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This is to certify that the
dissertation entitled

CHARACTERIZATION OF THE THERMODYNAMICS AND

DEFORMATION BEHAVIOR OF STYRENE-BUTADIENE- '

STYRENE GRAFTED WITH POLYHEDRAL OLIGOMERIC
SILSESQUIOXANES

presented by

Daniel B. Drazkowski

has been accepted towards fulﬁllment
of the requirements for the

Ph. D. degree in Materials Science

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M 30““, 2002

Date

 

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CHARACTERIZATION OF THE THERMODYNAMICS AND DEFORMATION
BEHAVIOR OF STYRENE-BUTADIENE-STYRENE GRAFTED WITH
POLYHEDRAL OLIGOMERIC SILSESQUIOXANES
By

Daniel B. Drazkowski

A DISSERTATION
Submitted to
Michigan State University
in partial ﬁilﬁllment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY

Department of Chemical Engineering and Materials Science

2007

ABSTRACT
CHARACTERIZATION OF THE THERMODYNAMICS AND DEFORMATION
BEHAVIOR OF STYRENE-BUTADIENE-STYRENE GRAF TED WITH
POLYHEDRAL OLIGOMERIC SILSESQUIOXANES
By
Daniel B. Drazkowski

This research study uses a model nanostructure-copolymer system in order to
develop a ﬁmdamental understanding of how polymers are affected by functionalized
nanostructures. For this study, polyhedral oligomeric silsesquioxanes (POSS) was
chosen as the model nanostructure and polystyrene-block-polybutadiene-block-
polystyrene copolymer (SBS) as the model polymer host. The choice of materials and
chemical reaction scheme for grafting the SBS-POSS copolymers allows for reproducible
products with the opportunity for wide selection of nanostructure grafting fractions.

In order to examine the effects that the nanostructure’s electronic properties have
on the host polymer, the organic group of the POSS nanostructures was varied. To
facilitate a rigorous comparison, four sterically similar, yet electronically different POSS
derivatives were selected (cyclopentyl (Cp), cyclohexyl (Cy), cyclohexenyl (Cye), and
phenyl (Ph)). Ph-POSS results in the greatest changes relative to the ungraﬁed SBS
block copolymer because its chemistry has the largest contrast to the block in which it is
grafted (polybutadiene) while simultaneously having the largest aﬁinity toward the
ungraﬁed block (polystyrene).

All four of the cyclic POSS were found to have some afﬁnity toward the

polystyrene phase, so iBu-POSS was investigated in order to observe the effects of

incorporating a noninteracting nanostructure. Two host morphologies were examined in

order to compare noninteracting (iBu) and strongly interacting (Ph) POSS nanostructures.
The morphology and phase behavior observed for noninteracting POSS is consistent with
simply changing polystyrene content with no noticeable change in x. Furthermore, local
and long-ranged order of the morphology is well-preserved. The interacting
nanostructures reduce x substantially and disrupt the local order of the morphology,
which is equivalent to a compatibilizing effect.

Deformation was studied to supplement the previous ﬁndings regarding the
equilibrium morphology, and give further information on the nature of the interactions
between POSS-polymer and POSS-POSS interactions. The mechanical properties for
both the grafted copolymers inherently drop because nanostructure grafting reduces the
polystyrene content. For the noninteracting iBu-POSS, the reduction in mechanical
properties was consistent with the fraction of polystyrene because the nanostructures are
noninteracting with the polystyrene block and do not qualitatively change the
morphology. This was observed at both low (30°C) and high (70°C) temperatures. The
interacting Ph-POSS behavior is more complex. With increasing Ph-POSS, the
morphology becomes more disrupted which should result in an additional drop in
mechanical properties. However, there is reinforcement at larger concentrations of Ph-
POSS. The disrupted morphology of the 10% and 20% Ph-POSS results in a smaller
grain size, which together with the presence of POSS crystallites reinforce, or network,
the morphology. Low strain reinforcement is more prominent at lower temperatures. At
high temperatures (but still below Tgys), the drop in mechanical preperties from the
disrupted morphology order outweighs the low strain reinforcement effects. Some

reinforcement is still observed at these higher temperatures due to POSS-POSS effects.

To Jenni

iv

ACKNOWLEDGEMENTS

I would ﬁrst like to thank Professor Andre Lee for the guidance and assistance
that he has provided me throughout the completion of this work. I would also like to
thank Professors Martin A. Crimp, Krishnamurthy Jayaraman, and Dahsin Liu for their
time and effort in serving on my doctoral committee.

I would like to thank ChemMatCARS, the Advanced Photon Source, and
Argonne National Lab for the use of their facilities in regards to the x-ray scattering
experiments. In particular, I would like to thank Dr. David J. Cookson and Dr. Jim
Viccaro. Dr. Cookson was able to answer many of the questions that I had small-angle
scattering, and the software that he has developed and reﬁned assisted me greatly in the
analysis of my scattering data.

I would like to thank the Air Force Research Lab at Edwards Air Force Base in
California and Dr. Timothy S. Haddad for developing and performing the chemistry in
this study. I would also like to thank the Air Force Ofﬁce of Scientiﬁc Research for their
funding.

Finally, I would like to thank Michigan State, the Department of Chemical

Engineering and Materials Science.

TABLE OF CONTENTS

 

 

 

 

 

 

LIST OF TABLES viii

LIST OF FIGURES ix

KEY TO SYMBOLS OR ABBREVIATIONS xvi
CHAPTER 1.

INTRODUCTION 1

1.1. INTRODUCTION AND BACKGROUND ................................................................. 1

1.2. RESEARCH OBJECTIVES .................................................................................... 9
CHAPTER 2.

THE SIGNIFICANCE OF NANOSTRUCTURE CHEMISTRY ON THE MORPHOLOGY AND

TRANSITION TEMPERATURES IN POSS-GRAFTED SBS COPOLYMERS 11

2.1. INTRODUCTION ............................................................................................... 11

2.2. EXPERIMENTAL .............................................................................................. 13

2.2.1. General information in synthesis ................................................... 13

2.2.2. Sample Preparation ........................................................................ 13

2.2.3. Small-Angle X-ray Scattering (SAXS) .......................................... 14

2.2.4. Rheological Characterization ......................................................... 19

2.3. RESULTS AND DISCUSSION ............................................................................. 19

2.3.1. Effect of POSS moieties on Morphology ...................................... 19

2.3.2. Effect on the Order-Disorder Transition ........................................ 33

2.3.3. Effect on the Rheology .................................................................. 39

2.4. CONCLUSIONS ................................................................................................ 44
CHAPTER 3.

PHASE BEHAVIOR OF POSS-GRAFED SBS WITH NONINTERACTING OR INTERACTING

POSS NANOSTRUCTURES 46

3.1. INTRODUCTION ............................................................................................... 46

3.2. EXPERIMENTAL .............................................................................................. 48

3.2.1. Materials ........................................................................................ 48

3.2.2. X-ray Scattering ............................................................................. 49

3.2.3. Rheology ........................................................................................ 51

3.3. RESULTS AND DISCUSSION ............................................................................. 52

3.3.1. Equilibrium Morphology ............................................................... 52

3.3.2. Morphology Transitions ................................................................. 72

3.4. CONCLUSIONS ................................................................................................ 84

vi

CHAPTER 4.
DEFORMATION BEHAVIOR OF POSS-GRAFTED SBS: MECHANICAL PROPERTIES,

 

 

 

MORPHOLOGY, AND POSS NANOSTRUCTURES 88

4.1. INTRODUCTION ............................................................................................... 88

4.2. EXPERIMENTAL .............................................................................................. 89

4.2.1. Materials ........................................................................................ 89

4.2.2. Mechanical Testing ........................................................................ 90

4.2.3. X-ray scattering .............................................................................. 90

4.3. RESULTS AND DISCUSSION ............................................................................. 92

4.3.1. Mechanical Testing ........................................................................ 92

4.3.2. Small Angle X-ray Scattering ...................................................... 117

4.3.3. Wide-angle X-ray Scattering (WAXS) ........................................ 130

4.4. CONCLUSIONS .............................................................................................. 136
CHAPTER 5.

CONCLUSIONS AND RECOMMENDATIONS - 137

5.1. CONCLUSIONS .............................................................................................. 137

5.2. RECOMMENDATIONS .................................................................................... 139

APPENDIX 142

CALCULATION FOR THE VOLUME FRACTION OF POLYSTYRENE ........................... 142

CALCULATIONS FOR N ......................................................................................... 143

CALCULATIONS FOR THE FORM FACTOR MINIMA: ............................................... 143

HERMAN’S ORIENTATION FUNCTION ................................................................... 147

TENSILE DEVICE FOR IN-SITU DEFORMATION EXPERIMENTS USING SAXS ......... 148

EXPERIMENTAL CALCULATIONS FOR STRETCHING DEVICE STRAIN .................... 150

REFERENCES 155

 

vii

LIST OF TABLES

Table 2.1. GPC data for pure and Ph-POSS grafted SBS. MW and Mn are weight average
and number average molecular weights respectively (determined by GPC in units of
kiloDaltons). PDI is the polydispersity index (MW/Mn). ................................................... 29

Table 3.1. Comparison of Host SBS. Mn and M... are number-average and weight-
average molecular weights, respectively (determined by GPC in units of kiloDaltons).
PDI is the polydispersity index (MW/Mn). Weight percent of polystyrene is listed by the
manufacturer and veriﬁed by integration of NMR signals. Self-assembled morphology is
determined by small-angle X-ray scattering at room temperature ..................................... 50

Table 3.2. Form Factor Minima for SBS-POSS Copolymers. The entire C-series and
20% L-Series were calculated using the cylindrical form factor. The lamellar form factor
was used for the 0%, 5%, and 10% L-series. qml and qmz are the ﬁrst and second form

factor minima respectively. q* is the position of the primary diffraction peak. ............... 61

Table 4.1. Values are calculated using Eyring’s model on the flow of solids. V7 is based
on the data at 70°C and AH is calculated using the data from the 0.0058'l Henky strain
rate .................................................................................................................................... 116

viii

LIST OF FIGURES

Figure 1.1. A schematic of the classical block copolymer morphologies of spherical (S),
cylindrical (C), and lamellar (L) along with the complex gyroid (G) and perforated layer
(PL) morphologies. This ﬁgure is after Matsen et al. J. Chem. Phys. 1999, 111, 7140. ....3

Figure 1.2. An experimentally determined phase diagram for polystyrene-polyisoprene
diblock copolymers. The degree of segregation, xN, is plotted vs. the fraction of
polystyrene, ﬁg. The morphologies represented in the diagram include Spherical (S),
cylindrical (C), and lamellar (L) are displayed schematically along with the complex
gyroid (G) and perforated layer (PL) morphologies. This ﬁgure is after Khandpur, A. K.
et al., Macromolecules 1995, 28, 8796. ............................................................................... 5

Figure 1.3. The reaction scheme for grafting of a POSS-hydride to the SBS triblock
copolymer. The POSS nanostructure can be chosen to have a selected chemistry. Some
potential chemical substituent groups are also listed. .......................................................... 8

Figure 2.1. Two dimensional SAXS pattern of pure SBS at 130°C. ............................... 16

Figure 2.2. SAXS intensity versus scattering vector, q, based on 360° azimuthal
integration of a 2-D image as depicted in Figure 2.1. ........................................................ 17

Figure 2.3. Integrated SAXS intensity versus scattering vector, q, for SBS triblock
copolymers grafted with cyclopentyl-POSS (Cp) at 130°C: SBS control with no POSS, 5
wt% POSS, 10 wt% POSS, 20 wt% POSS. ....................................................................... 21

Figure 2.4. Integrated SAXS intensity versus scattering vector, q, for SBS triblock
copolymers grafted with cyclohexyl-POSS (Cy) at 130°C: SBS control with no POSS, 5
wt% POSS, 10 wt% POSS, 20 wt% POSS. ....................................................................... 22

Figure 2.5. Integrated SAXS intensity versus scattering vector, q, for SBS triblock
copolymers grafted with cyclohexenyl-POSS (Cye) at 130°C: SBS control with no
POSS, 5 wt% POSS, 10 wt% POSS, 20 wt% POSS. ........................................................ 23

Figure 2.6. Integrated SAXS intensity versus scattering vector, q, for SBS triblock
copolymers grafted with phenyl-POSS (Ph) at 130°C: SBS control with no POSS, 5 wt%
POSS, 10 wt% POSS, 20 wt% POSS. ............................................................................... 24

Figure 2.7. The ﬁrst-order peak width at half maximum versus varying amount of POSS
nanostructures with speciﬁed moiety of POSS as indicated (0) cyclopentyl, Cp-POSS
(A) cyclohexenyl, Cy-POSS (V) cyclohexenyl, Cye-POSS (O)pheny1, Ph-POSS. ....... 27

Figure 2.8. d-Spacing of SBS triblock copolymer graﬁed with varying amounts of

speciﬁed moiety of POSS at 130°C: (0) cyclopentyl, Cp-POSS (A) cyclohexenyl, Cy-
POSS (V) cyclohexenyl, Cye-POSS (O) phenyl, Ph-POSS. ............................................ 31

ix

Figure 2.9. d-spacing of SBS triblock copolymer grafted with varying amounts of
speciﬁed moiety of POSS at 150°C: (0) cyclopentyl, Cp-POSS (A) cyclohexenyl, Cy-
POSS (V) cyclohexenyl, Cye-POSS (O) phenyl, Ph-POSS. ............................................ 32

Figure 2.10. Rheological behavior as represented by the storage modulus, G'((o) and
SAXS proﬁle as represented by the full-width at the half maximum of the ﬁrst-order
peak, 1", at the order-disorder region for pure SBS. ........................................................... 34

Figure 2.11. A comparison between Tom obtained from rheological and SAXS
measurements for Ph moiety of POSS. .............................................................................. 37

Figure 2.12. Tom of varying amounts of different moieties of POSS as determined using
rheological measurement. (0) cyclopentyl, Cp-POSS (A) cyclohexenyl, Cy-POSS (V)
cyclohexenyl, Cye-POSS (O) phenyl, Ph-POSS. .............................................................. 38

Figure 2.13. Storage modulus, G'(co), as a function of temperature at 1 radian per second
for pure and 10 wt% of POSS with Speciﬁed moiety as indicated. (Cl) pure SBS (A)
cyclohexenyl, Cy, POSS (V) cyclohexenyl, Cye, POSS (O) phenyl, Ph, POSS .............. 40

Figure 2.14. Storage modulus, G'(co), as a function of temperature at 1 radian per second
for pure and 20 wt% POSS with Speciﬁed POSS moiety as indicated. (CI) pure SBS (A)
cyclohexenyl, Cy, POSS (V) cyclohexenyl, Cye, POSS (O) phenyl, Ph, POSS .............. 42

Figure 2.15. Data for computing rheological and SAXS Tom for 20 wt% Ph-POSS ..... 43

Figure 3.1. Intensity vs. scattering vector, q, at 130°C for C-Series SBS (Vector® 8508)
grafted with isobutyl-POSS (iBu). At this temperature, the pure C-Series and iBu—POSS
grafted copolymers have a cylindrical morphology. The 2-D SAXS images were
integrated 360° azimuthally to obtain the proﬁles plotted in this ﬁgure, and the data are
shifted along the log intensity axis to increase clarity (5% -0.7, 10% -1.4, 20% -2.1). ....53

Figure 3.2. Intensity vs. scattering vector, q, at 130°C for C-Series SBS (Vector® 8508)
grafted with phenyl-POSS (Ph). At this temperature, the pure C-series and Ph-POSS
grafted copolymers have a cylindrical morphology. The 2-D SAXS images were
integrated 360° azimuthally to obtain the proﬁles plotted in this ﬁgure, and the data are
shifted along the log intensity axis to increase clarity (5% -0.7, 10% -1.4, 20% -2.l). ....54

