified in the plane of the as-cast film. This anisotropy could arise due to low surface energy of one phase w.r.t. the substrate during solution casting. Surface energy near the substrate can be minimized by one phase of the lamellar block copolymer, which in turn can lead to the preferential alignment of the lamellar sheets. Any other possibility would disrupt the isotropy observed when the x-ray beam is along the film normal

(Figure 2.2a, chapter 2). Given the extension of the arc (Figure 2.7, chapter 2) the lamellar sheets can be expected to have a preferred plane of alignment, with a fraction

of sheets somewhat tilted out of the plane. A schematic of such a transversely isotropic material and the corresponding 2-D SAXS pattern is shown in Figure 3.1. Figure 3.2 shows the TEM micrograph of this sample across the thickness in the unstretched state.

Most of the lamellar sheets have a preferred plane of orientation (as shown by the arrow in the micrograph) and thus explains the previously observed anisotropic scattering pattern.

(a) (b)

Figure 3.1 (a) Schematic of unstretched SEBS-30-lam with a transversely isotropic structure; (b) corresponding 2-D SAXS pattern

Preferred orientation

1 μm

Figure 3.2 TEM micrograph of SEBS-30-lam across thickness in the unstretched state

Deformation studies were performed with x-ray beam incident parallel to the film-plane (i.e. through the thickness) and perpendicular to the stretching direction

(SD). Figure 3.3 describes the test geometry for SAXS measurements. A large width in the figure is used to describe the x-ray beam direction w.r.t the block copolymer film.

For actual measurements much smaller sample width was used. At 50% strain a considerable change occurs in the 2-D SAXS pattern where intensity drops significantly along the equatorial axis, as shown in Figure 3.4. A schematic of this 2-D SAXS pattern, shown in Figure 3.5, corresponds to 4-point cross pattern similar to that observed for cylindrical block copolymers in chapter 2 and therefore indicates micro- buckling instability.

Stretching Direction (SD)

X-rays 5 mm

0.5 mm

Figure 3.3 Geometry of the experiment. (Film width was reduced to less than 1 mm during SAXS measurements)

Figure 3.4 2-D SAXS patterns for SEBS-30-lam with x-ray beam incident through the thickness at 50% strain

Figure 3.5 Schematic representation of Fig. 3.4

At higher strains the 2-D SAXS patterns in Figure 3.6 show that the angle of the cross pattern increases with strain. The increase in the angle indicates rotation of the bent lamellar domains.

100% 200% 350%

Figure 3.6 2-D SAXS patterns of SEBS-30-lam with x-ray beam incident through the thickness at 100, 200 and 350% strain

Note that the scattering pattern for this material at the same levels of strain, when x-ray beam is incident normal to film-plane, has already been discussed in chapter

2. This material shows a strong meridian signal in addition to the four-point cross pattern. The meridian signal suggests structures oriented horizontal to the x-ray beam direction. Since they appear at smaller scattering angles compared to the four points of the cross pattern, they indicate structures with larger d-spacings. This presents an

interesting situation where this material shows two distinct 2-D SAXS patterns in orthogonal directions at the same level of extension.

In an earlier work by Thomas and coworkers[42] meridonal streaks were reported at these positions during the perpendicular deformation of oriented lamellar systems. These were attributed to thin hinged regions where the layers are in a plane perpendicular to the SD with an increased lamellar spacing. This interpretation cannot be expected to apply in full to our results on polygrain lamellar systems in which the meridonal peaks are strong. The 1-D SAXS plots measured along the meridian axis obtained from the 2-D SAXS patterns (in chapter 2) when x-ray beam is incident normal to the film plane are shown in Figure 3.7a at various levels of strain. Note, the position of the broad peak in Figure 3.7a remains more or less unchanged with strain.

This peak typically indicates structures between 50 and 80 nm which is significantly larger than the lamellar spacing (37 nm) in the unstretched state. Example of such 2-D

SAXS pattern is shown in Figure 3.7b.

80nm 50nm

500%

400%

300%

200%

150% Log Intensity (a.r.b.) Intensity Log

100%

50% 0.1 1 q (nm-1)

(a)

(b)

Figure 3.7 (a) 1-D SAXS plots of SEBS-30-lam at various strains with normal incidence of the x-ray beam; (b) corresponding 2-D SAXS pattern, with arrow showing the direction of measurements at 100% strain

In order to understand the deformation behavior of SEBS-30-lam in more detail,

TEM was performed on the samples that were stretched at 100% strain and crosslinked under UV-exposure. After exposure, the samples retained a residual strain of about 80-

90%. TEM micrographs of this stretched sample with sections taken parallel to the film plane are shown in Figure 3.8. The micrograph in Figure 3.8a shows lamellae (marked with dashed circle) arranged in chevron (zig-zag) patterns which are associated with the four-point cross patterns as observed in Figure 3.7b. This confirms the buckling response of lamellar sheets. In addition, it also shows regions (marked with solid circles) where lamellae appear to show increased spacing. Note these regions also have reduced contrast between the lamellae. Figure 3.8b shows another micrograph under similar conditions, where the lamellae appear to undergo fragmentation (marked with solid circle). These micrographs suggest that the lamellar sheets undergo both micro- buckling as well as fragmentation. Meanwhile, the micrographs by themselves cannot explain the regions with increased lamellar spacing and will be discussed in the following sections.

500nm

(a)

500nm

(b) Figure 3.8 TEM micrographs ((a) & (b)) of SEBS-30-lam UV-cured at 100% strain with sections taken parallel to the film-plane

TEM studies were also performed across the thickness, both parallel and perpendicular to the SD. The TEM micrograph across the thickness and parallel to the

SD is shown in Figure 3.9. The material goes through a significant amount of deformation and the entire grain structure is disrupted. The material now forms several new grain boundaries oriented parallel to the SD. Regions showing chevron patterns are clearly seen and hence indicate micro-buckling. In addition considerable amount of fragmentation is also observed. Fragmentation length should become uniform due to shear lag load transfer to the sheets. However these fragmented lamellae length vary from 80 to 150 nm. These fragmented lamellar sheets are also inclined at an angle to the

SD (Note, the SD can be imagined parallel to the buckling axis). This suggests that upon deformation the glassy lamellar sheets either micro-buckle or undergo fragmentation and subsequent rotation to form a chevron pattern responsible for 4-point cross pattern as observed in the corresponding 2-D SAXS pattern (Figure 3.4b).

500nm

Figure 3.9 TEM micrograph of SEBS-30-lam UV-cured at 100% strain with sections taken across the thickness and parallel to SD

It may be observed that the TEM micrographs in Figure 3.9 do not show any region with increased lamellar spacing, as was observed in Figure 3.8a & 3.8b. Further, the corresponding 2-D SAXS patterns (Figure 3.4b and Figure 3.6) also lack meridonal scattering signal as seen in Figure 3.7b. From the TEM micrographs and corresponding

SAXS patterns in two orthogonal directions, it appears that the regions with increased lamellar spacing are associated with the meridonal scattering signal. These features are observed only when the material is analyzed normal to the film-plane. A direct measurement in Figure 3.8a reveals a lamellar spacing ranging from 50 to 80 nm for regions with increased spacing. Note this length scale matches with that obtained from the 1-D SAXS plot in Figure 3.7a.

Based on the results discussed so far, a possible mechanism of deformation can now be considered. A schematic diagram of the deformed state is presented in Figure

3.10 along with the schematic of the corresponding SAXS patterns with x-ray beam incident normal or through the film-plane. According to the model most of the grains, having a preferred lamellar orientation within the plane in the unstretched state (Figure

3.1), undergo fragmentation at small strain and subsequent rotation at higher strains to align with the loading direction. On the other hand, the grains initially at some off axis undergo rotation at small strains and then buckle at higher strains. Both rotation and buckling occurs in a manner such that the buckling or the rotation axis (see Figure 3.10) lies within the film-plane in most cases, while in few cases they lay out of the film- plane. This is partially due to the specimen geometry causing plane strain deformation.

Hence more chevron patterns are observed (Figure 3.9) when viewed through the thickness direction and perpendicular to the SD. This structure is responsible for 4-point cross pattern without meridonal signal in SAXS.

Figure 3.10 Schematic description of deformation of a solution cast lamellar BC and corresponding 2-D SAXS patterns in two orthogonal directions

When viewed normal to the film-plane very few chevrons are visible (Figure

3.8). In contrast this direction exposes the lamellar sheets which are tilted at large angles because of micro-buckling or lamellar rotation. These tilted sheets thus appear to have an increased lamellar spacing as observed in Figure 3.8. These structures may also responsible for the meridonal signal observed in 2-D SAXS pattern in Figure 3.7b. Gido and coworkers[67] have shown how the inclination of a set of flat lamella (no grain boundary) with respect to the projection direction changes both the observed lamellar spacing and the contrast using TEM. The projected image that is observed is a function of the lamellar long period, L, the section thickness, h, and the angle of inclination of lamella in the sample with respect to the projection direction. Contrast is maximized

and lamellar spacing is minimized in a projection directly along the lamellar planes. As the lamellar planes become increasingly inclined with respect to the projection direction the contrast undergoes damped oscillations while the observed lamellar spacing increases. The projected lamellar spacing is given by, L’ = L/sin θ, where ‘θ’ is the angle of micro-buckling or lamellar rotation, see Figure 3.11.

e- L’ =L/sin θ

L’ θ L

Figure 3.11 Illustration of the TEM projection of a deformed lamellar structure where increased lamellar spacing is observed due to lamellar rotation

The relationship described by Gido and coworkers[67] for projected lamellar spacing (Figure 3.11) can be used to verify our proposed mechanism of deformation.

Here, the lamellar long period obtained by analyzing the 2-D SAXS pattern in Figure

3.6 (i.e. along the cross axis) was found to be 30 nm at 100% strain. The inclination angle (or angle of buckling) can be obtained from the TEM micrographs obtained through the thickness and perpendicular to SD at 100% strain. The buckling angle is found to vary significantly (from 44° to 75°) in various micrographs and give an average value of 55°. Using the relationship described in Figure 3.11, the average

projected lamellar spacing was found to be 66 nm (and a range from 50-80 nm). Note this range matches with that obtained from Figure 3.7 and 3.8.

A TEM analysis was also performed in the third direction, i.e. through the thickness and perpendicular to the SD, see Figure 3.12. These micrographs are noticeably different from the ones in Figure 3.8 and 3.9. Although chevron patterns are clearly visible but they lack any preferred orientation. The formation of chevron patterns in this projection can be explained by a schematic in Figure 3.13 where the buckling axis can be at an angle (other than 90°) to the SD. Also note that the lamellar domains do not show any fragmentation in these micrographs. This can be expected as fragmentation can be observed only in the direction perpendicular to the SD.

500nm

Figure 3.12 TEM micrograph of UV-cured SEBS-30-lam at 100% strain viewed through the thickness and along the SD

Figure 3.13 Schematic diagram describing possible orientation of buckled lamellar sheets when observed along the SD using TEM

3.4 Conclusions

Solution cast lamellar block copolymers form a transversely isotropic structure where the lamellar sheets are preferentially aligned within the film plane. A combined study of SAXS and TEM in three directions is used to propose a mechanism of deformation. Upon deformation the individual grains either undergo micro-buckling or fragmentation and subsequent rotation to form chevron patterns responsible for a four point cross pattern in SAXS.