Figure 3.3. Intensity vs. scattering vector, q, at 130°C for L-series SBS (V ector® 6241)
grafted with isobutyl-POSS (iBu). At this temperature, the pure L-series along with the
5% and 10% iBu-POSS grafted copolymers have a lamellar morphology, but the 20%
iBu-POSS copolymer has a cylindrical morphology noted by the change in structure
factor. The 2-D SAXS images were integrated 360° azimuthally to obtain the proﬁles
plotted in this ﬁgure, and the data are shifted along the log intensity axis to increase
clarity (5% -1.3, 10% -2.6, 20% -3.9) ................................................................................ 55

Figure 3.4. Intensity vs. scattering vector, q, at 130°C for L-series SBS (V ector® 6241)
grafted with phenyl-POSS (Ph). At this temperature, the pure L-series and Ph-POSS
grafted copolymers have a lamellar morphology. The 2-D SAXS images were integrated

360° azimuthally to obtain the proﬁles plotted in this ﬁgure, and the data are shifted
along the log intensity axis to increase clarity (5% -1.3, 10% -2.6, 20% —4.6). ................ 56

Figure 3.5. The d-spacing normalized to the unmodiﬁed SBS for the C-series and L-
series at 130°C. For the L-series iBu-POSS (I), there is a change in morphology from
lamellar (0 to 10 wt%) to hexagonally packed cylinders (20 wt%). 61100 for the cylindrical
morphology corresponds to the nearest neighbor cylinder spacing which is consistent
with the lamellar d-spacing. Error bars are on the order of the symbol Size and were
removed for clarity. The d-spacing for unmodiﬁed C-series and L-series SBS are
25.71nm and 25.41nm respectively. .................................................................................. 64

Figure 3.6. Primary scattering peak width, F, is normalized to unmodiﬁed SBS for the
C-series and L-series SBS grafted with iBu and Ph-POSS at 130°C. Peak width is
measured as the full width at half the maximum scattering peak height on a plot of
intensity vs. q. Peak width for unmodiﬁed C-Series and L-series SBS are approximately
0.0168nm'l and 0.0129nm'l respectively. .......................................................................... 68

Figure 3.7. X-ray scattering data is plotted in the q-range for crystalline POSS for the C-
series. The intensity is in arbitrary units and is normalized to constant incident and
transmitted intensities. Crystalline POSS diffraction can be observed near q ~ 5 .87nm'l
((1 ~ 10.7A), and amorphous polymer scattering at q ~ 14nm'l (d ~ 4.5A). ...................... 70

Figure 3.8. X-ray scattering data is plotted in the q-range for crystalline POSS for the L-
series. The intensity is in arbitrary units and is normalized to constant incident and
transmitted intensities. Crystalline POSS diffraction can be observed near q ~ 5.87nm'l
(d ~ 10.7A), and amorphous polymer scattering at q ~ 14nm'l (d ~ 4.5A). ...................... 71

Figure 3.9. Storage modulus, G', versus temperature for C-series (Vector® 8508) SBS
grafted with varying amounts of isobutyl-POSS (iBu). G' was obtained using small-
strain oscillatory Shear with strain amplitude of 2% and oscillatory frequency of l
radian/s. The temperature ramp rate was 2°C/min. The rheological experiments were
done in a dry nitrogen environment to reduce thermal degradation. All four copolymers
plotted undergo a cylindrical to disorder transition. .......................................................... 73

Figure 3.10. Storage modulus, G', versus temperature for C-series (V ector® 8508) SBS
grafted with varying amounts of phenyl-POSS (Ph). G' was obtained using small-strain
oscillatory shear with strain amplitude of 2% and oscillatory frequency of l radian/s. The
temperature ramp rate was 2°C/min. The rheological experiments were done in a dry
nitrogen environment to reduce thermal degradation. All four copolymers plotted
undergo a cylindrical to disorder transition. ...................................................................... 74

Figure 3.11. Storage modulus, G', versus temperature for L-Series (Vector® 6241) SBS
grafted with varying amounts of isobutyl-POSS (iBu). G' was obtained using small-
strain oscillatory shear with strain amplitude of 2% and oscillatory frequency of 1
radian/S. The temperature ramp rate was 2°C/min. The rheological experiments were
done in a dry nitrogen environment to reduce thermal degradation. Pure SBS and 5%
iBu-POSS undergo a lamellar to disorder transition, 10% undergoes a lamellar to

xi

cylindrical and cylindrical to disorder transitions, and 20% iBu-POSS undergoes a
cylindrical to disorder transition. ....................................................................................... 75

Figure 3.12. Storage modulus, G', versus temperature for L-Series (V ector® 6241) SBS
grafted with varying amounts of phenyl-POSS (Ph). G' was obtained using small-strain
oscillatory Shear with strain amplitude of 2% and oscillatory frequency of 1 radian/S. The
temperature ramp rate was 2°C/min. The rheological experiments were done in a dry
nitrogen environment to reduce thermal degradation. All four copolymers plotted
undergo a lamellar to disorder transition. .......................................................................... 76

Figure 3.13. The order-disorder transition temperature, Tom, is plotted for C-series SBS
grafted with iBu and Ph-POSS. Data points were calculated from rheological
measurements, and all transitions were veriﬁed by SAXS. ............................................... 78

Figure 3.14. The T001~ and Tom are plotted for L-series SBS grafted with iBu and Ph-
POSS. There is an order-order transition for the 10 wt% iBu-POSS. For iBu-POSS, I
represents the lamellar-disorder transition, A represents the lamellar-cylindrical
transition, and Y represents the cylindrical-disorder transition. For Ph-POSS, the o
symbol represents the cylindrical-disorder transition. Data points were calculated from
rheological measurements, and all transitions were veriﬁed by SAXS. ............................ 79

Figure 3.15. The ﬁgure shows qu plotted vs. q/q* (where q* is the q-position of the
primary peak) for L-series 10% iBu-POSS at 130°C (I), 195°C (0), and 210°C (A).
The morphology is lamellar morphology at 130°C. Both lamellar and cylindrical
morphologies are present near the T001, 195°C. At 210°C only a cylindrical morphology
is present. ........................................................................................................................... 81

Figure 3.16. The transition temperatures are plotted in terms of xN vs. the volume
fraction of polystyrene, ﬂag, for both SBS series. Unmodiﬁed C-series and L-series
polymers have 0.256 and 0.389 fps, respectively. Lines are added to guide the eye and
separate the observed morphologies; solid lines connect Similar morphology transitions
and dashed lines are extrapolations. The El symbol represents the cylindrical-disorder
transition for the C-series. For the L-series, I represents the lamellar-disorder transition,
A represents the lamellar-cylindrical transition, and Y represents the cylindrical-
disorder transition. ............................................................................................................. 82

Figure 3.17. Schematic representation of the local morphology of 20% iBu-POSS
grafted copolymer (top), pure SBS (middle), and 20% Ph-POSS. Polystyrene is
represented by — (chain) and the color I, polybutadiene is represented by — (chain) and
the color white, and POSS is represented by . For 20% Ph-POSS (bottom), — — —
distinguishes the interphase region. ................................................................................... 86

Figure 4.1. Stress-Strain data for isobutyl-POSS copolymers. Testing was performed at
70°C and using a Henky strain rate of 0.0055'1 under tensile deformation for SBS-POSS
copolymers. ........................................................................................................................ 93

xii

Figure 4. 2. Stress-Strain data for phenyl- POSS copolymers. Testing was performed at
70°C and using a Henky strain rate of 0. 0053'l under tensile deformation for SBS- POSS
copolymers. ........................................................................................................................ 94

Figure 4. 3. Yield stress for the SBS- POSS copolymers at 70°C using a Henky strain rate
of O. 0053". ......................................................................................................................... 98

Figure 4. 4. The elastic modulus (or Young’s modulus) for the SBS- POSS copolymers at
70°C using a Henky strain rate of O. 0055". ....................................................................... 99

Figure 4.5. Stress-Strain data for 5 and1 10 wt% SBS- POSS copolymers at 70°C and
using a Henky strain rate of 0. 0058" under tensile deformation for SBS- POSS
copolymers. ...................................................................................................................... 101

Figure 4. 6. Stress-Strain data for isobutyl- POSS copolymers. Testing was performed at
30°C and using a Henky strain rate of 0. 0055'1 under tensile deformation for SBS- POSS
copolymers. ...................................................................................................................... 103

Figure 4. 7. Stress-Strain data for phenyl- POSS copolymers. Testing was performed at
30°C and using a Henky strain rate of 0. 0053" under tensile deformation for SBS- POSS
copolymers. ...................................................................................................................... 104

Figure 4.8. Stress-Strain data at 30°C and 0.0053" Henky strain rate for 5 and 10 wt%
SBS-POSS copolymers. ................................................................................................... 106

Figure 4. 9. Yield stress for the SBS- POSS copolymers at 30°C using a Henky strain rate
of 0.0055". ....................................................................................................................... 108

Figure 4.10. The elastic modulus (or Young’s modulus) for the SBS-POSS copolymers
at 30°C using a Henky strain rate of 0.0058". ................................................................. 109

Figure 4.11. The ratio of the yield stress, oy, at 30°C to the yield stress at 70°C for a
0. 0055'1 Henky strain rate. ............................................................................................... 111

Figure 4.12. The ratio of the elastic modulus at 30°C to the elastic modulus at 70°C for a
0.0055" Henky strain rate. ............................................................................................... 112

Figure 4.13. Yield stress data normalized to temperature (Kelvin) for three strain rates
(0.001, 0. 005, 0. 0505 ) and two temperatures (30°C and 70°C). Data 18 Shown for pure
SBS,10 wt% iBu-POSS, and 10 wt% Ph-POSS. ............................................................ 114

Figure 4.14. Two-dimensional SAXS patterns (through view) for (a) undeforrned, pure
SBS and (b) SBS deformed to a Henky strain of 0.3. Deformation was at a rate of 0.0053'
1 in the stretching direction shown (SD) and at 70°C. Intensity is in arbitrary units....118

Figure 4.15. The normalized peak width in the stretching direction is plotted vs. the
local strain, 8.0031, for all lamellar morphology copol ers. Tensile deformation was
performed at 70°C using a Henky strain rate of 0.0053' . To obtain the values of FSD, the

xiii

2-D diffraction pattern is integrated :1: 5° along the stretching direction. From the
subsequent plot of I vs. q, F is correlated to real-space measurements and is then
normalized to the undeformed peak width for each individual copolymer. .................... 120

Figure 4.16. The real-space peak width in the stretching direction is plotted vs. the local
strain, elm], for pure SBS and Ph-POSS copolymers. Tensile deformation was performed
at 70°C using a Henky strain rate of 0.005". To obtain the values of F30, the 2-D
diffraction pattern is integrated i 5° along the stretching direction. From the subsequent
plot of I vs. q, F is correlated to real-space measurements. ............................................. 122

Figure 4.17. Herman’s orientation function, f, is plotted vs. the local strain, Erocar, for the
lamellar morphology SBS-POSS copolymers under tensile deformation at 70°C using a
Henky strain rate of 0.0055". The Herman’s orientation function was calculated by
integrating over the primary scattering peak q-range. ..................................................... 124

Figure 4.18. The normalized peak width in the stretching direction is plotted vs. the
local strain, elm], for all lamellar morphology copol mers. Tensile deformation was
performed at 30°C using a Henky strain rate of 0.0055' . To obtain the values of FSD, the
2-D diffraction pattern is integrated :t 5° along the stretching direction. From the
subsequent plot of 1 vs. q, F is correlated to real-space measurements and is then
normalized to the undeformed peak width for each individual copolymer. .................... 127

Figure 4.19. Herman’s orientation function, f, is plotted vs. the local strain, elm], for the
lamellar morphology SBS-POSS copolymers under tensile deformation at 30°C using a
Henky strain rate of 0.0055". The Herman’s orientation function was calculated by
integrating over the primary scattering peak q-range. fat 1.0 Henky strain is measured at
the command strain. ......................................................................................................... 129

Figure 4.20. X-ray scattering data is plotted over a q-range of crystalline Ph-POSS
during the deformation of 20% Ph-POSS. Intensity is in arbitrary units and is normalized
to constant incident and transmitted intensities to compensate for thickness changes
during deformation. Deformation was performed at 30°C using a Henky strain rate of
0.0055". Data has been integrated 360° azimuthally. ..................................................... 131

Figure 4.21. The local Henky strain of the morphology and Ph-POSS crystallites (as
deﬁned by Equation 4.2) is plotted vs. the command Henky strain. Data are plotted for
the morphologies of pure SBS and 20% Ph-POSS along with crystallite data in the 20%
Ph—POSS copolymer. Tensile deformation was performed at 30°C using a Henky strain
rate of 0.005". .................................................................................................................. 133

Figure 4.22. The normalized peak width in the stretching direction is plotted vs. the
local strain for the morphologies of pure SBS and 20% Ph-POSS along with crystallite
data in the 20% Ph-POSS copolymer. Tensile deformation was performed at 30°C using
a Henky strain rate of 0.0055". To obtain the values of FSD, the 2-D diffraction pattern is
integrated :t 5° along the stretching direction. From the subsequent plot of I vs. q, F is
correlated to real-space measurements and is then normalized to the undeformed peak
width for each individual copolymer. .............................................................................. 134

xiv

Figure A.1. Plot of the form factor for the pure C-series and L-series SBS. ................. 146

Figure A.2. A schematic of the experimental setup for in situ deformation experiments
using small angle x-ray scattering .................................................................................... 149

Figure A.3. A schematic of the mechanical portion of the stretching device. ............... 151

XV

PDI

POSS
PS

KEY TO SYMBOLS OR ABBREVIATIONS

scattering angle

cylinder-cylinder distance

statistical segment length of polymer specie
d-spacing

d-spacing of the primary scattering peak
cylinder-cylinder distance, lamellar repeat distance
d-spacing in the stretching direction
Herman’s orientation function

volume fraction of polystyrene

isobutyl

kiloDaltons = 1000 Daltons = 1000 atomic mass units
scattering vector

position of the primary scattering peak
form factor is at a minimum

radians

weight percent

unknown parameter

arbitrary units

cylindrical morphology

cyclopentyl

cyclohexyl

cyclohexenyl

disordered morphology

structure amplitude

gyroid morphology

dynamic Storage Modulus

intensity

angular dependence of the diffracted intensity
Bessel function of the ﬁrst kind of order 1
lamellar morphology

number average molecular weight

weight average molecular weight

degree of polymerization

normalized orientation distribution function
polybutadiene

polydispersity index = Mw/Mn

phenyl

perforated layer morphology

polyhedral oligomeric silsesquioxane
polystyrene

radius

xvi

85

8 Engineering
8H

8Henky
E"Local

organic group, molar gas constant

reactive organic group

radius of gyration

spherical morphology

structure factor

small-angle X-ray scattering

styrene butadiene styrene triblock copolymer
ith solution to J1(x) = 0

thickness of the lamellae, temperature

glass transition temperature

glass transition temperature of polybutadiene
glass transition temperature of polystyrene
order-disorder transition temperature
order-order transition temperature

activation volume in which the polymer segment acts
weight fraction

wide angle X-ray scattering

strain

engineering strain

engineering strain

Henky strain

Henky strain

local strain of the morphology

applied strain rate

angle of diffraction, angular change in radians
wavelength of radiation

azimuthal angle

pi = 3.1415926535897932384626433832795...

density

stress

yield stress

chi-parameter, Flory—Huggins parameter, monomeric segregation
angular change in degrees

energy barrier for jumping,

peak width

peak width in the stretching direction

peak width at 0% strain, peak width for unmodiﬁed SBS
change

product (mathematical calculation)

degrees (angular or temperature)

xvii

CHAPTER 1.

INTRODUCTION

1.1. INTRODUCTION AND BACKGROUND

Over the last several decades, there has been a strong consumer demand to make
current technologies operate on an ever smaller scale which has lead to increasing
requirements on materials to bring these desires to practical application. Simultaneously,
fundamental research in physics on quantum theory has opened the door for new
technologies by pushing the materials scale even smaller — toward the atomic scale. This
has spawned nanotechnology as a new ﬁeld of research. Nanotechnology is the
understanding and control of matter on the length scales of 1 to 100 nanometers. At this
scale, matter functions differently from both the macroscopic level and scale of
individual atoms which presents unique material properties available for research. These
unique properties contribute to a breadth of nanotechnology application spanning from
electronics to medicine.

Block copolymers (BCPs) have received research interest over the past several
decades because of their ability to form self-assembled microstructures'f, however they
have been seriously considered for nanotechnology applications only in the last 15 years.
Their renewed interest stems from the ability to manipulate the shape and size of their
microdomains by controlling the properties of the polymer chain. In addition, BCPS offer
a cost-effective way to obtain nanoscale order over relatively large distances. Some
nanotechnology applications that block copolymers have been used in include:
nanostructured membranes, templates for nanoparticle synthesis, photonic crystals, and

high-density storage media“.

The attraction of block copolymers comes from the unique properties these
materials possess compared to their homopolymer components. The dramatic change in
properties is due to a self-assembled, ordered morphology that block copolymers are able
to attain. These properties are strongly affected by the geometry and orientation of the
morphology, so there have been many approaches to manipulate domain morphology
over the past twenty yearsé’ 9" 1.

The phase behavior of AB diblock and ABA triblock copolymers has been well-
studied in bulk and solution both theoretically and experimentally” ”'24. The
morphology of the block copolymer and its length scale depends on three critical factors:
the product xN which quantiﬁes the degree of segregation between the two blocks
species, the volume fraction of each block, and the molecular architecture (i.e. diblock,
triblock, star...) which includes copolymer asymmetry. N denotes the total degree of
polymerization, and x is the parameter which quantiﬁes the chemical interaction between
each block component. This parameter has both an enthalpic and entropic component
and scales with temperature as roughly A + B/T where A and B are constants and T is the
absolute temperature. The degree of polymerization, volume fraction of each component,
and molecular architecture are parameters that are controlled during material synthesis,
however x(T) is restricted to the choice of copolymer constituents.

At a sufﬁciently high degree of segregation, xN, block copolymer systems
undergo microphase separation into self-assembled, ordered morphologies. Figure 1.1

shows the classical block copolymer morphologies in order of increasing volume fraction

of minor component: spherical, cylindrical, and lamellar morphologies. The complex

Classical Morphologies

O O
0%
oQbO
O O
C L

8
Complex Morphologies

 

G PL

Figure 1.1. A schematic of the classical block copolymer morphologies of spherical (S),
cylindrical (C), and lamellar (L) along with the complex gyroid (G) and perforated layer
(PL) morphologies. This ﬁgure is after Matsen et al. J. Chem. Phys. 1999, 111, 7140.

gyroid and perforated lamellar morphologies may also exist in a narrow window Of
volume fractions between the cylindrical and lamellar morphologies" 12’ 25’ 26. The
speciﬁc range of minor component volume fractions needed to obtain a particular
morphology depends on the speciﬁc copolymer constituents and molecular architecture.
Upon heating, the enthalpic difference between the monomeric species is abated, x is
reduced, and the morphology will eventually undergo a transition to a disordered state at
the order-disorder transition temperature, Tom. It is also possible to have a thermally
induced transition from one ordered morphology to another at an order-order transition
temperature, Tom. Order-order transitions are only observed in small windows of
volume fraction makeup for a particular block copolymer system. A phase diagram for a
well studied diblock system can be seen in Figure 1.2. The phase diagram for a triblock
system is fundamentally similar. In fact, the same equilibrium morphologies are present,
but the position of the phase boundaries is shifted to higher xN due to the chain
connectivity of the triblock.

In current bulk applications, block copolymers are often used as a component in a
mixture of solvent or pure homopolymer. The addition of solvent or homopolymer to a
block copolymer system can change the length scale or lattice spacing of the morphology,

17. 19,20, 27. Solvents can range

the Tom and Tom, and possibly the type of morphology
from neutral to strongly selective depending on how it preferentially swells each
microdomain of the copolymer morphology. Homopolymers that are of type A or B of

the AB or ABA type copolymers have been shown to act as selective solvents in a block

copolymer-homopolymer blend, but there are limits to solubility where phase separation

 

 

 

 

C L C K S
40 F- 5 5
\ PL . ' /
.\ G /'
30 _ \'\. [fl
\
XN \ ' i /
20 "' \\‘ '/'/
\ ,/
\.\‘ ./,/
10 - Eggs;
0 l I l I I I I I I
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
ﬁg

Figure 1.2. An experimentally determined phase diagram for polystyrene-polyisoprene
diblock copolymers. The degree of segregation, xN, is plotted vs. the fraction of
polystyrene, fps. The morphologies represented in the diagram include spherical (S),
cylindrical (C), and lamellar (L) are displayed schematically along with the complex
gyroid (G) and perforated layer (PL) morphologies. This ﬁgure is after Khandpur, A. K.
eta1., Macromolecules 1995, 28, 8796.

takes placelz’ 14’ 26.

Thus understanding how solvents of varying selectivity affect the
copolymer morphology is important for block copolymer applications. The dependence
of the Tom, Tom, and lattice spacing (d-spacing) of block copolymers in neutral and
selective solvents, and the addition of homopolymer over a range of molecular weights
have been performed and documented in previous studies”’ 14’ '9’ 20’ 26'30.

Recent research interest has included the use of nanomaterials to further probe the
property space of block copolymers6’ 8’ '8’31‘42. Nanomaterials can be introduced into a
polymer system by blending or chemical attachment. Blending is simple and can be done
by a physical means, but there may be solubility limits resulting in phase separation.
Attachment requires chemistry, but nanostructure solubility is generally not an issue.
Chemical attachment can be performed during the initial polymerization reaction or by
post-polymerization grafting. During the initial polymerization, the introduction of the
nanostructure to the reactant mixture causes changes in the reaction chemistryls’ 32%.
Consequently, the reaction rates are dependent on the initial reactant and nanostructure
composition. This can make it difﬁcult to predict product molecular weight, molecular
weight distribution, and the chemical distribution along the polymer chain. The absence
of reproducibility is unfavorable for studies that hope to examine a wide range of well-
characterized materials. Post polymerization grafting, on the other hand, allows one to
use an initially well-characterized polymer system. Grafting can be performed by adding
nanostructures to a speciﬁc location (e. g. the chain end for telechelic or hemi-telechelic)
or by a random attachment to predetermined reaction sites along the polymer backbone.

In any attachment scheme, the chemistry of the attachment limits the choice of both the

host polymer and attached nanostructure.

In this study, the attachment approach is to graft a well-deﬁned nano-structured
chemical to a reactive segment of the copolymer37'39. If these nano-sized objects are on a
similar length scale to the periodicity of the block copolymer, one expects the surface
chemistry of the nano-structures to play a signiﬁcant role in altering the thermodynamics
and morphology of the copolymer matrix. A model group of nano-structured chemicals
is polyhedral oligomeric silsesquioxanes (POSS). A fully condensed POSS molecule
contains an inorganic Si-O core surrounded by organic groups. This gives the POSS a
well-deﬁned three dimensional structure, which is essential for performing a precise
scientiﬁc study. These organic groups can be chosen to effectively tune the surface
chemistry of the nanostructure and alter its interaction with the host copolymer blocks.
In this study, POSS of the type R'R7Si3012 was chosen because they allow for a variety
of choices for its organic constituents (R) and it offers a reactive group (R’). Polystyrene-
block-polybutadiene-block-polystyrene copolymer (SBS) is the model polymer host
because it offers a reaction site (1,2-butadiene segments), it is used as an engineering
material, and it is commercially available in narrow molecular weight. A chemical
reaction scheme for SBS-POSS copolymers is shown in Figure 1.3. In this reaction, the
POSS nanostructures are attached randomly to the 1,2-butadiene segments of the SBS in
prescribed amounts.

The choice of materials and chemical reaction scheme allow for ﬂexible choices
in nanostructure chemistry while maintaining precise host polymer properties (Mn,
PDI,...). The products are reproducible because grafting is done on an already

characterized polymer, so there are no confounding effects of .Mn or PDI. Additionally,

Me2

‘
RX )3 I POSS-Hydride
°\Soe~o1—i'~R +
"0’8:

R’
/ / /
O SBS 0
Platinum Catalyst
Toluene, 60°C
5, 10, 20% POSS
SiMezH
R\ 0
0,51/ \SIM Si
R‘SI 5(0))
/ O \R
o R~\ SBS POSS Copolymer
’Sl\o’SI:
R
Isobutyl Cyclopentyl Cyclohexyl Cyclohexenyl Phenyl

(iBt) (Cp) (CY) (Cye) (Ph)

Figure 1.3. The reaction scheme for grafting of a POSS-hydride to the SBS triblock
copolymer. The POSS nanostructure can be chosen to have a selected chemistry. Some
potential chemical substituent groups are also listed.

creating products that vary in nanostructure content is as simple as measuring the amount

to use as a reactant in the grafting reaction.

1.2. RESEARCH OBJECTIVES

The objective of this research is to develop a fundamental understanding of how
block copolymers are affected by the attachment of functionalized nanostructures. To
achieve this goal, the research will focus on two areas of study: thermodynamics and
deformation studies. It is not only desirable to identify the effects of the nanostructures,
but it is important to understand what factors are contributing to the observed changes.
This knowledge will not only establish a foundation of knowledge for block copolymer
systems incorporated with nanostructures, but the knowledge gained here can give insight
into the current understanding of block copolymers, nanocomposites, other areas of
nanotechnology, and the underdeveloped polymer-based quantum technology. The
knowledge gained will also aid in the design of materials through better control of the
microstructure, phase transition temperatures, and mechanical properties.

To understand thermodynamic inﬂuences on block copolymers one must examine
their morphology. The equilibrium morphology represents the lowest energy state for the
block copolymer. Changes in the morphology represent changes in the thermodynamics
of the system. It will be important to understand not only how the equilibrium
morphology is affected by nanostructure addition, but also what properties of the grafted
nanostructure contribute to the changes in morphology.

The study of deformation on the system will probe the role of the nanostructures
in the dynamics of the system. Because the mechanical properties are strongly related to

the morphology, a thorough understanding of the morphology changes is necessary.

Next, it is important to identify whether the property changes are a result of the
morphology or some other attribute of the nanostructure. Thus, one can uncover the
contribution that the nanostructures have at the nanoscopic level in determining the

mechanical properties.

10

CHAPTER 2.

THE SIGNIFICANCE OF NANOSTRUCTURE CHEMISTRY ON THE
MORPHOLOGY AND TRANSITION TEMPERATURES IN POSS-
GRAFTED SBS COPOLYMERS

2.1. INTRODUCTION

For a sufﬁciently high degree of segregation, block copolymers will undergo
micro-phase separation into self-assembled ordered morphologies” '3’ 17’ 19'2" 29’ 43'50.
Various approaches to manipulate domain morphology have been explored by

researchers over the past twentys' '3' ‘7’ ‘9‘2" 29’ 39,41 44,47-51

and have led to an important
class of engineering polymers often referred to as the thermoplastic elastomers. Hence,
the recent interest in nano-reinforced polymers has included the use of “nanomaterials” to
further explore the property space of block copolymerss’ 39’41’42. One such approach is to
append the block copolymers using a well-deﬁned name-structured chemical to a given
segment of the copolymer” 39. If these nano-sized objects are well dispersed on the
length scale comparable to periodicity of block copolymer matrix, one expects the
surface chemistry of the nano-structured chemicals and their interactions with different
components of the block copolymer to play a Signiﬁcant role in altering the
thermodynamics and morphology of the copolymer matrix. Polyhedral oligomeric
silsesquioxanes (POSS) are a type of model nano-structured chemical. A fully condensed
POSS contains an inorganic Si-O core surrounded with various organic groups useful for

tuning the surface chemistry and interaction with the host copolymer matrix. POSS

nanostructures can be either randomly blended or grafted to a particular phase of a

11

copolymer. This enables us to investigate the inﬂuence of nanomaterial chemistry on the
thermodynamics and morphology of a block copolymer matrix.

The object of this chapter is to identify the signiﬁcance of nanostructure
chemistry on the thermodynamics of the host block copolymer. To accomplish this, we
examine how the host copolymer morphology and its order-disorder transition
temperature, Tom, are affected by the chemistry of grafted nano-structured chemicals. It
is known that the addition of solvents or homopolymers to a block copolymer system can
change the length scale or lattice spacing of the morphology, the Tom and Tom, and
possibly the type of morphology. Solvents range from neutral to strongly selective
depending on how they preferentially swell each microdomain of the copolymer
morphology. Homopolymers that are of type A or B of the AB or ABA copolymers will
also exhibit behavior like that of selective solvents in a block copolymer-homopolymer
blend. Based on our previous work”, polystyrene-block-polybutadiene-block-
polystyrene (SBS) triblock copolymer was selected as the model copolymer matrix. SBS
was chosen as a host polymer because it is commercially available in narrow molecular
weight distributions, and it has been used in a wide range of applications. SBS also has
the ability to form various self-assembled morphologies that allow for direct examination
of how the insertion of a nano-structured chemical affects the morphology. The model
POSS nanostructures used in this study are inorganic silicon-oxygen cages on the order
of a nanometer in size with various organic moieties bonded to the silicon atoms" 52'56.
Four POSS moieties used in this study for grafting to SBS triblocks are all of the formula
R’RysigOn. R’ provides a single ﬂexible Si-H linkage for grafting to polybutadiene

while four different R groups, cyclopentyl (Cp), cyclohexyl (Cy), cyclohexenyl (Cye),

12

and phenyl (Ph), provide a range of sterically similar, yet electronically different organic
moieties for investigating the tunability of the POSS nanostructures. Cp and Cy-POSS
are saturated, Cye is unsaturated, and Ph is aromatic. Based on their electronic structure,
it might be assumed that Cp and Cy-POSS will have a greater afﬁnity for polybutadiene
than polystyrene, whereas Ph-POSS will have a greater afﬁnity toward polystyrene. Cye-
POSS, having an electronic structure between Cy and Ph, will likely have relative
compatibilities between the two as well. In addition, because the molecular weight and
size of each POSS molecule are nearly identical, any differences found between POSS-

grafted SBS copolymers will be directly attributable to R-group/SBS compatibility.

2.2. EXPERIMENTAL

2.2.1. General information in synthesis

The SBS used for this study of nanostructure chemistry was Vector® 6241
obtained from Dexco Polymers LP, a Dow/ExxonMobil Venture. According to the
manufacturer, it is a pure, linear symmetric triblock copolymer containing less than 1%
diblock with a polystyrene composition of 43 wt%. The number-average and weight-
average molecular weights are 71 kDa and 72 kDa, respectively. This gives SBS
respective degrees of polymerization of approximately 150-750-150. All initial POSS
trisilanols were obtained from Hybrid Plastics Inc. Details covering the synthesis of each

hydride reagent and the subsequent grafting reactions can be found in previously

published work”.

2. 2. 2. Sample Preparation
POSS-grafted SBS samples used for testing were prepared in the form of solvent

cast ﬁlms measuring approximately 0.3 mm in thickness. The copolymer samples were

13

dissolved in toluene, a neutral solvent, in a 3.0 wt% concentration. Approximately 0.5
wt% Irganox® 1010 antioxidant (relative to the polymer) was also added to the solution
to reduce possible degradation at high temperatures. The solvent was then allowed to
evaporate on glass at 20°C over a period of three days. The ﬁlms were removed from the

glass and annealed under vacuum at 60°C for seven days.

2. 2. 3. Small-A ngle X-ray Scattering (SAXS)
SAXS measurements were performed at beamline 15ID-D (ChemMatCARS) in

the Advanced Photon Source (APS) at Argonne National Laboratory. The energy of
radiation used for the experiments was 8.27 keV (AB/E =1 10"), which corresponds to an
x-ray wavelength of 1.50 A. SAXS images were collected using a two-dimensional
Bruker 6000 CCD x-ray detector with a 1024 x 1024 pixel array on a 94 x 94 mm area.
The sample to detector distance was approximately 1900 mm and was calibrated using
silver behenate.