CHAPTER 4

EFFECT OF MICRO-DOMAIN STRUCTURE AND PROCESS CONDITIONS

ON THE MECHANICAL BEHAVIOR OF CYLINDRICAL BLOCK

COPOLYMER SYSTEMS

4.1 Introduction

A common class of thermoplastic elastomers (TPE) includes block copolymers that are covalently joined homo-polymer chains. These materials undergo phase separation upon cooling to form ordered lattices such as spheres, cylinders and lamellae at nanometer scales. At a microscopic scale, the cylindrical and lamellar systems form individual grains with accompanying grain boundaries. Cylindrical and lamellar block copolymers develop a structural hierarchy because they nucleate and grow ordered domains randomly as the material is cooled. Due to their unique morphological and mechanical behavior, studies of TPEs are quite important for fundamental and practical knowledge. Most studies [55, 68-70] on thermoplastic elastomers have focused on characterizing their morphology and phase behavior. Thomas and coworkers[71] investigated the tensile behavior in oriented single-grain lamellar and cylindrical structures. However, relatively few studies[41, 71-74] have focused on what effect, if any, the structural characteristics such as grain size and grain boundaries have on the mechanical response of a poly-grain structure.

The Grain structure forms through a complex interplay between thermodynamic and kinetic factors. Hashimoto and coworkers have shown that annealing highly asymmetric block copolymers increases their grain size, resulting in a commensurate

decrease in the grain-boundary area as well as perfecting the order within the grain[75].

The grain size was also found to depend on the quench depth in quiescently cooled systems[76]. Gido and coworkers used transmission electron microscopy (TEM) to characterize and model the local morphology and grain boundaries in lamellar based systems[77-79]. Attempts have also been made to measure the grain size of block copolymers by various techniques including polarized light scattering, birefringence and electron microscopy[80-85]. Yet, how these structural characteristics control the mechanical behavior has not been reported. Further, lamellar block copolymer systems have been used in most of these studies because they are relatively easy to characterize.

However cylindrical block copolymer systems have more commercial relevance, since they exhibit the best overall elastomeric behavior.

Earlier work by Indukuri and Lesser[50] utilized small angle x-ray diffraction

(SAXS) and wide angle x-ray diffraction (WAXD) to evaluate and correlate structural changes to various amounts of strain in cylindrically phase separated systems. Their studies show that cooperative micro-buckling occurs in these systems and is responsible for the Mullins effect observed in these systems. This buckling instability is expected to depend on the modulus and diameter, but further studies are necessary to confirm this.

In some TPEs the resulting phase morphology can be altered with process conditions and thermal history. Hashimoto[86] and Balsara[87] showed that order-to- order transition (OOT) and order-to-disorder transition (ODT) are profoundly influenced by sample preparation and thermal history. Process conditions and temperature also have an effect on the d-spacing of block copolymers[75, 88, 89]. The

d-spacing is related to the distance between cylindrical domains as well as cylinder diameter[90]. In block copolymer systems showing an ODT with increasing temperature, it was observed that the d-spacing scales as d ~ T--1/3 where, T is absolute temperature. This effect is attributed to the change in interaction parameter (χ) (i.e. χ decreases with increase in temperature). However, what effect these subtle changes in microstructure have on the resulting mechanical behavior is not known.

In this paper we present results from systematic studies aimed at identifying what structural parameters in cylindrically phase separated systems govern their elastic response. Herein we correlate characteristic structural parameters to changes in elastic modulus. The effect of process conditions and thermal treatment are also investigated and discussed in terms of both structural characteristics and mechanical response.

4.2. Experimental

4.2.1. Materials and Sample Preparation

The material used in this study is a poly (styrene-ethylene-co-butylene-styrene)

(SEBS) triblock copolymer provided by Kraton polymers, US LLC. The chemical structure of the SEBS tri-block copolymer is shown in Figure 4.1. The number-average molecular weight, Mn, as determined by GPC is 107 K gm/mol and the poly-dispersity index, Mw/Mn, is 1.14 with Mw being the weight-average molecular weight. The weight fraction of PS for this tri-block copolymer is 18-22% and contains 0.06-0.14 wt. % of antioxidant. This material can be termed as SEBS-18-cyl.

Figure 4.1 Chemical structure of SEBS tri-block copolymer

Samples for mechanical and morphological characterization were prepared by three different methods. The first method involved melt processing of thick films using a PHI-PW225C bench press. The material was heated to a temperature well above the

ODT temperature (210-220ºC)[91] and below the degradation temperature (350ºC).

The samples were maintained at a temperature of 250-260ºC and a pressure of 950kPa for 30 minutes and then cooled at different rates, which will be discussed in detail later.

A second method involved solution casting films. The block copolymer was first dissolved in a non-preferential solvent (i.e. toluene) to obtain a 5-weight % by volume solution. Solvent evaporation then occurred over a period of 8-10 days at room temperature. The films were then dried at 45ºC for 6 hours to remove the excess solvent. Some of these films were characterized without further heat treatment, while others were subjected to different annealing temperatures and times followed by a quench in an ice water bath.

A third method involved extruding samples in a C.W. Brabender single-screw extruder with a screw of 3/4” diameter and length to diameter ratio of 25:1. The extruder has four zones along the screw where the temperature can be controlled. A

constant temperature was maintained throughout the length of the screw for two samples extruded at 170ºC and 190ºC. A higher temperature (T ~ 190ºC) near the hopper (zone-1) and a temperature of 165ºC at the opening of extruder were maintained for one of the sample.

4.2.2. Characterization and Testing

4.2.2.1. Morphological Characterization

cylindrical block copolymer systems corresponds to the spacing between (100) planes in hexagonally packed PS cylindrical domains.

4.2.2.2. Mechanical Testing and Thermal Analysis

Monotonic tensile and cyclic tests were performed on an Instron 5800 tensile testing machine. All the tests were performed on ASTM D1708 test geometry (gauge length = 22mm). All the tests (monotonic tensile and cyclic) were performed at room temperature at a crosshead speed of 10mm/min. Thermo-Gravimetric analysis (TGA) was done on TGA2950 Thermogravimetric Analyzer (of TA Instruments) on 7.97mg of sample at a heating rate of 10ºC/min, to measure the degradation temperature of the block copolymer. Differential scanning calorimetry (DSC) was performed on a TA

Instruments ® DSC Q1000 at a scan rate of 5ºC/min.

4.2.2.3. Deformation Calorimetry

Deformation calorimetry was performed to investigate if any strain-induced crystallization develops in this system. The incremental work done (dW), heat absorbed

(dQ) and hence the internal energy changes (dU) are measured during deformation as described previously[30, 50, 51]. The calorimeter has been used to study the heat and internal energy changes in strain-crystallizing natural rubber[52, 53] and thermoplastic elastomers[30]. The test in this study was performed on ASTM D1708 test geometry at a strain rate of 1.08 mm/mm/min and at a temperature of ~ 25 °C.

4.3 Results and Discussion

4.3.1 Deformation Calorimetry

In order to investigate if the composition used in this study undergoes strain- induced crystallization, deformation calorimetry was conducted. A melt-processed sample was used for this test. Figure 4.2 is a plot of the work done (ΔW), heat released

(ΔQ), the change in internal energy (ΔU), and the true stress (σ) all as a function of strain. Note that ΔU remains positive while loading the sample. This indicates that this material does not undergo strain-induced crystallization. Different compositions in different studies[30, 52] have shown to strain-induce crystallize and the extent of crystallization was measured by negative changes in ΔU. However, this does not occur in this system. DSC studies indicate an absence of melting-endotherm or crystallization-exotherm in heating and cooling scans, respectively. Therefore, this material lacks the ability to crystallize thermally as well.

10 Internal Energy 3 Stress 8 Heat 2 6 Work

4 1 2

0 0

1.0 2.0 3.0 4.0 5.0 (MPa) Stress -2

Energy (Joules/gm) -1 -4

-6 Extension ratio (λ) -2

Figure 4.2 Energetics of deformation of SEBS-18-cyl

4.3.2 Melt Processed Films: Effect of Cooling Rate

Melt processed samples were heated above the ODT (~ 210-220°C for this material[91]) and then cooled to room temperature at four different rates. The times taken to cool these samples from disordered state to room temperature were, less than

1minute (quenched), 5-6minutes (fast-cool), approximately 90minutes (medium-cool) and 6-7 hours (slow-cool). TEM images (Figure 4.3) reveal a significant difference in the grain size for these systems. As expected, the grain size is largest for the slow-cool system and decreases with increasing cooling rate. In the case of the medium-cool system, the grain size is between that of fast-cool and slow-cool systems, while the quenched system shows a worm-like structure.

Slow-cool (a) Fast-cool (c)

500nm 500nm

Medium-cool (b) Quenched (d)

500nm 500nm

Figure 4.3 TEM images of melt processed samples at different cooling rates. [(a) slow-cool (6-7 hours), (b) medium cool (approximately 90 minutes), (c) fast-cool (5- 6 minutes), (d) quenched (less than a minute)]. The dark phase corresponds to the (PS) cylindrical domains, since ruthenium tetroxide preferentially stains the styrenic phase, while the bright phase corresponds to (PEB) matrix.

Figure 4.4 compares the SAXS profiles for the melt-pressed samples cooled over four different rates together with solution cast samples annealed at different temperature (discussed later). In the melt-pressed samples (hollow symbols), note that higher-order maxima (√3, √4, √7, √9 and √12 relative to that of the first-order diffraction maximum) are observed for the slow-cool and medium-cool samples. This indicates a hexagonally packed cylindrical morphology for these thermal histories. On the other hand, fast-cool and quenched samples show broad higher-order maxima. This

indicates that both the order and the average length of PS cylinders increase with grain size.

√3 √4 √9 √7 √12 Slow-cool

Medium-cool Melt-pressed with changing cooling rate Fast-cool

1 Quenched √3 √4 √9 √7 √12 160C, 24hr

120C, 24hr Solution-cast with Intensity (arb.u.) different annealing 80C, 24hr temperatures

Un-annealed

0.1 1 q (nm-1)

Figure 4.4 1-D SAXS plots of the cylindrical system prepared by: (i) melt processing, prepared at different cooling rates (un-filled symbols), (ii) solution cast method and then annealed at 80ºC, 120ºC and 160ºC for 24hrs (filled symbols). The profiles have been shifted vertically for clarity.

Monotonic tensile tests were also performed on the melt-pressed samples.

Figure 4.5a shows the stress versus extension-ratio plots of these samples, where 6-8 specimens of each sample were tested. It can be noted that there is some variability in the tensile data. Figure 4.5b shows the representative curves which indicate an average

response of Figure 4.5a. A softer response for the quenched sample (fine grain- structure) and a stiffer response for the slow-cool sample (coarse grain-structure) are observed. The fast-cool and medium-cool samples show intermediate response. A

Mooney-Rivlin[92, 93] response was fit to the tensile data and values for the stiffness coefficients were obtained between extension ratios of 2.2 and 3.2. The Mooney-Rivlin equation can be written in the form shown in equation 1.

σ 2C eng = 2C + 2 (1) 1 1 2 λ − λ λ2 where, σeng is the engineering stress, λ is the extension ratio and C1 and C2 are the

Mooney-Rivlin stiffness coefficients. The constant C1 can be associated with the number of mechanically effective cross-links in an ideal network[94], and hence, is taken as the rubbery modulus. Table 4.1 shows the average C1 values for melt-pressed samples cooled over four different rates together with solution cast and melt-pressed samples annealed at different temperature (discussed later). The elastic-modulus (C1) increases with the order and grain size in the melt-pressed samples. This increase in elastic modulus may be associated with increasing grain size or other changes in the material’s microstructure. Additional structural parameters were investigated and a correlation between d-spacing and elastic modulus was also observed (see Table 4.1).

The d-spacing in cylindrical block copolymer systems corresponds to the spacing between (100) planes in hexagonally packed PS cylindrical domains. It is a measurable parameter which gives information about the micro-domain structure, such as the domain size (diameter) and the inter-domain distance. Subtle changes can be observed in the d-spacing (see Figure 4.6, as measured from SAXS patterns in Figure 4.4) with a

decrease in d-spacing occurring with increasing cooling rate (the precision of the SAXS instrument is 0.003nm-1).

12 10 Fast 8 cool Medium 6 cool 4 Slow cool Stress (MPa) 2 Quenched 0 246810 Extension ratio (λ)

(a)

12 Slow-cool 10 Medium-cool Fast-cool 8 Quenched 6

4 Stress (MPa) 2

0 246810 Extension ratio (λ)

(b)

Figure 4.5 Tensile behavior of melt pressed samples prepared at different cooling rates. [(a) stress versus extension ratio plots of all the samples, (b) representative curves of data in (a)]

Table 4.1 Change in d-spacing due to different sample preparation methods and thermal histories and corresponding changes in elastic modulus Treatment q d C1 Melt pressed at different cooling rates (nm-1) (Å) (MPa) Meltp Slow-cool 0.267 235.5 0.335 Meltp Medium-cool 0.27 232.6 0.297 Meltp Fast-cool 0.275 228.3 0.197 Meltp Quenched 0.287 218.8 0.188 Melt pressed and annealed* Meltp Fast-cool, 120ºC 1hr 0.273 229.6 0.2 Meltp Fast-cool, 180ºC 1hr 0.284 221.3 0.193 Meltp Fast-cool, 120ºC 24hrs 0.270 232.7 0.214 Meltp Fast-cool, 180ºC 24hrs 0.280 224.3 0.24 Meltp Slow-cool, 120ºC 24hrs 0.273 229.6 0.293 Meltp Slow-cool, 160ºC 24hrs 0.279 225.4 0.267 Solution Cast and annealed* Toluene Cast Un-annealed 0.263 238.6 0.374 Toluene Cast, 80ºC 24hrs 0.267 235.5 0.316 Toluene Cast, 120ºC 24hrs 0.274 229.6 0.265 Toluene Cast, 160ºC 24hrs 0.280 224.0 0.278

[* It may be noted that all the annealed samples (solution-cast and melt-pressed and further annealed) were quenched from the high temperature state to 0°C.]

Increasing 240 Slow-cool grain size Medium-cool 230 Fast-cool

220 Quenched d-spacing (A)

210 110100 Cooling rate (C/min)

Figure 4.6 Change in d-spacing with cooling rate of the samples prepared by melt processing. Cooling rate is calculated approximately from the ratio of total change in temperature to total time taken to reach room temperature

4.3.3 Solution Cast Films: Effect of Annealing

The TEM micrograph in Figure 4.7 shows that this block copolymer prepared by solution casting in toluene phase separates to form PS cylinders embedded in a PEB matrix. Therefore, toluene is not a preferential solvent for this system. SAXS measurement on these systems also confirms the hexagonal packing of PS cylinders in a PEB matrix (see Figure 4.4).

400nm

Figure 4.7 TEM image, showing the cylindrical morphology in the SEBS triblock copolymer prepared by solution cast method.

The micro-structural and the mechanical behavior of solution cast samples are sensitive to parameters such as annealing temperature and time. In order to study this effect, solution cast films were annealed at different temperatures (80°C, 120°C and

160°C) for 24 hours. TEM analysis was done to ascertain any differences in the grain- size that may be noted due to different annealing temperatures. Unfortunately all the

TEM images show large grains and no trends were established. It has been reported[75] that the grain-size can only increase with annealing temperature, as the grains will continue to achieve their thermodynamic lower energy state.

Figure 4.4 shows the SAXS pattern of solution cast films annealed at different temperatures (filled symbols). At annealing temperatures 120°C and 160°C (above the

Tg of PS-block), the SAXS patterns show a higher degree of ordering when compared to the un-annealed and 80°C annealed films. Annealing treatment also affects the d-

spacing of solution cast films. Note, that the d-spacing decreases with an increase in annealing temperature (see Figure 4.8).

245

240

235

230

d-spacing (A) d-spacing 225

220 40 80 120 160 Annealing Temperature (C)

Figure 4.8 Change in d-spacing with annealing temperature of solution cast samples.

Stress versus extension ratio curves for the solution-cast films annealed at 80°C and 160°C along with the un-annealed sample are shown in Figure 4.9a. Note that a higher degree of scatter in the tensile curves can be observed when compared with the melt-pressed systems. In order to statistically evaluate the variability in tensile data illustrated in Figure 4.9a, a t-test was performed on selected mechanical parameters.

Approximately 17-18 specimens for each temperature and process condition were tested. The t-test analysis suggests that, there is a significant difference in the elastic

80C modulus of the samples annealed at 80°C and at 160°C (i.e. the hypothesis that C1 =

160C C1 can be rejected with a confidence level of 99.9%). Figure 4.9b shows this difference in the average elastic modulus of the two samples.

The data demonstrate that the material becomes softer with the increase in annealing temperature. The sample annealed at 160°C, which shows the highest degree of order in SAXS patterns, shows the softest response. These results suggest that as the order increases with annealing temperature the elastic modulus (C1) of the system decreases, see Figure 4.9b.

12 Un-annealed 10 80C 24hr 160C 24hrs 8

4 Stress (MPa) 2

0 12345678910

Extension ratio (λ) (a) 0.5

0.4

0.3 C1 (MPa)

0.2 Un-annealed 80C 160C Annealing Temperature

(b) Figure 4.9 (a) Stress Vs extension ratio curves (tensile behavior) for solution cast films before and after annealing, (b) Average elastic modulus values represented by the Mooney-Rivlin constant C1 at two different annealing temperatures

The effect of annealing at longer times was also investigated. Samples annealed at 80°C, 120°C and 160°C for 8 days (see Figure 4.10) show a trend similar to those annealed for shorter times, (i.e. elastic-modulus decreased upon annealing at higher temperatures). Also the sample annealed at 160ºC shows a softer response than those annealed at 80°C and 120°C.

12 Annealed for 8days

10 80C 8 120C 160C 6

4 Stress (MPa) Stress 2

0 246810 Extension ratio (λ)

Figure 4.10 Stress vs extension ratio curves (tensile behavior) of solution cast films annealed for 8 days

The tensile behavior of these samples (solution cast films annealed at different temperatures) shows an apparent contradiction. As shown in Figure 4.9 the elastic- modulus decreases with an increase in order and a probable increase in the grain size.

This is opposite from the behavior observed in melt-pressed samples where the elastic- modulus increases with an increase in order and the grain size. From this apparent

contradiction, it may be perceived that the elastic-modulus is not affected by the grain- size.

However, with regard to d-spacing their does appear to be some correlation with modulus (C1) for both the melt-pressed and solution cast samples. This is shown for all cases in Table 4.1 with the d-spacing decreasing with the increase in annealing temperature. This observed correlation between the elastic-modulus (C1) and d-spacing, for both the melt-processed and solution cast films, is shown in Figure 4.11.

0.4

0.3

0.2

C1 (MPa) C1 Un-annealed 0.1 Solution cast 24hrs Solution cast 8days Solution cast 16days Meltp 0.0 216 219 222 225 228 231 234 237 240 243 d-spacing (A)

Figure 4.11 Linear fit showing a correlation of elastic-modulus (represented by the Mooney-Rivlin constant C1) and d-spacing

4.3.4 Effect of Temperature and Cooling Rate on d-spacing

The effect of temperature on the d-spacing of block copolymers was first observed by Kawai and coworkers in a series of work [55, 95]. They explained that, at

a low temperature, the block chains are stretched away from the interface due to a high segregation power (χ) and the segregation power (χ) decreases with increasing temperature (χ ~ 1/T). This results in a thicker or diffused domain boundary and a smaller end-to-end distance of A & B chains at higher temperatures. The smaller end- to-end distance, in turn, results in a smaller domain size and inter-domain distance.

This decrease in the domain size is easily adjusted by the displacement of chemical junction points along the interface. Hence, the domain size and inter-domain distance are primarily determined by the segregation power of the system (i.e. d = d(χ)). It is observed that the d-spacing decreases with increasing temperature as a function of d ~

(1/T)1/3.

Temperature resolved small angle x-ray diffraction performed on a solution cast film (Figure 4.12a) shows that the order increases at temperatures above T ~ 115°C, which is just above the glass transition of poly(styrene). The sample retains its cylindrical morphology up to 240ºC after which it shows a transition to a disordered state at 260ºC. This, rules out the possibility of any order-to-order transition (OOT) in this system. With the increase in temperature, a continuous shift in the position of first order maxima to higher scattering angles (or scattering wave vector ‘q’) can be noticed.

This shift corresponds to a decrease in d-spacing with temperature (Figure 4.12b) which is associated with the decrease in segregation power (χ), as explained above.

This result shows the behavior of d-spacing with temperature as d ~ (1/T)~1/3, which is in agreement with the findings of Kawai and coworkers.

Heating Change in d-spacing

260C

240C 1 220C √3 √4 200C 180C 160C 1 145C √3 √4 130C 1

Log Intensity 115C √3 √4 100C 80C

0.1 1 q (nm-1)

(a)

(b)

Figure 4.12 (a) Temperature resolved SAXS of the solution cast sample, (b) following changes in d-spacing with temperature. [* Measurements are taken in incremental steps of temperature and recorded for 30 mins. Changes in d-spacings are determined from the position of first-order maxima of the patterns shown in (a)]

The changes in d-spacing with cooling rate, for melt-pressed samples, can be explained in terms of the kinetics of the process. When a fast cooling is employed, the sample is unable to reach its thermodynamic equilibrium state of high segregation power (χ). This happens because the block chains do not have sufficient time to relax and stretch away from the interface. Hence, the fast-cool and quenched systems at room temperature, are far from their thermodynamic equilibrium state and a structure corresponding to low χ (or smaller d-spacing) is kinetically trapped. In a slow cooling process, the sample has sufficient time to approach its thermodynamic equilibrium state. Therefore the slow-cool sample has a structure corresponding to high χ or larger d-spacing. As shown in Figure 4.6, the d-spacing decreases with increasing cooling rate. Note, that the cooling rate is expected to affect the structure upto T ~ 110°C, which corresponds to the glass transition of PS block, below which the system is in frozen state.

4.3.5 Correlating Grain-Size and/or d-spacing to Elastic-Modulus

An additional series of experiments were conducted to further determine whether the mechanical response of these materials correlates only to the d-spacing, or if it also depends on the grain-size. Unfortunately the solution cast samples studied for annealing, already had large grains before the thermal treatment. Thus, the grain-size did not change significantly upon annealing. In order to study the effect of annealing on grain-size, a sample with small grains is required. Therefore, a melt-pressed sample that initially has small grains (i.e. fast-cool sample, see Figure 4.3c) was annealed at two

greatly different temperatures over various times. The fast-cool sample (fine grain- structure) was annealed at 120ºC and 180ºC, both for 1 hour and 24 hours.

The annealing temperatures were selected in order to allow the samples to develop significantly different d-spacings. The different annealing times would allow the grain-size to increase in both systems. In this way we can produce smaller grains with larger d-spacings and test their effect on modulus. This together with the prior melt-pressed data will allow us to separate grain-size from d-spacing. Figure 4.13 shows the TEM micrographs of these samples. The temperature and time correspond to a different grain-size, as the grain-size increases both with the annealing temperature and time. At 120ºC, the block copolymer chains lack sufficient mobility and the grain- size does not change after annealing for both 1 and 24 hours (see Figure 4.13a and

4.13b). However, at 180ºC the chains now attain greater mobility and the grain-size increases significantly. A noticeable difference can be seen for the samples annealed at

180 ºC for 1 hour and 24 hours (see Figure 4.13c and 4.13d).