Two types of SAXS experiments were performed: isothermal and temperature
ramp. The isothermal experiments were used to examine how the equilibrium block
copolymer morphology is affected by the type and amount of POSS grafted at selected
temperatures. The samples were heated in an electric heating cell that consisted of a
resistance heating element inside an enclosed 150 cubic centimeter volume. The heating
cell had two Kapton® windows that allowed the x-ray beam to pass through the cell with
little scattering and attenuation while containing the internal environment. A ﬂow of
nitrogen gas was used to both stabilize the temperature within the heating cell and reduce
the degradation of the samples. All isothermal scans were performed after a ﬁve minute

equilibration period. Data collection was performed over a period of several minutes by

14

taking one second exposures at several points on a two dimensional raster covering a
3mm by 3mm area of the sample ﬁlm. This was done to reduce the beam damage on the
sample and to achieve better SAXS proﬁle statistics by ensuring the sample morphology
reached equilibrium and to examine errors due to possible temperature variations and
morphological variations within the bulk material. Temperature ramp experiments were
performed to examine the Tom of each block copolymer sample. Samples were heated to
150°C and held isothermally for 5 minutes before increasing temperature at a rate of
2°C/min. A ﬂow of dry nitrogen gas was used to both stabilize the temperature within
the heating cell and reduce sample degradation. Tom was calculated by examining the
peak width as a function of temperature.

The 2-D SAXS images, like that in Figure 2.1, are through views of the cast ﬁlms
(i.e. the ﬁlm surface is normal to the incident x-ray beam). The 2-D images Show
concentric, uniform intensity rings which indicate that the solvent casting process results
in a random microdomain orientation analogous to a metallic polycrystal in the plane of
the ﬁlm surface. The 2-D SAXS images were integrated 360° azimuthally to give the
SAXS proﬁles shown in Figure 2.2. The SAXS proﬁles Show the intensity of scattered
radiation versus the magnitude of the scattering vector, q.

_ 47: sin 6
/l

 

(2.1)

where q is the magnitude of the scattering vector, 20 is the scattering angle, and A is the
wavelength of radiation.
There are three features of these SAXS proﬁles that will be of interest in the

results and discussion: the relative position and intensity of the higher order peaks that

15

 

Intensity (A.U.)

Figure 2.1. Two dimensional SAXS pattern of pure SBS at 130°C.

 

' ' I ' I r I ' r

I W‘

 

 

 

Intensity (A.U.)

 

 

 

 

I ' I I ' l

0.2 0.4 ' 0:6 I 0.8 1.0
qtnm")

Figure 2.2. SAXS intensity versus scattering vector, q, based on 360° azimuthal
integration of a 2-D image as depicted in Figure 2.1.

17

are deﬁned by the type of morphology, the primary peak position that determines the
lattice spacing (or d-spacing), and the primary peak width that is related to the local order
of the morphology. In order to determine precise changes in peak position and intensity,

peak statistics were calculated by ﬁtting curves using nonlinear least squares regression

analysis. The ﬁtting function included a Gaussian peak of the form A exp[—(x - q"‘)2 M]
and a background of the A ,x + A0 and/or a background of the form 2?: 0 Ax" where A ,-

> 0. For the Gaussian peak, A is the amplitude of the peak, F = 2Jb ln 2 is the full width
at half maximum of the peak, and q* is the location of the peak maximum. One can

obtain the relation between q* and the lattice spacing by substituting Equation 2.1 into

Bragg’s law:

q* = 211: / d (2.2)
where d is the periodicity, lattice spacing, or d-spacing. A Gaussian peak was used for
the ﬁt because it well-represented the peak shape. There was an under estimation of the
peak width/amplitude near the base of the peak, but this was small, symmetric, and did
not affect the comparison of peak width statistics across a copolymer series. The linear
and Ag" forms of the background ﬁtting were used because of their excellent rate of
convergence compared to exponentials and because they followed the monotonically
decreasing background. The background ranged from 1% to 8% of the primary peak
height on a linear scale, so both background forms have only a small effect on diffraction
peak position and width. Calculated values for peak position and width for both forms of

background were within the reproducibility of the experiment. The coefﬁcient of

18

determination, R2, was on the order of 0.99 over the entire peak proﬁle for a domain of

40 data points for many of the samples; this suggests a good ﬁt to the data.

2. 2. 4. Rheological Characterization
Rheological testing was performed using a TA Instruments AR2000 rheometer

with direct strain-control mode. The rheometer is equipped with an electric heater with a
dry N2 purge (purging rate used was 12 m1/minute); the temperature in the testing
chamber is monitored with an embedded thermocouple within the bottom tool of the
rheometer, which is in direct contact with the sample. Parallel plate geometry with
diameter of 25 mm and gap of 0.2 mm was used for all measurements obtained in this
study. The ﬁxture was preheated to the initial testing temperature of 150°C, and lowered
to obtain the zero-gap reference point. The disc-shaped specimen was then placed in the
rheometer, and the top ﬁxture was slowly lowered to the pre-set gap of 0.2 mm with
minimal normal force. Samples were annealed at 150°C for ﬁve minutes prior to
rheological testing. To determine order-disorder transition temperature, Tom, the
samples were subjected to a ﬁxed, small-strain oscillatory shear test with strain amplitude
of 2% and oscillatory frequency of 1 radian/second at a heating rate of 2°C/minute. The
strain amplitude of 2% is within the linear viscoelastic range at 1 rad/s for each material.
Software provided by TA Instruments Inc. was used to determine the temperature-

dependent storage modulus G'((o) that was used for Tom analysis.

2.3. RESULTS AND DISCUSSION

2.3.1. Effect of POSS moieties on Morphology
The morphology of POSS-grafted SBS triblock copolymers was investigated

using the small-angle X-ray scattering (SAXS) technique. SAXS offers not only a non-

19

destructive evaluation over a large volume of material but it also enables one to monitor
changes in morphology as a function of temperature. Transmission Electron Microscopy
(TEM) is another common technique used to investigate morphology of block
copolymers”. The main advantage of TEM is that it provides a real-Space image of the
material. However, there are several possible problems associated with this technique for
SBS with nanoscopic inclusions. First, it is common practice to enhance absorption
contrast by staining SBS with 0504 and thus better distinguish polybutadiene from
polystyrene in the block copolymer. The chemical nature of POSS will undoubtedly
affect the reaction between 0504 and butadiene, which may in turn alter the original
morphology. Without staining, there will not be enough electronic contrast to
investigate any morphology present. The POSS nanostructures in this study are
principally organic in composition, 50 the volume fraction of POSS present in the
butadiene segments will not provide enough contrast to reveal any useful morphological
information. Another issue with TEM is that it examines only a small volume of the
sample, 50 it will be uncertain as to whether the information gathered will be
representative of the entire sample. In addition, sample preparation, which commonly
includes lowering the temperature below the glass transition temperature of
polybutadiene, will also alter the equilibrium morphology of these copolymers. TEM
micrographs are not the best way to represent the bulk copolymer, especially when used
to study the effect of POSS-grafted copolymers.

The 2-D SAXS proﬁles in Figures 2.3, 2.4, 2.5, and 2.6 show the integrated

intensity as a function of scattering vector, q, for pure SBS along with 5, 10, and 20 wt%

20

 

 

     

Pure SBS

Intensity (A.U.)

 

0.2 0.4 0.6 0.8 1.0
-1
9 (nm )

Figure 2.3. Integrated SAXS intensity versus scattering vector, q, for SBS triblock
copolymers grafted with cyclopentyl-POSS (Cp) at 130°C: SBS control with no POSS, 5
wt% POSS, 10 wt% POSS, 20 wt% POSS.

21

 

 

     

Pure SBS

Intensity (A.U.)

 

0.2 0.4 0.6 0.8 1.0
-1
q (nm )

Figure 2.4. Integrated SAXS intensity versus scattering vector, q, for SBS triblock
copolymers grafted with cyclohexyl-POSS (Cy) at 130°C: SBS control with no POSS, 5
wt% POSS, 10 wt% POSS, 20 wt% POSS.

22

 

 

 

 

I T I ' I ' I T I
'!
[Cye-POSS]
i
2 Pure SBS .;
a .
'5 5% 1.
C :
9. .
E 10% 1.
'I
20% E
1.
I ' I ‘ r ' I f I .1

0.2 0.4 0.6 0.8 1.0

q mm")

Figure 2.5. Integrated SAXS intensity versus scattering vector, q, for SBS triblock
copolymers grafted with cyclohexenyl-POSS (Cye) at 130°C: SBS control with no
POSS, 5 wt% POSS, 10 wt% POSS, 20 wt% POSS.

23

 

r I I I' I Y I Y

IPh-POSSI

 

 
    

Pure SBS

Intensity (A.U.)

 

0.2 0.4 0.6 0.8 1.0
-1
0 (nm )

Figure 2.6. Integrated SAXS intensity versus scattering vector, q, for SBS triblock
copolymers grafted with phenyl-POSS (Ph) at 130°C: SBS control with no POSS, 5 wt%
POSS, 10 wt% POSS, 20 wt% POSS.

24

at 130°C for each POSS moiety used in this chapter. The relative locations of the peaks
are determined by the morphology. The pure SBS has relative peak spacings of q*, 2q*,

3q*, and 4q*’ where q* is the position of the ﬁrst and most intense scattering peak,
referred to as the primary diffraction peak. The observed integer spacing of the peaks is
equivalent to the allowed intensities for the structure factor of a lamellar morphology
which is anticipated for the 43 % polystyrene weight fraction based on other published
worksl’ 5’ 6’ '4. The 5% and 10 wt% POSS grafting of each moiety Show little qualitative
change from the pure SBS. The relative position and intensity of the higher order peaks
do not change, which shows that the lamellar morphology is qualitatively unchanged.
The presence and preserved intensity of the second, third, and fourth order peaks suggest
that the long-range periodicity of the lamellae is maintained at these grafted POSS
loadings. For samples with 20 wt% loadings the second order peak, though still present,
has signiﬁcantly diminished intensity, and there are no observed third or fourth order
peaks. This suggests for Dexco 6241 SBS, when grafted with 20 wt% POSS of this
chemistry, the basic form of the lamellar morphology exists on very short scales, but the
longer range order of the lamellae has been disrupted. These changes in the SAXS
proﬁles are similar to a perforated layer morpology'z' '4’ 26. The addition of POSS to SBS
alters the volume ratio of styrene and butadiene domains, and since the POSS is grafted
to the butadiene block, POSS will act to swell the polybutadiene layers. However, the
degree of selectivity may depend on the chemical substituent of POSS and its afﬁnity
toward polystyrene. Other than the order-disorder transition, no other morphological

phase transitions were observed for any of the POSS-grafted SBS investigated.

25

The width of the primary peak for a copolymer specimen is affected by a ntunber
of factors. For undeformed materials, some of the factors that contribute to peak
broadening in the lamellar morphology are: variance in lamellar thickness, a limited
number of lamellae in the diffracting stacks (i.e. small domain or grain size), defects in
the lamellae at the domain (grain) boundaries, curvature at the styrene-butadiene
interface, and the distribution of monomeric species at the lamellae interface. Thus, the
peak width can be used to quantify the relative local (or short range) order and/or defects
of the morphology.

Figure 2.7 shows the peak width for each POSS moiety at 150°C as a function of
POSS loading. The 5% and 10% grafted samples Show only a small amount of
broadening for all POSS moieties, but broadening becomes more signiﬁcant when
approaching 20%. At this high POSS loading, the noticeable increases in peak width can
be associated with an increase in local disorder. These disrupted lamellar morphologies
are similar to the qualities of a perforated layer morphology. The peak width data,
coupled with the observation of high order diffraction peaks discussed earlier, suggests
that grafting of up to 10 wt% of these types of POSS causes only negligible changes in
the qualitative morphology a5 a whole. Both local ordering and long-range periodicity
are maintained to a large degree. With the increased POSS grafting of 20 wt%, the
morphology becomes considerably disturbed as noted by the signiﬁcant peak broadening
in conjunction with the reduced intensity and disappearance of higher order peaks.

Another possible factor which may contribute to the peak broadening is the

alteration of the molecular weight distribution and polydispersity by grafting POSS

26

 

35 | V l f ' Y I I T

 

 

 

 

 

 

—<>— Cp-POSS -
+ Cy-POSS
30 - -v— Cye-POSS ‘
—o— Ph-POSS
¢?A 25 " J
O
3;
g 20- . -
I— /
.0
‘/\1/ __
15 q . ”VT—44’ -
10 I ' I ‘ I ' I ' I
0% 5% 10% 15% 20%

Wt.% POSS

Figure 2.7. The ﬁrst-order peak width at half maximum versus varying amount of POSS
nanostructures with speciﬁed moiety of POSS as indicated (0) cyclopentyl, Cp-POSS
(A) cyclohexenyl, Cy-POSS (V) cyclohexenyl, Cye-POSS (O) phenyl, Ph-POSS.

27

nanostructures to a nearly monodisperse SBS triblock copolymer. Assuming the
chemical attachment of POSS during the grafting reaction is random (i.e., each 1-2
polybutadiene reaction site is equally likely to undergo POSS attachment throughout the
reaction), the distribution of POSS nanostructures per chain would be nearly binomial,
which has a variance and thus will contribute to the overall polydispersity. This means
one can expect that the grafted POSS-copolymer system will possess an increased
variance and polydispersity.

To illustrate this effect, the molecular weight analyses of SBS grafted with
varying amounts of phenyl-POSS (Ph) are listed in Table 2.1. The polydispersity due to
the POSS attachment may account for some of the peak width and qualitative
morphological changes, but it is unlikely that it accounts for the entire peak broadening.
Compared to the overall SBS molecular weight, this variance is small, but nonetheless
may still be a factor. One observation that supports this is the ability to form well-
deﬁned self-assembled morphologies at 10 wt% POSS grafting. In order to have this
long range periodicity, the polymer must be sufﬁciently narrow in molecular weight. It is
also assumed that Cp, Cy, Cye, and Ph-POSS are similarly affected.

The differences in peak width across POSS moiety at each grafting fraction are
relatively small. In fact, other than the 20 wt% cyclopentyl (Cp) loading, all the data are
within experimental error of each other. This suggests that the observed changes in the
qualitative lamellar morphology may be similar for all of the POSS chemistries studied in
this chapter. The small changes in peak width across POSS moiety match qualitatively

with the SAXS proﬁle comparison.

28

Table 2.1. GPC data for pure and Ph-POSS grafted SBS. MW and Mn are weight average
and number average molecular weights respectively (determined by GPC in units of
kiloDaltons). PDI is the polydispersity index (MW/Mn).

 

 

wt% POSS M w Mn PDI
0% 72 71 1.01

5% 76 74 1.03
10% 78 76 1.03
20% 100 93 1.08

29

The length of the lamellar period, the d-spacing, is inversely proportional to the

position of the ﬁrst order peak, q* (Equation 2.2). Figures 2.8 and 2.9 show the d-
spacing at 130°C and 150°C, respectively, for the lamellar morphology with the Cp, Cy,
Cye, and Ph-POSS moieties. At both temperatures, signiﬁcant POSS moiety and grafting
fraction effects are observed. In general, a decrease in d-spacing with increasing amounts
of POSS attachment was observed. The 5% data Show the smallest decrease in d-
spacing, where most of the differences are within experimental error. At 10%, the d-
spacing decreases further for the Cye and Ph moieties while the Cp and Cy d—spacings
remain virtually unchanged. At the highest loading of 20%, the d-spacing drop is
signiﬁcantly greater for all but the Cp POSS, which remains nearly unchanged. Similar
analysis was performed at 150°C and the trend is similar, which is to be expected.