Fast-cool 120C, 1hr (a) Fast-cool 180C, 1hr (c)

500nm 500nm

Fast-cool 120C, 24hr (b) Fast-cool 180C, 24hr (d)

500nm 500nm

Figure 4.13 TEM micrographs of fast-cool sample annealed at: (a) 120ºC for 1 hour, (b) 120ºC for 24 hours, (c) 180ºC for 1 hour, and (d) 180ºC for 24hours

The annealing treatment also affects their d-spacing and as shown in Figure

4.14a. The d-spacing first increases after annealing at 120ºC for both 1 and 24 hours and decreases upon annealing at 180ºC. The fast-cool sample, before annealing, is far from its thermodynamic equilibrium state of high segregation power and large d- spacing. In other words, a structure corresponding to low-segregation power and small d-spacing is kinetically trapped. Upon annealing at 120°C, which is just above the glass transition of PS block, the block-chains acquire some mobility and the sample moves toward its thermodynamic equilibrium state of high segregation power and large d-

spacing. Hence, the d-spacing increases at 120°C. Note that this chain mobility is not sufficient for the growth of grains. At 180°C the thermodynamic equilibrium state corresponds to a state of low segregation power (χ), therefore, the d-spacing decreases.

Further, the sample that initially had large grains (slow-cool sample, see Figure

4.3a) was also annealed at 120ºC and 160ºC for 24 hours. The grain-size for this sample is not expected to increase much since it already has large grains. However the d- spacing decreases (see Figure 4.14 b) with temperature (d~ T-1/3), similar to the solution-cast samples. The slow-cool sample, before annealing, is close to its thermodynamic equilibrium of high segregation power (χ) and large d-spacing, as already explained in the previous section. Increasing the temperature results in decreasing segregation power (χ) and hence the d-spacing.

240 Fast-cool Fine grain-structure

230

220 1 hour d-spacing (A) 24 hours

210 40 80 120 160 200 Annealing Temperature (C)

(a)

240 Slow-cool Coarse grain-structure

230

220 24 hours d-spacing (A)

210 30 60 90 120 150 180 Annealing Temperature (C)

(b)

Figure 4.14 Change in d-spacing with annealing temperature and time, (a) fast- cool sample at and (b) slow-cool sample

These variations in d-spacing (Figure 4.14), due to different annealing temperatures, also affect material’s tensile behavior (see Figure 4.15 and 4.16). It may

be noted that the differences appear only at higher strains in these samples (6 < λ < 8).

Figure 4.15a shows that, the elastic-modulus (at higher strains) of the fast-cool sample increases when annealed at 120°C for 1 hour and it further increases when annealed for

24 hours. As previously noted, at 120°C there is no change in the grain-size, but the d- spacing increases. This implies that the change in modulus correlates with d-spacing as previously observed. Figure 4.15b shows the effect of temperature when annealed for

24 hours. It can be seen that, the elastic modulus (at higher strains) increases when annealed at 120°C and it decreases at 180°C. Hence, modulus decreases at 180°C together with the d-spacing even though the grain-size is increasing. This indicates that d-spacing is the primary factor governing the elastic modulus and grain-size has a secondary effect. The elastic-modulus of the slow-cool sample (already containing large grains) decreases upon annealing at 120°C and it further decreases on annealing at 160°C (see Figure 4.16). As shown in Figure 4.14b, the d-spacing for this system also decreases with increasing annealing temperature. These results again confirm the correlation between the elastic-modulus and the d-spacing and not the grain-size.

12 Un-annealed 10 120C, 1hour 8 120C, 24 hours

4 Stress (MPa) 2

0 246810 Extension ratio (λ)

(a)

12 Un-annealed 10 120C, 24 hours 8 180C, 24 hours

4 Stress (MPa) 2

0 246810 Extension ratio (λ)

(b)

Figure 4.15 Tensile behavior of fast-cool samples on annealing: (a) at 120ºC for 1 and 24 hours, (b) at 120 ºC and 180 ºC for 24 hours

14 Un-annealed 120C, 24h 12 160C, 24h 10 8 6

Stress (MPa) 4 2 0 246810 Extension ratio (λ)

Figure 4.16 Tensile behavior of slow-cool sample, on annealing at 120ºC and 160ºC for 24 hours

4.3.6 Cyclic Behavior

Cyclic tests were performed on the melt-pressed samples, where each sample was cycled five times after an initial stretch at various strains. It can be seen that all four samples (slow-cool, medium-cool, fast-cool and quenched) show a significant

Mullins effect[96] (see Figure 4.17), which is the difference in the first loading curve and subsequent loading and unloading curves. The extent of the Mullins effect increases with a decrease in cooling rate or an increase in d-spacing. The quenched sample shows the least Mullins effect, while the slow-cool sample shows the largest

Mullins effect. The Mullins effect in cylindrical block copolymers has been shown[50,

97] to be associated with a micro-buckling of PS-cylinders during the first loading cycle, after which the elastomer shows a softer response. Therefore the extent of

Mullins effect should depend on the relative stiffness of an individual cylindrical domain, which is a function of its diameter and modulus. Hence, the extent of Mullins

effect increases with the increase in domain diameter (which is directly related to the d- spacing). Effect of other structural parameters is not discussed here, as authors consider this a subject of future studies.

5 Meltp-slowcool (a) 5 Meltp-quenched (c) Coarse grains ) Fine grains 4 4

3 3

2 2 Stress (MPa) Stress (MPa) 1 1

0 0 123456 123456 Extension ratio (λ) Extension ratio (λ)

(b) (d) 5 Meltp 5 Meltp-fastcool mediumcool Fine grains 4 4

3 3

2 2 Stress (MPa) Stress (MPa) 1 1

0 0 123456 123456 Extension ratio (λ) Extension ratio (λ) Figure 4.17 Cyclic behaviors of melt pressed samples prepared at four different cooling rates, (a) slow-cool, (b) medium-cool, (c) quenched, and (d) fast-cool

4.3.7 Single Grain Systems

Extrusion can impart very high order and orientation in these samples in a single step process when processed below their ODT[98]. Single grain samples were

prepared below the ODT in the single-screw extruder. Due to the shearing effects inside the screw, the cylindrical domains orient along screw axis. The samples prepared at different temperatures showed differences in their d-spacing. The d-spacing decreases as the temperature of the extruder increases. As the sample, at a high temperature, comes out of the extruder, it cools quickly in air and hence a low χ-like structure is kinetically trapped. Upon annealing these samples at higher temperatures for 24 hours, the d-spacing first increases at 120ºC and then decreases at higher annealing temperatures (see Figure 4.18). This behavior is similar to what we have already seen for the fast-cool sample, (Figure 4.14a). This indicates that single grain systems also exhibit changes in the d-spacing due to different process conditions and thermal treatments. A change in the mechanical behavior of these single grain systems due to changes in d-spacing is a subject of future consideration.

250 Extruded-165C Extruded-170C Extruded-190C 240

230

220 d-spacing

210

200 extruded Annealed Annealed Annealed un-annealed 120C, 24hr 140C, 24hr 160C, 24hr

Figure 4.18 Changes in d-spacing of extruded samples on annealing at higher temperatures

4.4. Conclusions

In this paper, we present a correlation between a measurable structural parameter and the mechanical response of commercially relevant SEBS triblock copolymers containing cylindrical morphology. We show that a linear correlation exists between the elastic-modulus (C1) and d-spacing. This correlation exists over a broad range of thermal and process conditions including effects from annealing and cooling.

The d-spacing, associated with the domain size, decreases with an increase in the annealing temperature as the system evolves to a thermodynamic state. The d-spacing also decreases with an increase in the cooling rate, and the behavior is explained in terms of the kinetics of the process. The extent of Mullins effect also increases with the d-spacing.

Additional studies were also performed to isolate what effect, if any, the grain size has on the elastic modulus. It was shown that the grain-size has a secondary effect on the elastomer’s response. The grain-size was shown to increase with a corresponding decrease in cooling rate on melt-pressed samples. It was also shown that the grain-size increased with annealing temperature. However in both cases the elastic- modulus was shown to be relatively insensitive to the changes in grain-size.

CHAPTER 5

MOPHOLOGICAL TRANSITIONS IN BLOCK COPOLYMERS AND THEIR

CORRESPONDING MECHANICAL BEHAVIOR

5.1 Introduction

Block copolymer materials exhibit various phase transitions such as order-to- disorder transitions (ODT) and order-to-order transitions (OOT). In an ODT, the system changes from a phase separated state to a phase-mixed state. While, in an OOT, it changes from one phase separated state to another phase separated state. Studies of

OOT are quite significant both scientifically and commercially as physical properties of block copolymers depend strongly on their morphology[99]. Most of the works have focused their attention on thermally reversible OOTs both theoretically[68] and experimentally[100-102]. It has been observed that a morphology can change reversibly from lamellar to cylinder and from cylinder to sphere can with increasing temperature before going into disordered state. Hashimoto and coworkers[103] have explained the mechanisms of such thermo-reversible OOTs.

Alternatively, morphology can also be controlled by using selective solvents during solution casting. A kinetically trapped morphology is initially formed, that should in principle undergo thermally induced irreversible transition to a thermodynamically stable morphology in melt[104, 105]. Transitions of this sort have been observed with small angle x-ray scattering (SAXS) and transmission electron microscopy (TEM)[38, 101]. Such nonequilibrium-to-equilibrium transitions begin by forcing the system very far from equilibrium that the equilibrium state may be achieved

only in extreme conditions. When using high molecular weight materials, such transitions, though energetically favorable, may also be kinetically limited to moderate temperatures. Such changes in morphology can also occur in industries where plasticizers (e.g. mineral oil) are commonly used as a processing aid. The plasticizer can preferentially swell one phase relative to another, just like selective solvents, and thus affect the block copolymer morphology.

Although the behavior and mechanisms of such OOTs are well studied[106,

107], relatively less attention has been given to the effect that such transitions have on the resulting mechanical behavior. Winter and coworkers[108, 109] have shown that in the melt state a fundamental difference that exists between spherical domain morphology and other morphologies (cylindrical and lamellar) is its reduced molecular mobility. Whereas one-dimensional (lamellae) and two-dimensional (cylinders) structures allow molecules to rearrange in two or one direction, cubic structures have no such mobility. This is due to the fact that a deformation in any direction changes the intersphere distance causing a penalty in free energy. Because of this, cubic structures of block copolymers exhibit strikingly different rheological properties than other morphologies. However, in the solid state the mechanical properties are dominated by the continuity of the glassy PS domains. During a morphological transition from cylindrical to spherical, local anisotropy within the grains is completely lost. As discussed in Chapter 2 & 3, this local anisotropy is responsible for a micro-buckling behavior during deformation of cylindrical and lamellar block copolymers. Spherical systems, on the other hand, lack this structural anisotropy within the grains and also

continuous glassy PS domains. Hence, spherical systems can be expected to show lower stiffness compared to cylindrical systems.

In this chapter, effect that such irreversible morphological transitions have on the mechanical behavior is presented for a particular block copolymer system. The ability of this block copolymer to undergo a morphological transition from cylinder to sphere in the presence of a selective solvent provides an ideal opportunity to compare the mechanical response of cylindrical and spherical micro-domains with same composition.

5.2 Experimental

5.2.1 Materials and Sample Preparation

The material used in this study is a poly (styrene-ethylene-co-butylene-styrene)

(SEBS) triblock copolymer provided by Kraton polymers, US LLC. The number- average molecular weight, Mn, as determined by GPC is 107 K gm/mol and the poly- dispersity index, Mw/Mn, is 1.14 with Mw being the weight-average molecular weight.

The weight fraction of PS for this tri-block copolymer is 18-22%. It contains 0.06-0.14 wt.% of antioxidant. Equilibrium state morphology is cylindrical for this system.

Samples for testing are prepared by dissolving the block copolymer in a suitable solvent. The solutions thus obtained, are then dried at room temperature over a period of 8-9 days for solvent removal. The cast films are then subjected to annealing above the glass transition temperature of PS for 24 hours for the removal of trapped solvent.

The solution cast films prepared using toluene and heptane as solvents are also annealed at 120°C and 160°C for 24 hours followed by a quench in an ice-cooled water-bath.

5.2.2 Characterization

Sections, 40-50nm in thickness, were obtained by cryo-microtoming the bulk films with a Leica EM-FCS® microtome at -90ºC. These sections were stained with ruthenium tetroxide (RuO4) for approximately 20 min. TEM was performed using a

JEOL 100 CX TEM (Tungsten) operating at 100 kV.

SAXS measurements were performed on a Molecular Metrology® SAXS machine consisting of a sealed-tube x-ray source. The raw data is calibrated for the peak position with the standard silver-behenate, which has peak position at scattering vector, q = 1.076 nm-1. The sample to detector distance is found to be ~ 1.2m using the above calibration. Each profile was recorded at room temperature (~ 25ºC) over a period of 1h.

Monotonic tensile and cyclic tests were performed on an Instron 5800 tensile testing machine. All the tests were performed on ASTM D1708 test geometry. The gauge length for this ASTM standard is 22mm. All the tests (monotonic tensile and cyclic) were performed at room temperature at a crosshead speed of 10mm/min.

Thermo-Gravimetric analysis (TGA) was done on TGA2950 Thermogravimetric

Analyzer (of TA Instruments) on 7.97mg of sample at a heating rate of 10ºC/min, to measure the degradation temperature of the block copolymer. Differential scanning calorimetry (DSC) was performed on a TA Instruments® DSC Q1000 at a scan rate of

5ºC/min.

Deformation calorimetry was performed to study the presence/absence of strain- induced crystallization in this system, as described in Chapter 2. The test in this study was performed on ASTM D1708 test geometry at a strain rate of 1.08 mm/mm/min and at a temperature of ~ 25 °C.

5.3 Results and Discussion

The thermodynamic equilibrium state morphology for this block copolymer as prepared by melt process method (from our previous studies [110]), is of PS cylinders in poly ethylene/butylene (PEB) matrix. Toluene is a preferential solvent for styrenic phase, while heptane is a selective solvent for the ethylene/butylene phase. 1-D SAXS intensity plots for the films cast from toluene and heptane are shown in Figure 5.1. Also shown in Figure 5.1 are the SAXS intensity plots for the heptane cast samples annealed at 120° C and 160° C which will be discussed in detail later. The SAXS intensity plot for heptane cast sample indicates position of the scattering peaks in a ratio of 1:√2:√3, which indicates a spherical morphology. For toluene cast sample the scattering peaks are in a ratio of 1:√3:√4 which indicate a cylindrical morphology. The √4 peak appears as a shoulder upon the √3 peak. These results suggest that toluene swells PS domains to form a cylindrical morphology. In contrast heptane preferentially swells the matrix and it reduces the overall volume fraction of PS domains considerably resulting in a kinetically trapped spherical morphology. This effect of the solvents on morphology is also confirmed by TEM analysis in Figure 5.2.

√3q √4q √9 √12 q √7 Heptane Cast 160C, 24hr √3q

q Heptane Cast √2q 120C, 24hr √3q Heptane Cast q Spherical √3q Log Intensity Toluene Cast Cylindrical

0.1 1 q (nm-1)

Figure 5.1 SAXS patterns of samples before (un-filled symbols) and after annealing (filled symbols). (* Thick arrows here correspond to form factor scattering, i.e. scattering due to individual cylindrical and spherical domain)

Heptane cast Toluene Cast

200 nm 200 nm

Diameter of sphere ~ 140Å Diameter of cylinder ~ 108Å

Figure 5.2 TEM micrographs of the sample solution cast in heptane and toluene. Heptane cast shows spherical, while toluene cast sample shows cylindrical domains of PS in PEB matrix

The average radius of these spherical and cylindrical domains can be calculated from the relationships,

4π (Rs/λ) sin θm,i = 5.765 i = 1 (for spheres) (1)

4π (Rc/λ) sin θm,i = 4.98, i = 1 (for cylinders) (2)

where, Rs and Rc are the average radius of sphere and cylinder respectively, while 2θm,i is the peak position of intra-particle (or form-factor) scattering maxima in 1-D SAXS plot.

In order to study and provide evidence for the presence/absence of strain- induced crystallization in this system, deformation calorimetry has been employed. A melt-processed sample (cylindrical morphology) was used for this test. Internal energy measurements (change in internal energy, ΔU) as plotted in Figure 5.3 show that as work is done (ΔW) on the system, due to applied strain (ε), ΔU increases proportionately and remains positive during loading. Hence, positive ΔU during loading suggests that the sample does not have the tendency to show strain-crystallization.

Differential scanning calorimetry (DSC) studies performed on the system indicate an absence of melting or crystallization endotherm in heating and cooling scans, respectively. Therefore, this system also lacks the ability to crystallize thermally.

10 Internal Energy 3 Stress 8 Heat 2 6 Work

4 1 2

0 0

1.0 2.0 3.0 4.0 5.0 Stress (MPa) -2

Energy (Joules/gm) -1 -4

-6 Extension ratio (λ) -2

Figure 5.3 Energetics of deformation of the cylindrical block copolymer

The effect of morphology on the mechanical behavior is seen from the monotonic tensile testing (see Figure 5.4). Note that ultimate mechanical properties

(stress and strain to failure) improve as the morphology changes from cylindrical to spherical. It may be noted that both cylindrical and spherical block copolymer systems contain grain and accompanying grain boundaries. Grain boundaries in cylindrical block copolymers appear due to orientation mismatch of anisotropic cylindrical domains. Upon stress application these grain boundary areas can act as regions of high stress concentration and therefore can act as defects. Spherical block copolymers, on the other hand, have grain boundaries which appear due to the ordering mismatch between bcc/fcc/sc packed spherical domains. These grain boundaries differ from the ones in cylindrical systems from the fact that they separate regions which are isotropic. Such grain boundaries cannot act as region of stress concentration or in other words they can

have minimal effect on mechanical properties. Hence, the improvement in ultimate mechanical behavior upon morphological transition could be due to the change in the nature of grain boundaries from cylindrical to spherical morphology. The spherically cast samples also show lower stiffness compared to the cylindrically cast systems. This behavior is expected as the higher initial stiffness of cylindrical systems is associated with the micro-buckling instability as discussed in Chapter 2. Spherical systems lack these continuous PS-domains and have no structure to buckle, therefore show much lower stiffness.

18 Heptane Cast (Spherical) 15

9 Tol-unannealed 6 (Cylindrical) Stress (MPa) 3

0 246810 Extension ratio (λ)

Figure 5.4 Tensile behaviors of spherical (heptane cast) and cylindrical (toluene cast) samples

Cyclic testing has been performed to further understand the deformation behavior of spherical and cylindrical systems (see Figure 5.5). In addition the figure also shows the cyclic response of spherical and cylindrical systems that were annealed

at higher temperatures. Each sample was cycled five times after initial stretch. The behavior is analyzed in terms of changes in Mullins Effect, which is the difference in the first loading cycle and subsequent loading and unloading cycles. It has been shown that the Mullins effect in cylindrical block copolymer is due to the micro-buckling phenomenon during first loading cycle after which the elastomer shows a stress softening response[111]. The spherical block copolymer (heptane cast sample), on the other hand, has no structure to buckle and shows no Mullins effect (Figure 5.5a). When this kinetically trapped spherical system is annealed above the glass transition temperature of PS, the material is expected to achieve its thermodynamic equilibrium state of cylindrical morphlogy. However, after annealing (i.e. at 120°C and 160°C for

24 hours) the heptane cast sample shows an intermediate Mullins response between that of cylindrical and spherical system (Figure 5.5b and 5.5c).

4 4 Heptane Cast (a)4 Heptane Cast (b)Heptane Cast (c) Un-annealed Annealed 120C, 24hr Annealed: 160C, 24h Spherical domains 3 Cylindrical domains 3 3 Cylindrical domains

2 2 2 Stress (MPa) Stress

Stress (MPa) 1 1 (MPa) Stress 1 No Mullin’s effect 0 0 0 123456 123456 123456 Extension ratio Extension ratio (λ) Extension ratio (λ)

4 Toluene Cast 4 Toluene Cast Un-annealed Annealed: 160C, 24h Cylindrical Cylindrical domains 3 3 domains

2 2 Stress (MPa) 1 Stress (MPa) 1 (d) (e) 0 0 123456 123456 Extension ratio (λ) Extension ratio (λ)

Figure 5.5 Cyclic behavior expressed in terms of the extent of Mullins effect

Temperature resolved SAXS was performed to ascertain whether the kinetically trapped spherical system undergoes any OOT. Figure 5.6 shows that a sudden change in d-spacing occurs at about 100°C as the temperature of the system is increased. It appears that a phase transition occurs from thermodynamically quasi-stable spherical morphology to thermodynamically favorable cylindrical morphology. As mentioned before, this block copolymer has an equilibrium state morphology of cylindrical PS domains in PEB matrix. Selective solvent (i.e. heptane) forces the PS chains to contract while PB chains to expand resulting spherical domains of PS in PEB matrix. This unfavorable conformation is relaxed when the specimen is taken above Tg of the glassy

PS phase. Hence, the relaxation of the unfavorable chain conformations for both PS and

PEB blocks in the quasi-stable morphology frozen in the as-cast film causes a morphological phase transition. No such morphological transition is observed for toluene cast samples, as they already have a thermodynamically stable cylindrical morphology before annealing. The only change they can have with temperature is in the size and spacing of cylindrical domains. The toluene cast samples show the behavior of decreasing d-spacing with increasing temperature[110] as discussed in Chapter 4.

240

220

200

180

160

140

d-spacing (A) Heptane Cast 120 Toluene Cast

100 0 40 80 120 160 200 240 280 Temperature (C)

Figure 5.6 Change in d-spacing (as calculated from temperature resolved SAXS experiment) with temperature for heptane cast and toluene cast samples

Heptane (spherical) and toluene (cylindrical) cast samples annealed at 120°C and 160°C were further studied and compared in detail for their structure and mechanical behavior. The SAXS intensity plots for the heptane cast sample annealed above the OOT temperature (i.e. 100°C) are shown in Figure 5.1. Here the ratio of higher order scattering maxima changes from 1:√2:√3 to 1: √3:√4. This suggests that

the morphology has transformed from sphere to cylinder. However, the intermediate

Mullins response of these annealed samples (which is far from the expected response as seen in Figure 5.5d or 5.5e) presents an apparent contradiction. We regard the morphology of these samples as apparent cylindrical morphology. Circularly symmetric

2-D SAXS pattern after annealing confirms that there are no orientation effects during the transition from spherical to cylindrical domains.

Tensile response of heptane cast sample annealed at 120°C is shown in Figure

5.7a in comparison with the unannealed state. The stiffness increases as morphology changes from spherical to apparent cylindrical. This behavior is expected, as the cylindrical systems are likely to show higher stiffness than the spherical systems.

However a comparison of heptane and toluene cast samples after annealing (Figure

5.7b) reveals that the apparent cylindrical system (i.e. heptane cast sample annealed at

120°C) shows lower stiffness than the toluene cast sample also annealed at 120°C. The two samples also differ in their d-spacing (see Table 5.1), such that the sample having lower stiffness (i.e. heptane cast sample annealed at 120°C) shows smaller d-spacing.