The d-spacing data shows the ﬁrst observable differences between the types of
POSS grafted. The extent of the d-spacing change is strongly inﬂuenced by the POSS
substituent group chemistry. Cp—POSS has no statistical change at either temperature.
Of the remaining moieties, Cy has the smallest change, Ph-POSS has the greatest change,
while Cye-POSS lies in-between. In the case of the Cy, Cye, and Ph moieties, the d-
spacing decreases, which results in an increased speciﬁc interfacial surface area for the
morphology. This suggests a lesser degree of segregation between phase-separated
domains, or decreases in the x-parameter, for these grafted systems. The Cp-POSS
samples show almost no change in d-spacing, so the speciﬁc interfacial area remains
unchanged. This suggests that the Cp-POSS is strongly selective to polybutadiene in this

temperature range and has little or no afﬁnity toward the polystyrene block. For Cy-

30

 

26.0 1

 

 

 

 

   

 

 

 

25.5 -
A 25.0 -
E
5
g) 24.5 - -
'5 J
8
it) 24.0 T
'O
1 —<>— Cp-POSS
23.5 _ + Cy-POSS
—-v— Cye-POSS
+ Ph-POSS ‘
23.0 1 T I ' l T I ' I
0% 5% 10% 15% 20%
Wt.% POSS

Figure 2.8. d-spacing of SBS triblock copolymer grafted with varying amounts of
speciﬁed moiety of POSS at 130°C: (0) cyclopentyl, Cp-POSS (A) cyclohexenyl, Cy-
POSS (V) cyclohexenyl, Cye-POSS (O) phenyl, Ph—POSS.

31

26.0 , r a . I . r - I

 

25.5 -

 

 

T
I
.44

 

 

 

 

 

A 25 o- a
E \
o: 24 54 ‘K _ -
c
'5 _l_.
3
«p 24.0- -
'0 ‘ f
—<>— Cp-POSS
23.0 I ' I ' 1 ‘ I ‘ I
0% 5% 10% 15% 20%

wt% POSS

Figure 2.9. d-spacing of SBS triblock copolymer grafted with varying amounts of
speciﬁed moiety of POSS at 150°C: (0) cyclopentyl, Cp-POSS (A) cyclohexenyl, Cy-
POSS (V) cyclohexenyl, Cye-POSS (O) phenyl, Ph-POSS.

32

POSS, minor changes in d-spacing are observed at 5% and 10% similar to the Cp data,
but at higher loading of POSS there is a drop in d-spacing. This is attributed to a known
compatibility difference between Cp-POSS and Cy-POSS with polystyrene“. The
greater affinity of Cy—POSS toward polystyrene effectively reduces the x-parameter,
which subsequently causes a greater drop in d-spacing. For SBS grafted with Ph—POSS,
the observed drop in d-spacing occurs at the lower POSS loadings. The Ph-POSS and the
polystyrene repeat units of the block copolymer both possess aromatic moieties, while
polybutadiene is aliphatic; this suggests that the Ph-POSS would have the greatest
afﬁnity to the polystyrene phase. The unsaturated Cye-POSS has more of a neutral
chemistry, and its data lies between the Cy and Ph moieties as expected.

As stated earlier, high loading of POSS-grafted triblock copolymers have a
disordered or disrupted morphology. This morphology results in a further decrease in d-
spacing in addition to the compatibility argument alone. The extent of disruption is also

likely affected by the chemical substituents of POSS examined.

2. 3. 2. Effect on the Order-Disorder Transition
Block copolymers have a limited temperature range of stability. Upon heating,

entropic forces of mixing begin to overtake the entropic forces of segregation. The
temperature that separates the ordered morphology from a disordered one is the order-
disorder transition temperature, Tom. Figure 2.10 compares the behavior of pure SBS
when it undergoes a transition from an ordered morphology to a disordered-state during
heating as observed by means of both rheology and SAXS. The left axis shows the

storage modulus, G'((o), as determined from rheology and the right axis shows the peak

33

 

 

 

 

 

 

10" q
’a? ‘ I ..."
a . o
v I ‘—
3 - 4o ‘_><
5’ E
E” 5
3 Pure SBS ‘7
2 —l— Rheology (D
8 —CI-— SAXS I E
.C
a: I I ' - 20
102 I I I I I I I U)
1
1
160 180 200 220 240

Temperature (°C)

Figure 2.10. Rheological behavior as represented by the storage modulus, G'((o) and
SAXS proﬁle as represented by the full-width at the half maximum of the ﬁrst-order
peak, F, at the order-disorder region for pure SBS.

34

width, F, as determined from SAXS; both are plotted over the same temperature range.
During the rheological experiments, block copolymers exhibit a discontinuity in the plot
of Log[G'(o))] versus temperature. Here, the onset temperature of this discontinuity in
G’((:)) is interpreted as Tom. In practice, Tom is a function of both frequency and
temperature ramp rate, so the listed value does not coincide precisely with the

equilibrium Tom”.

However, this interpretation is consistently applied throughout the
pure and POSS grafted series and thus, the effect of POSS attachments on the value of
Tom are all comparable. The onset point was calculated by determining the intersection
of a line ﬁtted in the ordered morphological state below the Tom, and a line ﬁtted
through the drop just after the Tom. The range of temperatures used for the ﬁtting varied
slightly based on the linearity of the two regions. The point of intersection for the two
lines is largely inﬂuenced by the difference in slope of the ﬁtted lines. Shallow or broad
drops produce more uncertainty in the Tom determination. Sample-to-sarnple variation
also contributes to Tom error and stems from morphological differences originating in
sample preparation. Evaporation rates during the solvent casting process must be similar
and annealing times must be long and of comparative duration to ensure reproducibility
in copolymer morphology. If the solvent is evaporated too quickly or if the solvent is not
completely removed during annealing, there will be noticeable changes in Tom. By
performing multiple runs, sample variability was fractions of a degree for the
casting/annealing scheme in place. Time sweeps were also performed at temperatures

near Tom for some samples to ensure that confounding effects due to kinetics did not

play a signiﬁcant role in Tom determination.

35

In SAXS experiments concerning Tom, there are two common ways to measure
Tom: the discontinuity in the plot of l/intensity versus NT or the discontinuity in the plot
of UT versus l/T 1’ 44’ 49’ 50. For the purposes of this paper, plots of 1/ 1" versus l/T were
used to determine the Tom from SAXS data because the discontinuities were more
distinct than in plots of l/intensity. The Tom was interpreted as the midpoint of the 1/ I‘
discontinuity.

A comparison of measured Tom data for SBS grafted with varying amounts of
Ph-POSS is shown in Figure 2.11. Although both rheological and SAXS measurements
show the same trend of decreasing Tom with increasing POSS content, there is a
disagreement in measured values. Another observation is that the rheological
experiments showed less variation because they had sharper transitions and were more
reproducible across multiple tests than the SAXS experiments.

Rheological determination of Tom for SBS grafted with different amounts of Cp,
Cy, Cye, and Ph—POSS moieties are plotted in Figure 2.12. For all POSS loadings, there
is a decrease in the Tom relative to pure SBS. At low weight fractions, the data trends
are similar. At 5% grafting, there is a 4 to 7°C drop in Tom for all moieties. Increasing
to 10% grafting results in a further drop in Tom for all moieties. At large weight
fractions of grafted POSS, there is a change in Tom trend. The Tom for the Ph-POSS
continues to decrease signiﬁcantly but there is a divergence from this monotonic behavior
for the Cp, Cy, and Cye moieties. This is attributed to the perforated layer-like
morphology observed at high POSS loading. In this POSS-grafted SBS system, the

perforated layer morphology is more thermally stable than the lamellar. Others have

36

 

230 . . , , T , .

 

220-
210-

,r 200-

4
:5190-
O

l.—

(33

180~

 

 

  
 
    

Phenyl POSS
+ SAXS - FWHM
—O— Rheology

170-

1

 

 

 

160 r - I - u - u . I
0% 5% 10% 15% 20%
Wt.% POSS

Figure 2.11. A comparison between Tom obtained from rheological and SAXS
measurements for Ph moiety of POSS.

37

230 - l . u r r

 

 

 

     
      

 

 

 

O
01
220 - _
T
1 v r
2104 -
J .
A 200 - -
0
L ‘ .
'5 190 - -
o
I... .. .4
180 a -
, —<>— Cp-POSS ,
170 + Cy-POSS
- —v— Cye-POSS '
. —o— Ph-POSS
160 . . . - . . u . u
0% 5% 10% 15% 20%

Wt.% POSS

Figure 2.12. Tom of varying amounts of different moieties of POSS as determined using
rheological measurement. (0) cyclopentyl, Cp-POSS (A) cyclohexenyl, Cy-POSS (V)
cyclohexenyl, Cye-POSS (D) phenyl, Ph—POSS.

38

made similar observations in different block copolymer systems where Tom, pL > T0911,
'2’ '4’ '6’ 26. The Tom- for Ph-POSS continues to decrease for 20 wt% grafting, contrasting
the other types of POSS. Unlike the other moieties, the Ph-POSS has a much stronger
afﬁnity toward the styrene block. This was seen in the d-spacing of Figures 2.8 and 2.9,
so it is likely to lead to different phase behavior than the other moieties. In another word,
the decrease in x—parameter overcomes the contribution attributed to the perforated layer

morphology.

2.3.3. Effect on the Rheology

In the discussion of rheology to follow, a comparison is made for only Cy, Cye
and Ph-POSS grafted SBS because they have the same number of carbon atoms in similar
stereochemistry for each POSS attachment, which reduces confounding effects due to
size and molecular weight. Thus, observed differences can generally be attributed to
chemistry differences in the POSS nanostructures. Figure 2.l3 shows the rheological
data for the pure and 10% POSS grafted copolymers. For the temperature ranges
examined, the Ph-POSS has nearly the same storage modulus as the pure SBS while the
Cy and Cye moieties show a higher value for the temperature dependent storage modulus.
The observed increase in storage modulus at low frequencies suggests that the POSS acts
as reinforcement for the polybutadiene in the system. Exactly how the POSS
nanostructures contribute is uncertain. For instance, there could be contributions to
reinforcement deriving from POSS-polymer effects, POSS-POSS effects, or even from a
change in morphology as a result of POSS grafting. The ampliﬁed modulus observed for

the Cy and Cye moieties appears to be retained through the Tom explaining the

39

G'(c0) (Pa)

 

 

 

   

-0— Pure SBS

-I-— 10% Cy-POSS
-v— 10% Cye-POSS

—o— 10% Ph-POSS

 

\
\V

l ALA—111

 

 

f

160

I
180

Temperature (°C)

200

220

 

240

Figure 2.13. Storage modulus, G'(a)), as a function of temperature at 1 radian per second
for pure and 10 wt% of POSS with speciﬁed moiety as indicated. (El) pure SBS (A)
cyclohexenyl, Cy, POSS (V) cyclohexenyl, Cye, POSS (O) phenyl, Ph, POSS.

40

diminished drop in modulus after the onset of order-disorder transition. The reinforced
disordered state would hint that the reinforcement has less to do with the morphology and
more to do with POSS—POSS effects. The relatively large POSS-POSS reinforcement
may arise from the neutrality of the chemistry. Cy and Cye-POSS do not have an afﬁnity
toward either polybutadiene or polystyrene and may be more thermodynamically stable
agglomerating or forming crystallites. Though no crystalline POSS was observed by x-
ray diffraction at room temperature for these specimens, the behavior of POSS in the
copolymers at high temperatures is uncertain. The 10% Ph-POSS does not show a
modulus increase. This is almost certainly because the Ph moiety has a high afﬁnity
towards polystyrene segments, which in effect plasticizes the SBS copolymer.

The rheological data for the 20% SBS-POSS copolymers is shown in Figure 2.14.
The Tom for the Cy and Cye moieties increases relative to the 10% due to the
morphology change. Again, there is an observed increase in modulus for Cy and Cye
that may be due to POSS reinforcement. Never the less, the reinforcement is greater and
the drop in modulus is clearer. Both observations support a change to a perforated
morphology. Other copolymers have noted an increase in the modulus on the order-order
transition from a lamellar to a perforated layer morphology'z’ 14’ 26.

The Tom of the 20 wt% Ph-POSS does not increase like that of Cp, Cy, and Cye
moieties, however the temperature range of the order-disorder transition as measured by
rheology becomes broader. Figure 2.15 depicts the rheological and SAXS data for 20

wt% Ph—POSS through the order-disorder transition on the same plot. Though the

rheological transition is broad (spanning nearly 50°C), the SAXS transition is narrower

41

 

G'(m) (Pa)

 

 

  
 
      

—D— Pure SBS
+ 20% Cy-POSS

-v— 20% Cye-POSS
—o— 20% Ph-POSS

  

‘
q
u
1
q

 

 

 

160 1 80 200 220 240

Temperature (°C)

Figure 2.14. Storage modulus, G'(o)), as a function of temperature at l radian per second
for pure and 20 wt% POSS with speciﬁed POSS moiety as indicated. (El) pure SBS (A)
cyclohexenyl, Cy, POSS (V) cyclohexenyl, Cye, POSS (O) phenyl, Ph, POSS.

42

 

 

 

 

 

 

4 o
10 - o
o ' 4
1 0 '
O . MA
76‘ * 0 - 60 '0
£5 . ' 3'.
ED . I ‘7
. 1033 . . o 20 wt% Ph-POSS E
3 1 O O +Rheology L.
.g —O—SAXS .
g . - 40 U)
m 55.
o
102_ o ’
T , T . , . . . 20
160 180 200 220 240

Temperature (°C)

Figure 2.15. Data for computing rheological and SAXS Tom for 20 wt% Ph-POSS

43

(about 10°C). In each case, the respective transitions are broader than that of the pure
SBS. This transition broadening, though magniﬁed in this case, is observed in the other
grafted systems. This broadening of the order-disorder transition may be due to some
changes in the kinetics as affected by the POSS attachment, the change to perforated
layer morphology, or there may be a variance to the SBS phases caused by an increase in

polydispersity /complex phase behavior.

2.4. CONCLUSIONS

Using rheology and X-ray scattering, the effect of grafting four sterically similar,
yet electronically different POSS derivatives onto the polybutadiene phase of a lamellar
SBS triblock has been investigated. It is concluded that the POSS derivatives affect the
SBS by changing the effective ratio of styrene to butadiene and by altering the styrene-
butadiene segregation. Order-disorder transition temperature and d-spacing data show
clear trends that follow POSS nanostructure chemistry: Ph > Cye > Cy > Cp. Here,
grafting Ph-POSS results in greater changes when compared to the ungrafted SBS block
copolymer. The reason being that the phenyl chemistry has the largest contrast to the
block in which it is grafted (polybutadiene) while simultaneously having the largest
afﬁnity toward the ungrafted block (polystyrene). Cp-POSS has the smallest effect aﬁer
grafting because it is most similar to the block in which it is grafted while simultaneously
having the smallest afﬁnity toward the ungrafted block.

All of the POSS grafted in this study resulted in a more disordered or disrupted
morphology. This suggests that all of these POSS chemistries have at least some afﬁnity
toward the polystyrene phase. The POSS with phenyl moiety shows interesting behavior,

as it is grafted to the polybutadiene phase and appears to be strongly interacting well with

44

 

the polystyrene phase. This causes a decrease in the lamellae d—spacing and also causes a
drop in the order-disorder transition temperature due to an effect whereby the Ph-POSS is
solvated by the polystyrene phase. The partly-unsaturated Cye-POSS shows a somewhat
lessened attraction to the polystyrene phase, which in turn is greater than that exhibited
by completely unsaturated Cy or Cp-POSS. At 20 wt% POSS grafting, SAXS and
rheology have revealed that there is a change to a perforated layer morphology for the
Cp, Cy, and Cye-POSS. For 20 wt% Ph-POSS, a perforated morphology is not present,
but the lamellar morphology is disrupted. Complicated POSS-POSS effects convoluted
with changes in morphology result in a greater dynamic storage modulus, G', for these

POSS.

45

CHAPTER 3.