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14 14 (a) Heptane Cast (b) 12 12 Heptane Cast Spherical 120C, 24hr 10 10 Cylindrical 8 8 Toluene Cast Heptane Cast 6 6 120C, 24hr 120C, 24hr Cylindrical Stress (MPa) 4 Cylindrical Stress (MPa) 4 2 2

0 0 246810 246810

Extension ratio (λ) Extension ratio (λ)

Figure 5.7 Tensile behavior of samples, (a) heptane cast before and after annealing at 120°C, (b) heptane cast and toluene cast samples after annealing at 120°C

Table 5.1. The d-spacing and stiffness (C1) of heptane cast and toluene cast samples before and after annealing at 120°C & 160°C Sample treatment Heptane Heptane Toluene Toluene cast cast cast cast * d-spacing C1 (MPa) d-spacing C1 (MPa) unannealed 199.6 0.149 238.6 0.374

Annealed at 120C, 226.8 0.181 229.6 0.265 24hrs Annealed at 160C, 221.2 0.156 224.0 0.278 24hrs

* C1 corresponds to the Mooney-Rivlin constant, which is related to the number of mechanically effective cross-links within the network and hence related to the stiffness of the sample.

An unusual behavior is seen in the tensile response of heptane cast sample which is annealed at 160°C as shown in Figure 5.8a. Although SAXS intensity plots, in

Figure 5.1, suggest a hexagonally packed cylindrical morphology for this system, the tensile response is similar to that of samples with the spherical micro-domains. Even

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after the morphological transition from spherical to apparent cylindrical, the initial (i.e. at lower extension ratios, λ = 1 to 7) mechanical behavior does not change at all.

Comparison with toluene cast sample (Figure 5.8b) also annealed at this temperature shows behavior similar to that seen at 120°C in Figure 5.7b. Note that in both the samples, i.e. heptane cast samples annealed at 120°C and 160°C, the morphology appears to be cylindrical as suggested by SAXS intensity plots in Figure 5.1. However the elastic modulus is far from that expected for cylindrical systems (see the response of toluene cast samples for comparison). Again, these two samples also differ in their d- spacings, such that heptane cast sample annealed at 160°C showing lower stiffness shows smaller d-spacing (5.1).

16 14 (a) Heptane Cast (b) Heptane Cast 14 12 Spherical 160C, 24hr 12 10 Cylindrical 10 8 8 Heptane Cast 6 Toluene Cast 6 160C, 24hr 160C, 24hr Stress (MPa) Stress Stress (MPa) Stress 4 4 Cylindrical Cylindrical 2 2 0 0 246810 246810

Extension ratio (λ) Extension ratio (λ)

Figure 5.8 Tensile behavior of samples, (a) heptane cast before and after annealing at 160°C, (b) heptane cast and toluene cast samples after annealing at 160°C

In chapter 4, it has been shown that this block copolymer with cylindrical morphology shows a correlation between d-spacing (or domain-size) and elastic

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modulus (C1) of the material[110]. Here the Mooney-Rivlin constant C1 is used as a measure of elastic modulus, as it is related to the number of mechanically effective cross-links within the network[94]. According to the correlation, as the d-spacing (or domain-size) decreases due to different process conditions and thermal histories, the elastic modulus also decreases. Figure 5.9 shows a comparison of heptane cast samples annealed at 120°C and 160°C along with the previously observed correlation by the samples with cylindrical morphology. It can be observed that the two samples fall slightly away from the observed correlation. This indicates that the change in d-spacing is not the primary reason for such low modulus of the annealed heptane cast samples and some other parameters may be associated.

0.4

0.3

0.2 TolCast-anneal24h 120ºC TolCast-annl8days Stiffness (C1) 160ºC 0.1 Meltp TolCast TolCast-annl16days Heptane Cast-annl24hrs 0 215 220 225 230 235 240 245 d-spacing (A)

Figure 5.9 Variation of stiffness (C1) with changes in d-spacing of the sample under different process conditions and thermal histories

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Hashimoto and coworkers have explained the mechanism of OOT from spheres to cylinders[103]. During this phase transition, spheres first deform into ellipsoids along

[111] direction of the BCC lattice. These ellipsoids then coalesce to form an intermediate beaded-necklace structure (a structure where the ellipsoids are weakly connected). This beaded-necklace structure then evolves into complete cylinders. Upon annealing the heptane cast sample at 160°C, the transition from sphere to cylinder may have stopped at some intermediate structure such as beaded-necklace structure. This could be due to the insufficient mobility of chains in the melt state, at 160ºC, to transform into a full cylinder. However a detailed TEM analysis is necessary to confirm this. As shown in chapter 2 the cylindrical block copolymers undergo micro-buckling and/or fragmentation during deformation[112]. This is responsible for higher initial stiffness of cylindrical block copolymers over the ones with spherical morphology. An intermediate structure like ‘beaded-necklace’ would micro-buckle or breakdown at much lower stress levels.

Due to the probable connectivity of ellipsoids, heptane cast sample annealed at

160° C shows Mullins effect, unlike BCC packed un-annealed heptane cast sample that shows zero Mullins effect. In other words, this structure has some similarity with cylindrical morphology. However, due to the tendency of this structure to micro-buckle with ease, it shows small Mullins effect. Comparing the cyclic response of heptane cast samples with toluene cast samples, it is clear that the samples with complete cylindrical morphology show large Mullins effect.

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5.4. Conclusions

SEBS block copolymers with cylindrical morphology show a pronounced

Mullins effect. The mechanism is associated with the micro-buckling of cylindrical domains during initial loading, after which the system shows a softening response in the subsequent loading/unloading cycles. The samples with spherical morphology lack continuous PS domains and grain structures required for micro-buckling, and hence show no Mullins effect. The transition from sphere to cylinder is a gradual response.

The process is thermodynamically feasible but kinetically restricted. Intermediate morphologies and mechanical responses have been identified during this transition. The mechanical response of these materials is more sensitive to such morphological transition during OOT when compared to SAXS. SAXS fails to distinguish between complete cylindrical and intermediate morphologies. Maximum stiffness is observed for toluene cast samples prior to annealing, as cylindrical domains in these systems were formed from solutions where the chains had highest entropy/mobility to organize into complete (with sharp domain-boundary) and larger cylindrical domains.

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CHAPTER 6

CHARACTERIZATION OF HYBRID BLOCK COPOLYMERS DEVELOPED

THROUGH BLENDING

6.1 Introduction

One major characteristic of block copolymers comprised of incompatible blocks is their micro-phase separation in solid state. Gido and co-workers have used electron microscopy to characterize and model the local morphology and grain boundaries[77-

79]. They report that the structure at grain boundary only attains a local equilibrium and not a global equilibrium. In another study they observed that with increasing number of blocks in graft copolymers the long range order is considerably reduced[113]. They came to this conclusion by qualitatively estimating the grain sizes. Balsara and coworkers showed that the average grain size did not significantly affect the rheological properties of ordered block copolymers[114]. In another work, block copolymer grain structure and grain boundary morphology have been found to have significant effect on transport properties of these materials[115]. In previous chapters we have shown that grain size does not affect the elastic modulus, but it may change the ultimate mechanical properties.

Stadler and coworkers observed some complex and disordered micro phase morphologies in ABC type triblock copolymers systems[116]. They regard this observed morphological disorder an inherent property of such block copolymer systems. However what affect such disordered structure has on the mechanical properties of block copolymer systems has not been studied so far. In another study it

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has been observed that by mixing similar elastomers of varying chain lengths synergistic improvements in mechanical properties could be obtained[117]. The two polymers differ only in chain length. The short chains of this bimodal network improve the tensile strength, while long chains improve the elongations to break. Mixing behavior of similar block copolymers has been studied well [118-130] in terms of their morphology without any attention to their mechanical properties.

In this work, we have presented another attempt to study the effect of grain boundaries on the mechanical behavior of block copolymers. It is possible to disrupt the local order present in block copolymers by mixing two block copolymers which differ in their block copolymer composition and morphology. The effect of various process conditions on the mixing behavior is presented. Finally the mechanical properties of the mixed block copolymers are investigated.

6.2 Experimental

6.2.1 Materials and Sample Preparation

The materials were poly (styrene-b-ethylene-co-butylene-b-styrene) (SEBS) based triblock copolymers and poly (styrene-b-ethylene-co-propylene) (SEP) based diblock copolymers supplied by KRATON Polymers, U.S. LLC. The block copolymers with different compositions have been used which form spherical, cylindrical and lamellar morphologies. Samples are named such that the first three or four letters correspond to the type of block copolymer (SEBS or SEP). The first letter after the dash tells the kind of morphology that system shows (S-spherical, C-cylindrical, and L-

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lamellar). And the number represents the amount of polystyrene (weight fraction). The compositions of these systems are listed in the Table 6.1.

Table 6.1 Compositional details Polymer % PS Expected Morphology SEBS-S13 13 Spherical SEP-L37 37 Lamellar SEBS-S12 12 Spherical SEBS-C18 18 Cylindrical

The samples were prepared by fabricating solution cast films, or by melt processing. The solution cast films were fabricated in two ways. First method involved dissolving the polymers in toluene to obtain 5 weight % by volume solutions followed by controlled evaporation over a two week period. Mixing of two or more block copolymers was done by dissolving equal amounts of two different block copolymers in toluene to keep the concentration of the total block copolymer in solvent to be 5% by weight. The samples prepared in this way are termed as solution cast samples. An alternative method involved dissolving the polymer (50:50 mixture of two block copolymers) in toluene to obtain a 5 weight % solution followed by spin-coating at high speed (20,000 r.p.m.) on a silica substrate. These samples are called spin coated samples.

Melt mixing was also done in two ways. The block copolymer powders were first hand-mixed followed by extrusion in a single screw extruder at temperatures ranging between 220-270ºC depending on the required conditions which will be discussed in detail later. The samples prepared in this way are called extruded mix. The second method involved subjecting the hand-mixed powders directly to compression

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molding machine at temperatures ranging from 250-270ºC. These are called melt mix samples. The single block copolymers were melt pressed directly at temperatures ranging from 250-270ºC.

6.2.2 Characterization and Testing

Transmission electron Microscopy (TEM) was performed using a JEOL 100 CX

TEM (Tungsten) at 100 KV on RuO4 stained samples obtained by cyro-microtoming 50 nm sections of SEBS bulk samples. Atomic force microscopy (AFM) was performed on

Digital Instruments AFM machine using tapping mode. AFM was performed on our spin coated samples.

Tensile and cyclic tests were performed on an Instron 5800 tensile testing machine. All the tests were performed on dog-bone shaped samples (solution cast and melt pressed) of standard ASTM D1708 size for elastomers. All the tests were performed at room temperature at a cross-head speed of 10mm/min. Rheological tests were performed on a rotational rheometer (Viscotech of ATS rheosystems) with a parallel plate fixture of 25mm in diameter involving a frequency-temperature sweep at constant stress of 200Pa. The tests were performed at frequencies varying from 10+1 to

10-2 rad/s at temperatures from 200ºC to 300ºC at a step of 10ºC.

6.3 Results and Discussion

The mixing behavior of SEBS-S13 and SEP-L37 by spin coating is shown in

Figure 6.1. Note, since solvent is removed at a fast rate the spin coating method represents a non-equilibrium state of mixing. SEP-L37 initially shows local order and

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grain structure which is completely disrupted upon mixing with SEBS-S13. We refer this mixed-state morphology as a hybrid structure.

SEBS-S13 Spherical

0 1µm +

SEP-L37 Lamellar 0 1µm

50:50 mixture

0 1µm

Figure 6.1 AFM images showing the mixing of spherical and lamellar block copolymers in non-equilibrium state

The equilibrium state mixing can be obtained using solution casting method.

Figure 6.2 shows such mixing behavior of SEBS-S13 and SEP-L37 in equilibrium state.