PHASE BEHAVIOR OF POSS-GRAFED SBS WITH
NONINTERACTING OR INTERACTING POSS NANOSTRUCTURES

3.1. INTRODUCTION

Block copolymers have most recently received interest for uses in
nanotechnology. The main focus of their nanotechnology application is rooted in the
ability to form self-assembled microstructures on the nanometer scale, which has lead to
applications in membranes, templates for nanoparticle synthesis, photonic crystals, high-
density information storage media, and beyond.6' 7 More recently, block copolymers have
been used in conjunction with nanoparticles, and the self-assembled copolymer
microstructure has been exploited to control nanoparticle ordering within a particular
phase or at the phase interface of the block copolymer matrix.8’ 4‘ Hence, it is critical to a
gain better understanding of how the surface chemistry of nanoparticles can inﬂuence the
morphology of block copolymers. To accomplish this, it is advantageous to eliminate
complications of phase separation and mixing interactions between particles and polymer
components. Thus, the task may be simpliﬁed by conﬁning the nanostructures to a
particular domain of the block copolymer by grafting nanostructured chemicals to a
speciﬁc copolymer block38’ 39. The preceding chapter reported that the surface chemistry
of the grafted nanostructures has profound effects on the host block copolymer
morphology.38 More speciﬁcally, polyhedral oligomeric silsesquioxane (POSS) was used
as a model nanostructured chemical and was grafted to the polybutadiene midblock Of a
symmetric SBS copolymer. Different chemical substituents of POSS (i.e., cyclopentyl

(Cp), cyclohexyl (Cy), cyclohexenyl (Cye), and phenyl (Ph)) were studied because of

46

their similar stereochemistry, similar molecular weight, and contrasting electronic
properties. It was shown that the morphology of the host SBS copolymer became more
disrupted with an increasing amount of grafting, which was supported by a two-fold
increase in primary scattering peak width and the disappearance of high order scattering
peaks. Based on these observations and the fact that the POSS nanostructures were
grafted to the butadiene, it was concluded that those POSS moieties investigated favor
polystyrene more than polybutadiene. This afﬁnity to the styrene phase leads to a
competition between entropic and enthalpic forces: the POSS enthalpically favors the
polystyrene phase while disfavoring the polybutadiene phase in which it is grafted and
the POSS entropically favors the polybutadiene phase. This results in a deterioration of
the well-segregated interface which in turn affects the order of the morphology. With the
addition of these interacting POSS nanostructures, there is a change from a lamellar to a
perforated layer or disrupted morphology as the amount Of POSS grafting increases and
the level of perforation and stability of this morphology depends on the degree of POSS-
polystyrene compatibility.

These results, although interesting, do not take full advantage of the self-
assembled microstructure. The motivation for this next work is to create a model system
in which nanostructures are conﬁned and dispersed within a single domain of a block
copolymer. This model system can then be utilized to explore particle-particle and
particle-polymer interaction energies, and it can be extended to aid in the design of
nanocomposite materials. In order to conﬁne the nanostructures within the grafted
domain and maintain a well-segregated morphology, it is necessary to remove the

enthalpic interactions which lead to deterioration of the interface. To accomplish this, the

47

surface chemistry of the nanostructure must be selected so it is enthalpically favorable to
the domain in which it is grafted and unfavorable to the other block. Isobutyl (iBu) was
selected because it has an aliphatic chemistry similar to polybutadiene, which contrasts
with the aromatic polystyrene. The new iBu-POSS copolymers will be contrasted with a
new batch of Ph-POSS copolymers. The chemical reaction scheme was slightly altered
from the previous batch to obtain a more random Ph-POSS attachment”. This study also
differs from the previous electronic effect study in that the iBu-POSS has does not have
the same stereochemistry or molecular weight as the Ph-POSS, but the main focus is its
noninteracting nature.

In the following sections, an attempt is made to probe the particle-polymer
interaction energies and present results for the morphological changes in SBS grafted
with iBu-POSS to the butadiene domain. The iBu-POSS was grafted to SBS in the
amounts of 5, 10, and 20 weight percent, and two SBS of similar overall degree of
polymerization but with different styrene content were used. The morphology of the host
SBS was either cylindrical or lamellar depending on the styrene content. Small angle x-
ray scattering (SAXS) was used to quantify the morphological changes in SBS modiﬁed
by different amounts of grafted iBu-POSS. Additionally, in combination with
rheological measurements, morphological transitions and their transition temperatures as

a function of POSS content is reported.

3.2. EXPERIMENTAL

3. 2. 1. Materials

The host polymers for this study were obtained from Dexco Polymers: Vector®

8508 and Vector® 6241. Both are symmetric SBS triblock copolymers and similar in

48

their overall degree of polymerization, but due to their styrene content they have different
morphologies at temperatures far below the order-disorder transition temperature, Tom.
To avoid continually referencing the abstract material numbers, Vector® 8508 will be
referred to as the C-series polymer because it has a cylindrical morphology at
temperatures far below TOD-r. For similar reasons, Vector® 6241 will be referred to as the
L-series polymer because it has a lamellar morphology. A more detailed comparison of
the two materials is available in Table 3.1.

POSS grafting was accomplished via a hydrosilation reaction in toluene. The
procedures used to synthesized the iBu-POSS hydride and the conditions used for
grafting to 1,2-butadiene were identical to some of our published work.38 iBu-POSS was
grafted to each type of SBS in amounts Of 5, 10, and 20 weight percent. Samples were
prepared in the form Of solvent cast ﬁlms of approximately 0.3 mm thickness. The
copolymer samples were dissolved in a toluene, a neutral solvent, in a 3.0 wt%
concentration. Approximately 0.1 wt% Irganox® 1010 antioxidant (relative to the
polymer) was also added to the solution to reduce degradation at high temperatures. The
solvent was then allowed to evaporate slowly on glass at 20°C over a period of three
days. The ﬁlms were removed from the glass and were then annealed under vacuum at

60°C for seven days.

3. 2. 2. X-ray Scattering
Small-angle X-ray scattering (SAXS) was used to quantify the morphology

changes, since it is capable of examining a large volume of material in the bulk state.

The SAXS experiments were performed at beamline 151D (ChemMatCARS) in the

49

Table 3.1. Comparison of Host SBS. Mn and M... are number-average and weight-
average molecular weights, respectively (determined by GPC in units of kiloDaltons).
PDI is the polydispersity index (MW/Mn). Weight percent of polystyrene is listed by the
manufacturer and veriﬁed by integration of NMR signals. Self-assembled morphology is
determined by small-angle X-ray scattering at room temperature.

 

Polystyrene Self-Assembled
Material MW Mn PDI Content Morphology Series Name

Vector® 8508 62 59 1.05 29 wt.% cylindrical C-series
Vector® 6241 72 71 1.02 43 wt.% lamellar L-series

 

50

Advanced Photon Source (APS) at Argonne National Laboratory. The energy of
radiation used for the experiments was 8.27 keV (AB/E z 10“), which corresponds to an
x-ray wavelength of 1.50 A. SAXS patterns were collected using a two-dimensional
Bruker 6000 CCD X-ray detector with a 1024 x 1024 pixel array with a 92 x 92 um pixel
size. The camera length was 1.915 meters and was calibrated using silver behenate. The
SAXS experiments were performed in order to observe the equilibrium morphologies and
to verify thermally induced phase transitions. Isothermal experiments were sufficient to
observe these phenomena. The protocol implemented for the isothermal experiments
included a 10 minutes annealing time at the required temperature followed by a two-
dimensional raster of 1 second exposures covering a 3 x 3 mm area of the ﬁlm over a 5
minute time period. There are several purposes for performing the raster: it minimizes
possible beam damage to the sample, it allows for greater statistical sampling, and it
ensures that the sample has reached equilibrium.

Wide-angle X-ray scattering (WAXS) was performed to observe whether there
was any POSS crystal structure. To observe this crystal structure, a camera distance of
0.549 meters and a wavelength of 0.6199A were used to access a larger q-range. This
allowed for investigation from 0.6nm'l to 16.6nm'I (0.38nm to 10.5nm d—spacing), which
is within the diffraction range of POSS crystalline diffraction. Data was collected at
30°C using 5 second exposures for the undeformed specimens. Deformation was also

performed at this camera length and temperature using 1 second exposures.

3. 2.3. Rheology

Small-strain amplitude oscillatory shear experiments were used to measure the

order-order and order-disorder transition temperatures, Tom and Tom respectively.

51

Experiments were performed using a TA Instruments AR2000 rheometer with 25 mm
parallel plate geometry equipped with an electric heating chamber. Samples were
annealed at 150°C for 5 min then subjected to a temperature ramp with a heating rate of
2°C/min. To minimize sample degradation, a dry N2 purge of 12 ml/min was
implemented. The instrument software was used to determine the dynamic storage
modulus G'(o)) as a function of temperature at a ﬁxed strain amplitude of 2% and
oscillatory frequency Of 1 radian/s. The onset of each G'(m) versus temperature
discontinuity was used to determine the Tom and Tom. In practice, Tom and Tom are a
function of both frequency and temperature ramp rate, so the listed value does not
coincide precisely with the equilibrium transition temperature. However, this calculation
is consistently applied throughout the unmodiﬁed SBS and SBS-POSS grafted series, and

thus the effects Of POSS attachments on the transition temperatures are comparable.

3.3. RESULTS AND DISCUSSION

The ﬁrst portion of this section will examine the effects of grafting iBu-POSS and
Ph-POSS on the equilibrium morphology of SBS: the long-range and local order, and the
d-Spacing. Comparisons are in the melt state at 130°C to ensure equilibrium morphology
and well below the Tom. The latter portion, the Morphology Transitions section, will
focus the effects on Tom and Tour. which will tie in to theories presented in the

Equilibrium Morphology section.

3.3.1. Equilibrium Morphology

Figures 3.1, 3.2, 3.3, and 3.4 Show the one-dimensional scattering proﬁles for all

SBS-POSS copolymers investigated as measured by SAXS at 130°C. Intensity is plotted

52

 

I ' I ' I j

 

-<>- Pure SBS

—£l- 5% iBu-POSS

‘ —B— 10% iBu-POSS "
-I— 20% iBu-POSS

 

Log Intensity (A.U.)

 

 

 

 

0.2 0.4 0.6 ' 0.8
-1
q (nm )

Figure 3.1. Intensity vs. scattering vector, q, at 130°C for C-series SBS (V ector® 8508)
grafted with isobutyl-POSS (iBu). At this temperature, the pure C-series and iBu-POSS
grafted copolymers have a cylindrical morphology. The 2-D SAXS images were
integrated 360° azimuthally to obtain the proﬁles plotted in this ﬁgure, and the data are
shifted along the log intensity axis to increase clarity (5% -0.7, 10% -1.4, 20% -2. l).

53

 

I ' l ' I T

 

-<>- Pure SBS

--0— 5% iBu-POSS
.. -O— 10% iBu-POSS .
+ 20% iBu-POSS

 

Log Intensity (A.U.)

 

 

 

 

0.2 0.4 0.6 0.8
q (nm'1)

Figure 3.2. Intensity vs. scattering vector, q, at 130°C for C-series SBS (V ector® 8508)
grafted with phenyl-POSS (Ph). At this temperature, the pure C-series and Ph-POSS
grafted copolymers have a cylindrical morphology. The 2-D SAXS images were
integrated 360° azimuthally to obtain the proﬁles plotted in this ﬁgure, and the data are
shifted along the log intensity axis to increase clarity (5% -0.7, 10% -1.4, 20% -2.1).

54

 

l ' l ' l ' l T I

-<>- Pure SBS

_ 2 —u— 5% iBu-POSS
t +10% iBu-POSS

+ 20% iBu-POSS

 

 

 

 

 

 

32
s '1
2: _
a
C
.93 . _ -
5 .
O) " l
o W
-J -
V3 4L 1 l
I I I 7' V9 I
0.2 0.4 0.6 0.8 1.0
-1
MM )

Figure 3.3. Intensity vs. scattering vector, q, at 130°C for L-series SBS (V ector® 6241)
grafted with isobutyl-POSS (iBu). At this temperature, the pure L-series along with the
5% and 10% iBu-POSS grafted copolymers have a lamellar morphology, but the 20%
iBu-POSS copolymer has a cylindrical morphology noted by the change in structure
factor. The 2-D SAXS images were integrated 360° azimuthally to obtain the proﬁles
plotted in this ﬁgure, and the data are shifted along the log intensity axis to increase
clarity (5% -1.3, 10% -2.6, 20% -3.9).

55

 

' I ' l
-<>- Pure SBS
_ 2 —o— 5% Ph-POSS _
T —O— 10% Ph-POSS
+ 20% Ph-POSS

 

 

 

Log Intensity (A.U.)

 

 

 

 

0.2 0.4 0.6 0.8 1.0
-1
q (nm )

Figure 3.4. Intensity vs. scattering vector, q, at 130°C for L-series SBS (Vector® 6241)
grafted with phenyl-POSS (Ph). At this temperature, the pure L-series and Ph-POSS
grafted copolymers have a lamellar morphology. The 2-D SAXS images were integrated
360° azimuthally to Obtain the proﬁles plotted in this ﬁgure, and the data are Shifted
along the log intensity axis to increase clarity (5% -1.3, 10% -2.6, 20% -4.6).

56

vs. the magnitude of the scattering vector q. The C-series, which has a cylindrical
morphology for the ungrafted SBS, is shown in Figures 3.1 and 3.2 for iBu and Ph-POSS
respectively. The scattering patterns of the C-series grafted with iBu-POSS show little
difference from the unmodiﬁed SBS. The peak positions are consistent with the allowed
intensities for the structure factor of a hexagonally packed cylindrical morphology
(1:\/3:\/4:\l7:\/9...). Grafting up to 20 weight percent iBu—POSS to the host cylindrical
morphology has little effect on relative peak position, primary scattering intensity, and
even the intensities of the high order V7 and ‘19 peaks. All of these indicate that the
cylindrical morphology is well-preserved after grafting. There is, however, a change in
the relative intensity for the 3rd diffraction peak, which will be discussed in more detail
later in this section.

The SAXS proﬁles in Figure 3.2 are for the C-series grafted with Ph-POSS series.
Like the iBu-POSS grafts in Figure 3.1, the relative peak positions are consistent with the
allowed intensities for the structure factor of a cylindrical morphology. Unlike the iBu-
POSS, the cylindrical morphology becomes disrupted with increased Ph-POSS grafting.
The difference in scattering proﬁles from the iBu-POSS shows that there is a difference
in how the Ph-POSS interacts with the block components. The Ph-POSS series shows
noticeable peak broadening and diminished diffraction intensity. The SAXS pattern for
the 5% Ph-POSS graft shows little qualitative change from the pure SBS. The relative
position and intensity of the higher order peaks do not change signifying the cylindrical
morphology is well-preserved. For the 10% Ph-POSS, the diffraction intensity is
relatively unchanged for the ﬁrst diffraction peak, but the higher order diffraction peaks

are visibly less than the pure and 5 wt%. The 20 wt% Ph-POSS grafted SBS shows a

57

sizeable decline in diffraction intensity along with substantial peak broadening. A
cylindrical morphology is barely discemable and is qualitatively different than that
observed in the pure SBS.

Scattering proﬁles of the L-series, which have varying amounts of iBu-POSS
grafted on Vector® 6241, are shown in Figure 3.3. The relative peak positions for the
pure, 5%, and 10% are consistent with the allowed intensities for the structure factor of a
lamellar morphology (1:2:3:4...). However, when grafted with 20 wt% iBu-POSS, the
observed morphology changes to that of hexagonally packed cylinders. This change in
Vector® 6241 morphology after grafting can be attributed simply to changes in the
overall polystyrene content. By grafting 20 wt% iBu-POSS, the weight fraction of
polystyrene is reduced from 43 wt% for the unmodiﬁed Vector 6241® to 34 wt% in 20%
iBu-POSS grafted Vector® 6241. This reduction in polystyrene content is large enough
to change the morphology from lamellar to cylindrical. An underlying assumption in this
reasoning is that the grafting of iBu-POSS to the polybutadiene does not affect the degree
of segregation between the butadiene and styrene domains. Thus, the morphology of
modiﬁed SBS only depends on the overall volume fraction of a particular block. The
argument is in parallel to those studies on highly selective solvent swelling of block
copolymers.” '9’ 43 In this case, the iBu-POSS is akin to the solvent molecules that are
selective only to the polybutadiene domain. This is a reasonable comparison because the
iBu-POSS are chemically grafted to polybutadiene, and thus they are conﬁned within the
butadiene domain. As a result, when iBu-POSS is grafted with polybutadiene, the
modiﬁed SBS-POSS copolymer can be characterized by a resulting shift in composition

of the host polymer system along the xN vs. f phase diagram, where x is the Flory-

58

Huggins parameter, N is the effective degree of polymerization, and f is the volume
fraction of a particular block copolymer component.” '9 This lyotropic phase transition
does not occur for the C-series. The reason for this is because 43 wt% PS is closer to the
lamellar-cylindrical boundary on the xN vs. f phase diagram than the 29 wt% PS is to the
cylindrical-sphere boundary.

The SAXS proﬁles in Figure 3.4 are for the Ph-POSS series. The relative peak
positions are consistent with the allowed intensities for the structure factor of a lamellar
morphology. Unlike the iBu-POSS, the lamellar morphology is present for all the SBS-
POSS copolymers. Again, this difference in phase behavior from the iBu-POSS shows
that there is a difference in how the Ph-POSS interacts with the block components.
Instead of a shift in phase behavior, the Ph-POSS series show noticeable peak broadening
and diminished diffraction intensity. The SAXS pattern for the 5% Ph-POSS graft shows
little qualitative change from the pure SBS. The relative position and intensity of the
higher order peaks do not change signifying the lamellar morphology is well-preserved.
For the 10% Ph-POSS, the diffraction intensity is visibly less than the pure and 5 wt%.
The 20 wt% Ph-POSS grafted SBS Shows a further decline in diffraction intensity along
with substantial peak broadening; despite these observations, the 3rd and 4th order
diffraction peaks are still discernible. Thus, a lamellar morphology is still present, but it
is qualitatively different than that observed in the pure SBS.

The hypothesized noninteracting nature of iBu-POSS with the polystyrene
domain can be further supported by revisiting the scattering data. The total scattering in
Figures 3.1 and 3.2 has contributions from interparticle and intraparticle interferences,

which are Often referred to as lattice and particle scattering, respectively. Lattice

59

scattering determines the structure factor, while the particle scattering exhibits
constructive and destructive interference depending on the size and shape of the particle.
The diffraction peak disappears when its angular position coincides with that of the
destructive interference of the particle scattering. Thus, some changes in relative
diffraction intensity can be explained by a shift in the scattering form factor minimum,
which again is related to the size of the particles contributing to scattering. In the case of
the C-series, the polystyrene cylinders, or rods, contribute to the particle scattering. The
particle dimension Of interest is the cylinder radiussg’ 60. The cylinder radius is related to
the volume fraction of polystyrene, ﬂag, which changes as a result of grafting as stated
previously. For the L-series, the thickness of the polystyrene domains contributes to the
particle scattering59’61'63. The relative thickness of the polystyrene layer thickness to that
of the lamellae repeat distance is related to ﬂag. The calculations used to derive fps and the
form factor minima can be found in the Appendix, and the values of the ﬁrst two form
factor minima normalized to the primary scattering peak position are displayed in Table

3.2 for both the C-series and L-series. The form factor minimum, q,,,, is divided by the

primary scattering peak position, q*, to obtain qm/q* so it can be related directly to the
structure factor.
As mentioned previously for the C-series grafted with iBu-POSS in Figure 3.1,

there is a change in the relative intensity for the 3rd relative-diffraction peak at position

\l4q*, where q* is the position of the primary diffraction peak. This peak is nearly
unnoticeable in the unmodiﬁed SBS but steadily grows with increased iBu-POSS

grafting. For the pure C-series SBS, the ﬁrst form factor minimum, qm 1, is approximately

60

Table 3.2. Form Factor Minima for SBS-POSS Copolymers. The entire C-series and
20% L-series were calculated using the cylindrical form factor. The lamellar form factor
was used for the 0%, 5%, and 10% L-series. qml and qmz are the ﬁrst and second form

factor minima respectively. q* is the position of the primary diffraction peak.

 

 

wt% Poss fps qu/q’ qmz/q‘
Vector® 8508 0% 25.6% 1.99 3.64
C-series 5% 24.9% 2.02 3.69
10% 24.2% 2.05 3.75
20% 22.6% 2.12 3.88
Vector® 6241 0% 38.9% 2.57 5.14
L-series 5% 37.8% 2.65 5.29
10% 36.6% 2.73 5.46
20% 34.2% 1.72 3.15

61

1.99 and nearly coincides with the \/4q* peak. This explains the nearly absent scattering
peak. Grafting 5%, 10%, and 20% POSS reduces the volume fraction. Consequently, the

form factor minimum is shifted to higher q, toward the value of 2.18 for 20% C-series,

and away from the \/4q* peak. The second form factor minimum, qmz, is outside the
range of interest for the C-series in this discussion.

By examining the L-series grafted with iBu-POSS in Figure 3.3, one observes a
similar shift in the form factor. Here, the 3q* peak decreases in relative intensity for the

5% and is nearly indistinguishable for the 10%, while the 4q* peak is still present for

both systems. The data in Table 3.2 show that the ﬁrst form factor minimum increases
from 2.57 for the unmodiﬁed SBS to 2.81 for the 10 wt% L-series. The diminishing 3q*

peak corresponds to a shift in form factor minimum toward 3q*. The 20% L-series
grafted with iBu-POSS has a cylindrical morphology, so its form factor minima

calculations show a discontinuity from the rest of the L-series. For this cylindrical
morphology, the ﬁrst minimum in the form factor is at 1.77 q/q*. This value is between
the \l3q* and \/4q* peaks and clariﬁes the relative peak intensity difference when

compared to the C-series. The second form factor minimum is at 3.24, near the ‘19q*
peak, and can also be related to relative peak intensity differences compared to the C-
series. The form factor observations are consistent with iBu-POSS conﬁnement in the
polybutadiene domain. This supports the theory that the iBu-POSS are conﬁned within
the polybutadiene domain and are not interacting with polystyrene.

The form factor minimum is derived from the volume fraction of polystyrene, so
it should be the same for both iBu-POSS and Ph-POSS at each grafting fraction.

However, the C-series Ph-POSS of Figure 3.3 do not follow the same form factor trends

62

of the iBu-POSS. This is because the Ph-POSS are interacting with the polystyrene
phase. Instead of simply reducing the polystyrene content, Ph-POSS penetrate the
polystyrene phase resulting in a reduced monomeric segregation at the polystyrene-
polybutadiene interface. This will be discussed in further detail later. Thus, complete
selectivity is lost and the phase shift theory does not apply. For the L-series grafted with
Ph—POSS, as with the C-series, the morphology changes do not follow a simple shift in
phase behavior.

The lattice spacing, or d-spacing, is calculated from the primary diffraction peak
position (Equation 2.2) for both series of iBu-POSS grafted SBS are shown in Figure 3.5.
In order to facilitate a comparison between morphologies, the measured d-spacing of
SBS-POSS copolymers were normalized to the unmodiﬁed SBS. For iBu-POSS, the C-
series shows a small, but measurable, amount of systematic increase in d-spacing was
Observed as the amount of grafted POSS increases. The d-spacing for block copolymers
depends on a number of factors including the degree Of polymerization, N, and
monomeric segregation, x. In this system of SBS grafted with POSS, the degree of
polymerization does not change, but the overall molecular weight of the macromolecules
does. The iBu-POSS is grafted to the polybutadiene block and is subsequently conﬁned
there. The iBu-POSS occupies volume within the butadiene phase and may contribute to
a greater self-avoiding polymer chain conformation. This results in a more expanded
chain conformation for the polybutadiene, which leads to an increase in Rg for this block.
The polystyrene block is unaffected, and the ﬁnal result is an Observed increase in d-

spacing. The monomeric segregation can also affect d-spacing which may be altered by

63

 

1.15 | l I

 

  
  
 
 
   

 

 

 

 

 

l I
C-series
-U— iBu-POSS
$1.101 -O—Ph-POSS 4
‘02 L-series
v + iBu-POSS
(D
l
E A;
~35 1 00 ‘ ‘V "l
b . d
0.95 4 g .4
J
0.90 I I I I I
0% 5% 10% 15% 20%

Wt.% POSS

Figure 3.5. The d-spacing normalized to the unmodiﬁed SBS for the C-series and L-
series at 130°C. For the L-series iBu-POSS (I), there is a change in morphology from
lamellar (0 to 10 wt%) to hexagonally packed cylinders (20 wt%). droo for the cylindrical
morphology corresponds to the nearest neighbor cylinder spacing which is consistent
with the lamellar d-spacing. Error bars are on the order of the symbol size and were
removed for clarity. The d-spacing for unmodiﬁed C-series and L-series SBS are
25.71nm and 25.41nm respectively.

64

grafting. The Observed increase in d-spacing shown in Figure 3.5 along with the
preceding Rg arguments implies that changes in x after grafting iBu-POSS are small. It
also conﬁrms that the iBu-POSS does not have favorable compatibility with polystyrene
which would reduce x and subsequently the d-spacing.

For the L-series polymers grafted with iBu-POSS, the analysis of d-spacing as
affected by grafting iBu-POSS is somewhat more complicated due to the fact that there is
a change in the morphology from lamellar to cylindrical morphology as the amount of
grafting per chain increases. The d-spacing for the 20 wt% iBu-POSS must be multiplied
by \l(4/3) to correspond to the nearest neighbor distance, d100, so it can be consistent with
the other calculated d-spacings in the L-series that have a lamellar morphology. As seen
in Figure 3.5, there was an increase of about 10% in the d-spacing for Vector® 6241
grafted with 20 wt% of iBu-POSS. This relatively large increase may, in part, be due to
the comparison between the cylindrical and lamellar morphologies. However, it is more
likely due to the greater volumetric grafting density for the L-series. At the same weight
fraction of grafting, both L-series and C-series have nearly equal overall volume fractions
of POSS; however, the C-series has more polybutadiene by volume resulting in a 20%
greater volume fraction of POSS within the polybutadiene domain of the corresponding
L-series grafting. The consequential conﬁnement of POSS for the L-series may
introduce a noticeable POSS-POSS effect that contributes to a larger R8 for the SBS
polymer chain or a greater segregation between the polybutadiene and polystyrene
monomers. The increase in d-spacing observed for the iBu—POSS contrasts to our
previous study where the d-spacing decreases for Vector® 6241 grafted with Cy, Cye, and

Ph—POSS.

65

The C-series and L-series SBS grafted with Ph—POSS again Show different
behavior than the iBu-POSS series. The Ph-POSS d-spacing decreases with larger
grafting fractions; the L-series decreases more than the C-Series. This drop in repeat
distance can be explained by a concurrent drop in monomeric segregation, the x-
parameter. Unlike the iBu-POSS, which is non-interacting with polystyrene, the Ph-
POSS have a greater afﬁnity to the polystyrene block than the polybutadiene block
because both polystyrene and Ph-POSS have a similar aromatic electronic structure. The
enthalpic contribution to the monomeric segregation, x, between the polystyrene and
grafted polybutadiene will decrease when the Ph—POSS are situated near the block
interface. Thus, a consequence of grafting Ph-POSS to the polybutadiene block is that
the Ph-POSS modiﬁed polybutadiene block is more compatible with the polystyrene
block. The reduced x—parameter will result in a smaller d-spacing. With a larger fraction
of Ph—POSS grafting, the modiﬁed polybutadiene block becomes more compatible with
the polystyrene block and the d-spacing decreases further. Qualitatively, the Ph-POSS is
acting as a compatibilizing agent for the two blocks. With higher concentrations of
POSS, it is possible that an interphase region is created where polybutadiene and grafted
Ph-POSS mingle with the polystyrene block. This mechanism for d-spacing change
contrasts greatly with the iBu-POSS series, where iBu-POSS is compatible with
polybutadiene and non-interacting with the polystyrene block.

Another quantitative measure of morphology is the full width at one half of the
maximum intensity for the primary peak, I‘. Primary scattering peak width is correlated
to the local order of the morphology. Factors that contribute to a broadening of peak

width include: an increased variance in domain thickness, a limited grain size, defects at

66

grain boundaries, and a reduced monomeric segregation at the polystyrene-polybutadiene
interface. All of these are associated with a disruption of the local lamellar order. In
Figure 3.6, the peak width is plotted vs. the weight percent of grafted iBu-POSS and Ph-
POSS for both SBS series. Analogous to the d-spacing data, F are normalized to
unmodiﬁed SBS of each series to facilitate comparison between the two morphologies.
Figure 3.6 shows that the peak width increases with a greater weight percent of POSS
grafting, but the magnitude of change is different for each POSS type. One cause of peak
broadening may originate from an introduced polydispersity during the grafting process.
Because the POSS attachment is random during the grafting reaction, one can expect a
nearly binomial distribution Of POSS per chain. This added variation in molecular
weight for the grafted systems is a likely contribution to the increase in peak width. At 5
wt% grafting, changes in F are minimal regardless of POSS type or morphology. When
grafting 10%, there is a clear distinction drawn between the iBu and Ph-POSS. For the
highest weight fractions, the overall peak broadening for iBu-POSS is much smaller (on
the order of 10%) compared to the Ph-POSS (on the order of 200%). Both morphologies
follow closely with one another based on the POSS type with the L-series having a
slightly larger F. The large difference in peak width between the two POSS types clearly
illustrates that there is an additional mechanism for peak broadening in the Ph-POSS
series, and it must be related to the POSS chemistry. The reduced x—parameter caused by
Ph-POSS grafting leads to a larger interfacial thickness. More disorder or defects along
the thickness of the lamellae should be accompanied by more disorder along its length,

and a small domain size will contribute to peak broadening. Thus, it can also be deduced

67

3.0 . ,

 

 

  
  
 
 
   

 

I j r
T C-series o
—D— iBu-POSS
2 5 -O— Ph-POSS
' ‘ L-series '
—I— iBu-POSS
+ Ph-POSS
2.0 - -

F I I“Unmodiﬁed SBS

..L
01

L
l

 

 

A: 4
1.04 ”r“

44

d

 

 

 

0% 5% 10% 15% 20%
Wt.% POSS

Figure 3.6. Primary scattering peak width, F, is normalized to unmodiﬁed SBS for the
C-Series and L-series SBS grafted with iBu and Ph-POSS at 130°C. Peak width is
measured as the full width at half the maximum scattering peak height on a plot of
intensity vs. q. Peak width for unmodiﬁed C-Series and L-series SBS are approximately
0.0168mn'l and 0.0129nm'l respectively.

68

that the copolymers with larger peak widths will correlate to smaller domain (grain) size.
The F increase is Observed even for the 5 wt% Ph-POSS, but it becomes much more
substantial in the 10 and 20 wt% Ph-POSS. The iBu-POSS is non-interacting with the
polystyrene block, so the introduced polydispersity is likely the only signiﬁcant
contribution to peak broadening.

Wide-angle x-ray scattering, WAXS, was performed to probe the POSS length-
scale. Figures 3.7 and 3.8 show the WAXS data for C-series and L-series SBS
respectively. Data for pure SBS, 10%, and 20% POSS loadings are shown for each
substituent group. It is nearly impossible to differentiate the high q-range data for the
different SBS. This is because the high q-range examines small length scales; length
scales on the order of POSS and polymer segments. The data for pure SBS shows
scattering due to the morphology at the lowest q-range, a strong amorphous polymer peak
near 14nm'l, and a weaker amorphous shoulder at 7nm". Upon grafting iBu-POSS, an
amorphous peak appears near 6nm'l for the 10% and grows more intense for the 20%.
The amorphous scattering, as a result of POSS grafting, conﬁrms that the iBu-POSS do
not crystallize and are soluble in the polybutadiene phase. This again supports the
noninteracting nature of the iBu-POSS leading to the preserved morphology order after
grafting. The Ph-POSS copolymers show different behavior. There is a weak crystalline
POSS diffraction peak at 5.87nm'1 (d ~ 10.7A) for the 10% Ph-POSS copolymer. For the
20% Ph-POSS, this peak is more intense and is accompanied by additional diffraction

peaks.

69

 

 

 

Intensity (A.U.)