A macro-phase separation occurs where the TEM micrograph (in Figure 6.2) displays regions with lamellar domains of SEP-L37 as well as regions with spherical domains of

SEBS-S13. In addition an irregular morphology is observed between the regions of spherical and lamellar domains. This structure resembles closely to the hybrid structure seen in Figure 6.1. Tensile tests performed on these solution mixed samples

(equilibrium state mixing) revealed a composite response.

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1 μm

Figure 6.2 TEM micrograph showing mixing of spherical (SEBS-S13) and lamellar (SEP-L37) block copolymers in equilibrium state

The results above indicate that the non-equilibrium process provides a better mixing. The mixing behavior can be expected to enhance if block copolymers with similar molecular weights are used. Therefore a new set of block copolymers SEBS-S12 and SEBS-C18, having similar range of molecular weight, are selected for further investigation. In addition, process conditions are also expected to play role on the mixing behavior. We anticipate that mixing is likely to be improved if the two block copolymers are mixed above their order-to-disorder transition (ODT) temperature.

Rheological tests were performed in order to determine the ODT temperatures.

A sudden drop in storage (G’) or loss modulus (G”) at low frequencies was used as a measure of ODT. Figure 6.3 shows the rheological response for SEBS-S12 and SEBS-

C18. A sudden drop in the storage modulus between 210ºC and 220ºC is observed for

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SEBS-C18 (Figure 6.3a), indicating its ODT. On the other hand SEBS-S12 shows an

ODT between 200ºC and 210ºC (Figure 6.3b).

5 200C 10 4 SEBS-C18 SEBS-S12 10 210C 4 200C 220C 10 3 210C 10 230C 220C 240C 3 2 10 230C 10 250C 240C 260C 2 1 10 250C 10 270C 260C 280C 1 0 10 270C 10 290C 280C 0 G' (Pa)

300C G' (Pa) 10-1 10 290C 300C -1 10-2 10

-2 10-3 10

10-4 10-3 0.1 1 10 100 0.1 1 10 100 Freq. (rad/s) Freq. (rad/s)

(a) (b)

Figure 6.3 Rheological measurements showing ODT measurements of: (a) SEBS- C18 and (b) SEBS-S12

The mixing behavior for SEBS-S12 and SEBS-C18 in non-equilibrium state was studied by performing TEM on the extruded mix samples (see Figure 6.4). The TEM micrograph of SEBS-C18 shows well aligned cylinders showing a long range order.

Note that upon mixing with SEBS-S12, the long range order present in SEBS-C18 is completely disrupted. The two block copolymers were mixed by solution cast method as well.

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SEBS-C18

500nm Mixed elastomer (Extruded) + SEBS-S12 500nm

500nm

Figure 6.4 TEM analysis of mixing behavior of SEBS-C18 and SEBS-S12 in melt process conditions

Tensile tests performed on the extruded-mix (non-equilibrium state) and solution-cast (equilibrium state) mixtures of SEBS-S12 and SEBS-C18 are shown in

Figure 6.5. A significant improvement in the tensile strength and ultimate strain to failure from solution cast mixed to extruded-mix state is observed. Hence, by disrupting the local order of SEBS-C18 using SEBS-S12 by extrusion, the mixed state shows tensile strength similar to that of SEBS-C18 while elongation to break is improved.

Solution cast mixed system, on the other hand, shows lower tensile strength and lower elongation to failure.

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SEBS-C18 10 Solution cast Melt processed 8 8 Extruded SEBS-S12 mix 6 Mixed 6 Melt mixed 4 SEBS-C18 4 SEBS-S12 Stress (MPa) Stress (MPa) 2 2

0 0 0246810 0246810 Extension ratio (λ) Extension ratio (λ)

(a) (b)

Figure 6.5 Tensile response upon mixing of SEBS-S12 and SEBS-C18: (a) solution cast mixing, (b) melt mixing (melt mix and extruded mix)

Cyclic tests were performed on these samples, with each sample cycled five times after its initial stretch (see Figure 6.6). A large Mullins effect is observed for

SEBS-C18. SEBS-S12 on the other hand shows no Mullins effect at all. The absence of

Mullins effect in spherical system has been explained in chapter 4. The extruded-mix system shows negligible Mullin’s effect. The melt-mix system still shows some Mullins effect, but it is much smaller than SEBS-C18. These results suggest that by disrupting the local order of SEBS-C18 the Mullins effect can also be reduced considerably. The results also indicate a better mixing obtained by extrusion method.

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6 2.0 5 SEBS-C18 SEBS-S12

cylindrical 1.5 spherical 4

3 1.0

Stress (MPa) 0.5 Stress (MPa) Stress 1

0.0 0

123456 123456 Extension ratio (λ) Extension ratio (λ)

2.5 3.0

Extruded mix2.5 Melt mixed 2.0 2.0 1.5 1.5 1.0 1.0 Stress (MPa) 0.5 Stress (MPa) 0.5

0.0 0.0

123456 123456 Extension ratio (λ) Extension ratio (λ)

Figure 6.6 Cyclic behavior of SEBS-C18, SEBS-S12 and their mixed state in melt processed state (extruded mix and melt mix)

6.4 Conclusions

In this work we study the mixing behavior of ordered block copolymers. Local order present in ordered block copolymers can be disrupted by mixing block copolymers, which differ in their styrene to ethylene/butylene ratio (and hence show different morphologies), in the non-equilibrium state. In solution cast mixing (which is

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close to equilibrium state) the mixed block copolymers show poor mixing behavior and a macro-phase separation occurs resulting in poor tensile and cyclic properties. The mixing was improved in melt process conditions when block copolymers with similar range of molecular weight are mixed above their ODT temperature.

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CHAPTER 7

HIGH STRAIN-RATE TENSILE TESTING OF POLYMERIC FILMS

7.1 Introduction

Commercial processing of polymeric films often involves high speeds and it is important to understand their high strain-rate mechanical behavior. However most of the conventional testing methods either offer slow speeds or provide limited information. Some of the common methods used to test polymers at high speeds include drop/driven dart test, Elmendorf tear test, pendulum tests (Izod) and Flex tests (dynatup or instrumented drop weight impact test)[131-133]. These methods although give good qualitative information between different materials but provide only limited information about the fracture behavior. All they offer is a number (i.e energy to failure) and they do not tell if the material failed in a brittle or ductile manner. Further the sample goes through complex stress states and it is quite difficult to translate results into actual applications as intrinsic film properties are not measured. To measure the intrinsic properties of materials uni-axial tensile tests are commonly used. Among the common tensile test methods (Screw-type, Servo-Hydraulic and Split Hopkinson bar [134, 135]) as the test-speed increases the range of strain, up to which the material can be tested, reduces drastically. Servo-hydraulic machines can although offer most of the above mentioned requirements but the cost involved are very high.

MTS® recently developed a dynamic nano-indentation technique[136, 137] where they superimpose small sinusoidal oscillations on a primary loading signal and resultant displacement response is measured. From the ratio of amplitude and phase

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difference between loading and displacement signal, various mechanical properties such as storage and loss modulus are measured. However, these measurements involve very small strains and the response at higher strains is not obtained.

The objective of this work is to develop a new test technique which will offer an economical method to provide tensile data on polymeric films at high strain rates. In addition we would also analyze the dynamic visco-elastic response of polymeric materials at high strain-rates.

7.2 Materials and Devices

Strain gages with a grid resistance of 350.0±0.3% Ω and a Gage Factor

(+1.3±0.2), from VISHAY Micro-Measurements, are used to build a loadcell for force measurements. A rotatory inductive position sensor (RIPS-500), from Positek Limited® is used for displacement measurements. The sensor has an angular range up to 100 degrees. The rotatory sensor is used at an excitation voltage of +15V.

National Instrument hardwares are used for data acquisition. A SCXI-1321 terminal block is connected to a SCXI-1121 module, which is further connected to a

SCXI-1000 chassis. The analogue signal collected from this setup is converted to a digital signal using a PCI-MIO-16E-1 analogue-to-digital (A/D) card installed on a PC.

7.3 Device Setup

An existing Charpy device has been modified and instrumented. A schematic of the device is shown in Figure 7.1. The device consists of a movable and a fixed clamp.

The fixed clamp also acts as a loadcell and is used for force measurements. The

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movable clamp is made of wood. The hammer arm is equipped with heavy weights and is allowed to fall from a certain height. A high kinetic energy achieved at the bottom

(which corresponds to an impact velocity of 3.95 m/s) is used to cause failure in a polymeric film clamped between the fixed and movable clamp. The moving end of the hammer arm is designed such that it passes through the fixed clamp without any contact. The hammer then hits the movable clamp and takes it along with itself, thus causing failure in the sample at a high speed. Small grooves in the hammer arm hold the movable clamp and prevent any sliding between them.

RIPS (Rotatory Inductive Position Sensor)

Load Cell Setup

Figure 7.1 Schematic representation of the modified Charpy device with a load-cell setup

Displacement measurement is done with the RIPS attached at the axis about which the hammer rotates. A schematic of the load cell setup is shown in Figure 7.2. As

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load is applied to one end of the cantilever beam, a compressive and tensile strain (both equal in magnitude) develops on the two sides. From simple beam theory, it is known that this strain is directly proportional to the applied load, see equation 1.

Movable Clamp Sample

Fixed Clamp

Strain Load Cell Gage (Cantilever Beam)

Figure 7.2 Schematic of the movable and fixed clamps. The fixed clamp is a cantilever beam and acts as load-cell

6P(L − x) ε = (1) xx Ewt 2 here, ‘P’ is the applied load, ‘x’ is some distance from the fixed end where strain is being measured, ‘E’ the modulus, ‘L’ the length, ‘w’ the width and ‘t’ the thickness of the cantilever beam. The measurement of strain using strain-gage gives a direct estimate of the force (according to equation 1). Four strain gages are attached to the cantilever beam, two on the compressive side and two on the tensile side as shown in Figure 7.3.

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The gages are attached near the fixed-end of the cantilever beam (region of maximum strain) in order to maximize the sensitivity of the loadcell.

P L Strain gages

x C T

Figure 7.3 Schematic representation of the custom designed load-cell. Two strain- gages are attached on the two sides, but only one is shown on each side

The strain gages are connected to a SCXI-1321 terminal block to develop a full wheatstone bridge configuration. The gages in tension (or compression) are connected to the opposite legs of the bridge in order to maximize the sensitivity of the bridge. In this connection the axial component is negated and only the bending component is measured. The module SCXI-1121 provides an excitation voltage of 10V to the bridge.

The analog output from the wheatstone bridge and the RIPS is acquired and converted into digital signal using an A/D converter from National Instruments. The data acquisition is done at a rate of 20k Hz for both force and displacement measurements.

Calibrations were performed in order to translate the output obtained in voltage to force and displacement. The loadcell was calibrated by hanging dead weights to the cantilever beam while the rotatory sensor (RIPS) was calibrated by manually measuring

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the angle of the hammer arm. Figure 7.4 shows the voltages obtained at different weights (a) and at various angles of the hammer arm (b). Both of them show a linear response.

30 y = 211.91x - 0.1454 25 20 15 10 Force (N) Force 5 0 0 0.05 0.1 0.15 Voltage

(a)

70 s y = 11.908x - 22.778 60 50 40 30 20 10 Angle in degree 0 02468 Voltage

(b) Figure 7.4 Calibrations curves for the: (a) cantilever beam load cell, (b) rotatory indicative position sensor (RIPS)

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7.4 Working Principle

As the hammer falls due to gravity and hits the movable clamp a large force is transferred in a very short span of time. This generates an impulse, which is transferred to the cantilever beam loadcell through the sample. As a result the cantilever beam is set to free oscillations. The amount of impulse transferred is dependent on the stiffness of the material being tested. This also governs the amplitude of oscillation of the cantilever beam. After the impulse, the hammer arm takes the movable clamp along with its rotatory movement. This movement of the movable clamp thus puts a monotonic loading on the sample. Due to the combined effect of the cantilever beam oscillations and the movable clamp movement, the sample receives a monotonic loading which is superimposed with the harmonic oscillations of the cantilever beam.

The frequency of oscillations of the cantilever beam is a function of both the material and geometry and is given by equation 2.

3 1 K 1 Ew ⎛ t ⎞ N = = ⎜ ⎟ (2) 2π m 2π 4m ⎝ L ⎠ where, ‘K’ is the bending stiffness and ‘m’ is the effective mass located at the center of mass of the cantilever beam. Eq.2 shows that the frequency response of the cantilever beam has a strong dependence on the thickness as well as on the length of the cantilever beam. Based on this model a series of loadcells have been designed with varying thickness. Table 7.1 shows the dimensions along with the natural frequency response measured in comparison with the predicted ones. The frequency response is seen to increase with the thickness and measured values match with the predicted values using equation 2.

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Table 7.1 Natural frequency (theoretical and measured) response of various loadcells Natural frequency Natural frequency L (mm) w (mm) t (mm) Predicted* Measured Loadcell-1m 45 31 1.3 119 115 Loadcell-2m 42 31 1.92 297 224 Loadcell-3m 42 31 3.09 521 430 Loadcell-8m 45 15 8 836 833 * The predicted values are calculated using eq. 2.

A typical response of an elastomeric material using this device is shown in

Figure 7.5. Note the sample receives a monotonic loading, which is superimposed with the harmonic oscillations of the cantilever beam. As the sample fails, the cantilever beams is set free to oscillate about its mean axis (at rest) with a decay response which associated with the cantilever loadcell alone. However during the sample deformation, the decay observed is a combined response of the cantilever loadcell and that of the polymer sample.

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100 Angle (deg.) Vs time 80 Force (N) Vs time

60 40

20 0 -201.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2

-40 -60 Time (s)

Figure 7.5 A typical response of an elastomeric material (SEBS-18-cyl) using this device. Force is measured by the custom designed loadcell while the angle is measured by the rotatory sensor which gives a measure of displacement

The device by itself can be considered equivalent to a spring-mass system with damping as shown in Figure 7.6. The equation of motion for this system, with the applied force set equal to zero, can be written in the form:

mu&&(t) + cu&(t) + ku(t) = 0 (3) here, ‘m’ is the mass, ‘k’ is the spring constant, ‘c’ is the damping coefficient and ‘u’ is the displacement.

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Figure 7.6 Spring-mass system with damping

The solution to equation 3 is of the form:

u(t) = Gest (4) here, ‘G’ is a constant and ‘s’ is time constant. Substituting eq.4 in eq.3 and introducing notation for natural frequency (ω = √(k/m)) leads to:

c s2 + s +ω 2 = 0 (5) m

The value of ‘s’, which can be derived from the expression above, depends on the value of ‘c’; thus the type of motion represented by eq.4 will depend on the damping in the system. For, c = 0 there is no damping in the system and the solution represents a simple harmonic motion. If damping is present in the system, the solution of eq.5 which defines the response is given by:

2 c ⎛ c ⎞ s = − ± ⎜ ⎟ −ω 2 (6) 2m ⎝ 2m ⎠

Three types of motion are represented by this expression, according as the quantity under the square-root sign is positive, negative, or zero. For a limiting case, the radical vanishes and this is called the critical damping (cc = 2mω). If the damping is less than critical (also called under-damping), it is evident that c < 2mω and thus the

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radical in eq.6 is negative. To evaluate the free vibration response in this case, it is convenient to express the damping as a ratio ξ to the critical damping value; thus

c c ξ = = (7) cc 2mω in which ξ is called the damping ratio. Introducing eq.7 into eq.6 leads to:

s = −ξω ± ()ξω 2 − ω 2 (8) and introducing a new symbol ωD gives:

s = −ξω ± iω D (9)

2 where, ωD = ω 1−ξ (10)

The quantity ωD is called the damped vibration frequency. The free vibration response of an underdamped system can be evaluated by substituting eq.9 in to eq.4 and is described by the equation below:

−ξωt u(t) = ρe cos(ωDt −θ ) (11)

1/ 2 ⎧ 2 ⎫ ⎪⎡u&(0) + u(0)ξω ⎤ 2 ⎪ ρ = ⎨⎢ ⎥ + []u(0) ⎬ ω where, ⎩⎪⎣ D ⎦ ⎭⎪ u(0) + u(0)ξω θ = tan −1 & ωDu(0)

A typical example of free-vibrations in under-damped system is shown in Figure 7.7.

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u u(0) 0 u1 u2

Figure 7.7 Free-vibration response of under-damped system

7.5 Results and Discussion

The device has been used to test various thermoplastic elastomers (TPEs). An example is shown in Figure 7.8a, where this device was able to distinguish between

SEBS tri-block copolymer (SEBS-18) with spherical and cylindrical morphology using selective solvents as described in chapter 4. Figure 7.8b shows the response of two

TPEs obtained at a crosshead speed of 10 mm/min using a conventional Instron

Machine. Loadcell-3m was used for this test.

18 Spherical 15

9 Cylindrical 6 Stress (MPa) 3

0 246810 Extension ratio (λ)

Figure 7.8 Tensile response of spherical and cylindrical block copolymers: (a) using instrumented Charpy device, (b) conventional Instron machine

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The cylindrical block copolymer (SEBS-18-cyl) was further investigated using loadcell-8m to measure the visco-elastic response, see Figure 7.9. A higher frequency loadcell is used, as it captures a better harmonic response compared to a lower frequency loadcell. In order to estimate the visco-elastic response, the data obtained in

Figure 7.9 can be analyzed before and after the sample-failure separately using eq.11.

Here, it is assumed that the rate of monotonic loading is much slower than the rate at which the cantilever beam oscillates. Thus the decay response during the sample deformation can be decoupled from the combined response of monotonic loading and oscillations. Figure 7.10 shows the oscillatory response of the sample, where the monotonic loading response has been subtracted from the response seen in Figure 7.9.

1.2

0.8

0.6

0.4

0.2

Stress (MPa) Stress 0 2 2.5 3 3.5 4 4.5 5 -0.2

-0.4 Angle (volts)

-0.6

-0.8

Figure 7.9 High speed tensile response of SEBS-18-cyl

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0.050

0.025

0.000

-0.025 Stress Amplitude (volts) Amplitude Stress -0.050 0.000 0.003 0.006 0.009 0.012 0.015 Time (s)

Figure 7.10 Oscillatory response of SEBS-18-cyl obtained from Figure 7.9 after subtracting the monotonic loading signal

The amount of damping can be evaluated in terms of the damping ratio ‘ξ’ from such a response using eq. 12 by considering response peaks which are several cycles apart, say ‘l’ cycles.

c u − u = ξ = n n+l (12) 2mω 2lπun+l

However, considering the extent of scattering observed in Figure 7.10, a Sine Damp function (see eq. 11) is fit to the data using Origin® software (see Figure 7.11) instead of usng eq.12.

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Data: Data1_B Model: SineDamp

0.050 -x/t Chi^2 = 0 y(x) = Ae 0 Sin(π (x-x )/w) c R^2 = 0

xc 1.5 ±-- w 0.00058 ±-- t0 0.03 ±-- 0.025 A0.04±--

0.000

-0.025

Stress Amplitude (volts) -0.050 0.000 0.003 0.006 0.009 0.012 0.015 Time (s)

Figure 7.11 Sine-Damp function fit to the data in Figure 7.10

After the sample-failure, in Figure 7.9, cantilever loadcell shows a pure under- damping response. Free-vibration response of such an under-damped system (a spring- mass system with damping) is also shown in Figure 7.7. A Sine-Damp function is again fit to the data obtained after the sample-failure and is shown in Figure 7.12. The damping ratio (ξ) values obtained at room temperature using the non-linear curve fitting in Figure 7.11 and 7.12 are shown in Table 7.2. The damping ratio of the sample is obtained by subtracting the device response from the combined response. In addition,

Table 7.2 shows the damping ratio of this block copolymer obtained using a conventional Dynamic Mechanical Analyzer (DMA) at different frequencies and at 25

°C for comparison.

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Data: Data1_B Model: SineDamp -x/t y(x) = Ae 0 Sin(π (x-x )/w) c Chi^2 = 0 0.6 R^2 = 0

xc 0.0009 ±-- w 0.00058 ±-- 0.4 t0 0.05 ±-- A 1600000000 ±-- 0.2

0.0

-0.2

-0.4 Stress (MPa) -0.6

-0.8 1.086 1.089 1.092 1.095 Time (s)

Figure 7.12 Sine-Damp function fit to the data in Figure 7.9 after sample-failure

Table 7.2 Damping ratio values obtained using instrumented charpy device and a conventional DMA

Material Device Used Damping Ratio Frequency (Hz) Device Instrumented Charpy 3.7 x 10-3 833 SEBS-18-cyl + Device Instrumented Charpy 6.2 x 10-3 833 SEBS-18-cyl Instrumented Charpy 2.5 x 10-3 833 SEBS-18-cyl DMA 0.101 10 SEBS-18-cyl DMA 0.135 25 SEBS-18-cyl DMA 0.0675 50

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7.6 Conclusions

A high strain rate tensile testing device has been set up. Custom designed loadcell has been used for force measurements, where cantilever beam shape is used for its simple geometry. Four sets of strain gages are used to form a full wheatstone bridge configuration whose output is calibrated to get force response. A rotatory sensor is used for displacement measurement. Therefore a simultaneous measurement of force and displacement is possible at a high speed of 4 m/s. The device can thus be used to perform high strain rate tensile testing at much higher strains. During the test, sample receives a monotonic loading which is superimposed with the harmonic oscillations of the cantilever beam. Such a response can be used to analyze visco-elastic response of polymeric films at frequencies much higher than a conventional DMA. The harmonic response can be easily controlled from the design of the cantilever load-cell.

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CHAPTER 8

FINAL COMMENTS AND FUTURE WORK

In this thesis, we have described the structure-process-property relationships in

SEBS TPEs in detail. We have shown that it is essential to understand the deformation mechanism in order to understand the relationships between the structures at different length scales. The knowledge of microbuckling behavior during deformation of cylindrical and lamellar block copolymers, explains the correlation between the elastic modulus and the cylinder diameter (or d-spacing).

A mechanism of deformation in lamellar systems that occurs in three dimensions has been described. Here we have outlined a nice experimental path for

TEM and SAXS analysis in deformed state on this material to allow for more detailed investigation. A distinct feature observed is the formation of a meridian peak in SAXS.

A similar signal (although weak) was also observed by Thomas and coworkers[42] during perpendicular deformation of highly oriented lamellar block copolymer systems.

In our transversely isotropic lamellar system the intensity of this signal increases with strain, whereas it decreases and later diminishes at higher strains for Thomas and coworkers. Although a model has been proposed based on the three-dimensional investigation using SAXS and TEM, more work has to be done to further prove this model.

In conclusion, we have outlined a methodology to describe deformational mechanisms done at various levels deformation. We have clearly shown an anisotropic

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response in unstretched and stretched states. Rich structural details occur upon deformation and further controlled experiments may be required.

It is interesting to note that in the deformation calorimetry studies during the period of time when the displacement is stopped and the material is hold at a constant displacement for a couple of minutes, it undergoes a stress relaxation. During this time the internal energy shows a decrease. This indicates the internal energy changes during stress relaxation. Future work can be done to further understand the energetics of viscoelastic behavior such as relaxation and creep.

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