 

 

I f I ' l j l T ' I j l

. , .
2 4 6 8 10 12 14 16

4 mm“)

—o— 20% Ph-POSS
—O— 10% Ph-POSS
—<>— Pure SBS

—EI—- 10% iBu-POSS
+ 20% iBu-POSS

 

 
  
 
    

 

Figure 3.7. X-ray scattering data is plotted in the q-range for crystalline POSS for the C-
series. The intensity is in arbitrary units and is normalized to constant incident and
transmitted intensities. Crystalline POSS diffraction can be observed near q ~ 5.87nm'l
(d ~ 10.7A), and amorphous polymer scattering at q ~ 14nm'l (d ~ 4.5A).

7O

 

 

 

 

 

 

3' I
3:, o .
.é‘ _
m
c o
.93 b :
.E ' 2
I ' I ' I ' I ' I f I ' j ' I '
2 4 6 8 10 12 14 16
-1
4 (nm )

 

+ 20% Ph-POSS
—O— 10% Ph-POSS
-<>- Pure SBS

—i— 10% iBu-POSS
—I— 20% iBu-POSS

   
   

 

  

Figure 3.8. X-ray scattering data is plotted in the q-range for crystalline POSS for the L-
series. The intensity is in arbitrary units and is normalized to constant incident and
transmitted intensities. Crystalline POSS diffraction can be Observed near q ~ 5.87nm'l
(d ~ 10.7A), and amorphous polymer scattering at q ~ 14nm'l (d ~ 4.5A).

71

 

The presence Of Ph-POSS crystallites is a consequence Of poor Ph-POSS
compatibility with polybutadiene. The chemical constraints of the grafting attachment do
not allow the Ph—POSS to fully inﬁltrate the polystyrene phase and makes complete phase
separation is impossible. At sufﬁcient concentration, the Ph-POSS agglomerate to form
crystallites in order to mitigate the unfavorable enthalpic interactions within the
polybutadiene domain. The crystallite size and uniformity is limited by the steric
constraints of the polybutadiene polymer chain in which it is grafted to. It is also shown,
by comparing the 10% and 20%, that greater Ph-POSS grafting leads to more and likely

larger crystallites.

3. 3. 2. Morphology Transitions

The morphology phase behavior as a ftmction of temperature can be examined by
the order-disorder and order-order transition temperatures. These transition temperatures
were Obtained from rheology and determined by abrupt changes in the storage modulus,
G'. For the order-disorder transition temperature, Tom, at low frequencies there is a
precipitous drop in G' with increasing temperature, and the onset temperature of this drop
is referred to as the Tom. Order-order transition temperature, Tom, may not always be
as apparent as the Tom. Though there is often a discontinuity in G', it may be a
discontinuous increase or decrease. Additionally, SAXS measurements were performed
near the Tom and Tom to insure the accurate designation of transition temperatures and
morphologies. Traces of storage modulus, G', versus temperature for C-series iBu and
Ph-POSS grafted block copolymers are shown in Figures 3.9 and 3.10, respectively. L-
series iBu and Ph-POSS grafted copolymers are shown in Figures 3.11 and 3.12,

respectively.

72

 

   
  
 
 
 

 

C-series
103 -. —<>— Pure SBS

1 -£l— 5% iBu-POSS
j —i— 10% iBu-POSS
. -I— 20% iBu-POSS

 

  

 

 

 

140 160 1 80 200 220 240 260
Temperature (°C)

Figure 3.9. Storage modulus, G', versus temperature for C-series (V ector® 8508) SBS
grafted with varying amounts of isobutyl-POSS (iBu). G' was obtained using small-
strain oscillatory shear with strain amplitude of 2% and oscillatory frequency of 1
radian/s. The temperature ramp rate was 2°C/min. The rheological experiments were
done in a dry nitrogen environment to reduce thermal degradation. All four copolymers
plotted undergo a cylindrical to disorder transition.

73

 

 

  
  
   

 

u “f - ’
4 ‘ I --I ....
j J

A I at
g .
V ‘ A q
0 .

C-series

-<>- Pure SBS

3
1° '2 —o— 5% Ph-POSS
' +10% Ph-POSS
+ 20% Ph-POSS

 

  

 

 

 

140 160 180 200 220 240
Temperature (°C)

Figure 3.10. Storage modulus, G', versus temperature for C-series O/ector® 8508) SBS
grafted with varying amounts of phenyl-POSS (Ph). G’ was obtained using small-strain
oscillatory shear with strain amplitude of 2% and oscillatory frequency of l radian/s. The
temperature ramp rate was 2°C/min. The rheological experiments were done in a dry
nitrogen environment to reduce thermal degradation. All four copolymers plotted
undergo a cylindrical to disorder transition.

74

 

   
 
 
 
 

 

- L-series
: -<>-Pure SBS

. —[l— 5% iBu-POSS
- +10%iBu-POSS
+ 20% iBu-POSS
102 . u - u - u ' r
140 160 180 200 220

Temperature (°C)

 

 

  

 

 

 

T

. .
240 260

Figure 3.11. Storage modulus, G', versus temperature for L-series (V ector® 6241) SBS
grafted with varying amounts of isobutyl-POSS (iBu). G’ was Obtained using small-
strain oscillatory shear with strain amplitude of 2% and oscillatory frequency of 1
radian/s. The temperature ramp rate was 2°C/min. The rheological experiments were
done in a dry nitrogen environment to reduce thermal degradation. Pure SBS and 5%
iBu-POSS undergo a lamellar to disorder transition, 10% undergoes a lamellar to
cylindrical and cylindrical to disorder transitions, and 20% iBu-POSS undergoes a
cylindrical to disorder transition.

75

 

  
    
 

 

 

  

 

 

 

a“: 103 T: ':
v j -
0 q 3
L-series O
-<>- Pure SBS L "
1o2 —: —o— 5% Ph-POSS __
3 —O— 10% Ph-POSS ‘
1 —o— 20% Ph-POSS ,. _ -
' I ' l T l . 1 '
140 160 180 200 220 240

Temperature (°C)

Figure 3.12. Storage modulus, G', versus temperature for L-series (V ector® 6241) SBS
grafted with varying amounts of phenyl-POSS (Ph). G’ was Obtained using small-strain
oscillatory shear with strain amplitude of 2% and oscillatory frequency of l radian/s. The
temperature ramp rate was 2°C/min. The rheological experiments were done in a dry
nitrogen environment to reduce thermal degradation. All four copolymers plotted
undergo a lamellar to disorder transition.

76

In Figure 3.13, the Tom are plotted versus weight percent of grafted POSS for the
cylindrical morphology C-series. The trend is the same for both types of POSS. The
entire C-series maintains a cylindrical morphology at all temperatures below Tom, and
there is a continual decrease in the Tom with increased POSS grafting for this series.
However, there is a difference in magnitude. Ph-POSS has a larger drop in Tom than
iBu-POSS. This is because of a reduction in the x—parameter, as stated earlier. With
greater Ph-POSS grafting, the x—parameter is reduced, which further reduces the Tom. At
20 wt% Ph—POSS grafting, the initial morphology is so disturbed (and thus nearly
disordered) that no order-disorder transition was observed.

The transition temperature data for the L-series grafted with iBu and Ph-POSS is
displayed in Figure 3.14. The iBu-POSS copolymer phase behavior is relatively complex
when compared to the Ph-POSS series. At all temperatures below Tom, the unmodiﬁed
SBS and the entire Ph-POSS series have a lamellar morphology. The 5 wt% iBu-POSS
also has a lamellar morphology below the Tom. However, the 10 wt% iBu-POSS
undergoes an order-order transition between a lamellar and a cylindrical morphology, and
it undergoes an order-disorder transition at a higher temperature. Finally, the 20 wt%
iBu-POSS has a cylindrical morphology for all temperatures below Tom. Although the
transition temperature behavior for the iBu-POSS series appears complicated, it is merely
related to the polystyrene content of the grafted materiallz‘ 17’ 19’ 20’ 64. The Ph-POSS
series lacks any order-order transitions, so all of the Ph-POSS grafting yields a lamellar
morphology for all temperatures below the Tom. Tom decreases with increasing grafting

for the Ph-POSS series, which is related to a reduction in the x-parameter, as stated

77

 

 

 

 

 

 

220 - -
210 - -
.3
v 200 - -
E
O I .
I...
190 - -
C-Series 4
—D— iBu-POSS
-O— Ph-POSS
10 15 20
Wt.% POSS

Figure 3.13. The order-disorder transition temperature, Tom, is plotted for C-series SBS
grafted with iBu and Ph-POSS. Data points were calculated from rheological
measurements, and all transitions were veriﬁed by SAXS.

78

260 I . . . r . r

 

N N
N 4:
o o
/.

C

1\
r 1

 

Transition Temperature (°C)

 

 

 

 

200 - _
i
180 - .\ q
160 - O'
0 5 10 15 20
Wt.% POSS
L-Series
iBu-POSS

—I- Lamellar-Disordered (Tour)
+ Lamellar—Cylindrical (T OOT)
+ Cylindrical-Disordered (T

Ph-POSS
+ Lamellar—Disordered (T

ODT)

 

ODT)

 

Figure 3.14. The Tom and Tom are plotted for L-series SBS grafted with iBu and Ph-
POSS. There is an order-order transition for the 10 wt% iBu-POSS. For iBu-POSS, I
represents the lamellar-disorder transition, A represents the lamellar-cylindrical
transition, and Y represents the cylindrical-disorder transition. For Ph-POSS, the o
symbol represents the cylindrical-disorder transition. Data points were calculated from
rheological measurements, and all transitions were veriﬁed by SAXS.

79

earlier. With greater Ph-POSS grafting, the x-parameter is reduced, which further
reduces the Tom.

SAXS was performed to corroborate the phase changes observed in rheological
experiments. Figure 3.15 shows the scattering patterns for 10 wt% iBu-POSS grafted to
the L-series copolymer. This is the only grafted copolymer in this study that undergoes
an order-order transition. At 130°C, a lamellar morphology is present. At 195°C, which
is near the Tom, both lamellar (l, 2, 3) and cylindrical (1, 1.73, 2, 2.65) morphologies are
present. Further heating past the Tom results in a cylindrical morphology.

To put the Tom and Tom data in the context of the noninteracting/phase shift
ideas discussed earlier, the transition temperatures are plotted in terms of xN vs. fps
(volume percent of polystyrene) in Figure 3.16. The solid lines are intended to connect
the like transitions of each series, and the dashed lines are extrapolations outside the like
transitions to illustrate a relation to the phase shift idea presented earlier in the discussion.
The dashed line in the center of the ﬁgure relates the C-series and L-series cylindrical
morphologies and separates the cylindrical and disordered morphologies. In actuality,
there is a ternary system of polystyrene, polybutadiene, and iBu-POSS. However, based
on the phase shift arguments mentioned earlier, the data is plotted assuming the iBu-
POSS grafting only affects the weight fraction of polystyrene and has little effect on
segregation between polystyrene and polybutadiene. It is also assumed that N, the
effective degree Of polymerization, has not been signiﬁcantly affected after grafting. The
purpose of this plot is not to precisely deﬁne the phase space of the SBS-POSS grafts, but

to put the Tom changes in the context of the reduction of polystyrene content by grafting

8O

 

 

 

 

 

 

 

 

 

 

 

 

0.5 1.0 1.5 2.0 2.5 ”3.0' '35

Figure 3.15. The ﬁgure shows qu plotted vs. q/q* (where q’ is the q-position of the
primary peak) for L-series 10% iBu-POSS at 130°C (I), 195°C (0), and 210°C (A).
The morphology is lamellar morphology at 130°C. Both lamellar and cylindrical
morphologies are present near the Tom, 195°C. At 210°C only a cylindrical morphology
is present.

81

35

 

 

 

 

 

I I 'l I I
"X Lamellar
.1
30 _ Cylrndrrcal q
2 i
X 4
‘ El
25- -
Disordered
20.........,....,....f.ﬁ..
0.20 0.25 0.30 0.35 0.40 0.45

Figure 3.16. The transition temperatures are plotted in terms of W vs. the volume
fraction of polystyrene, fps, for both SBS series. Unmodiﬁed C-series and L-series
polymers have 0.256 and 0.389 fps, respectively. Lines are added to guide the eye and
separate the Observed morphologies; solid lines connect similar morphology transitions
and dashed lines are extrapolations. The El symbol represents the cylindrical-disorder
transition for the C-series. For the L-series, I represents the lamellar-disorder transition,

A represents the lamellar-cylindrical transition, and V represents the cylindrical-
disorder transition.

82

which was discussed earlier. The values for x were calculated using the ﬁtted parameters
obtained by Owens et al.65 N was calculated using the average monomer density from the
calculations in the Appendix. The transition temperature data are plotted as xN vs. fps
polystyrene Show consistency with other styrene-rubber phase diagrams]; 17’ 19’ 20’ 64
Lines are added to guide the eye and separate the observed morphologies. The plot
explains the Tom drop for the C-series in the context of a shift in composition, it clariﬁes
the Tom increase for the 10% and 20% L-series data, and it relates the phase behavior
between the two SBS polymer series. It is important to note that no complex phases such
as the bicontinuous gyroid or the hexagonally perforated lamellae morphologies were
observed. It is possible that these phases exist, but they may not have been observed
because of their narrow range of stability and the few grafting fractions implemented.
Figure 3.16 was plotted with three central assumptions: (1) grafting affects the
fraction of polystyrene (ﬁns), (2) grafting iBu-POSS does not affect the monomeric
segregation between polystyrene and polybutadiene (x), and (3) the effective degree of
polymerization is not affected by grafting (N). Support for these assumptions has been
given in the preceding discussion and all are reasonable within the context of the phase
shift argument. Nevertheless, it is important to comment on how deviations from these
assumptions will affect Figure 3.16. The fraction of polystyrene is a straightforward
calculation, but it does not take into account the changes due to thermal expansion
differences between the polystyrene, polybutadiene, and iBu-POSS. This change is small
and will only contribute to a fps difference of approximately 0.005 for the 20 wt% iBu-
POSS grafts. Grafting does not affect the overall effective degree of polymerization, N,

but it may contribute to a small increase in the chain size, Rg, as mentioned in the d-

83

Spacing discussion. For grafting fractions of 20 wt% iBu-POSS, this may be a more
important factor. The deviation is expected to be only signiﬁcant for the 20% L-series
because it is the only grafted copolymer in this study to deviate more than 2% from the
unmodiﬁed SBS d-spacings. If one was to adjust N for changes in Rg, it would result in a
small vertical shift upward from the uncorrected point on the xN axis. The x—parameter
also contains a degree of uncertainty. x has been calculated for SB diblocks and triblocks
with and without symmetry considerations, but its precise value can vary on the order of
a few percent.“ 65’ 66 The ﬁtted x that was used in Figure 3.16 was from Owens et al.
because the polymer was well-characterized and had similar polydispersity. It is likely
that iBu-POSS contributes to changes within the polybutadiene block, and further studies
will be performed. However, it appears that grafting iBu-POSS to the butadiene block of
SBS has little effect on the monomeric segregation between the polybutadiene and
polystyrene blocks based on the observation of a preserved morphology, small increases

in d-spacing and peak width, and the Tom and Tom behavior.

3.4. CONCLUSIONS

In this work, the phase behavior and morphology changes of SBS grafted with
iBu and Ph-POSS have been investigated. Two host SBS morphologies were examined
with POSS grafting at 0, 5, 10, and 20 wt% for noninteracting (iBu) and interacting (Ph)
POSS. The morphology and phase behavior observed for iBu-POSS is consistent with
that of a shift in polystyrene content with little change in x. The local and long-ranged
order of the morphology is preserved for all SBS grafted with iBu-POSS copolymers

investigated. The Ph-POSS copolymers which interact with the polystyrene phase reduce

84

x and disrupt the local order of the morphology. This is equivalent to a compatibilizing
effect.

The information gathered in this study has yielded more information about how
POSS affects the morphology of SBS. Figure 3.17 attempts to schematically represent
and summarize the main ﬁndings. In this ﬁgure, a slice of the block copolymer structure
is displayed stretching from the polystyrene phase (I) through the polybutadiene phase
(B) and reaching to another polystyrene phase for 20% iBu-POSS grafted copolymer
(top), pure SBS (middle), and 20% Ph-POSS. Polystyrene and polybutadiene polymer
chains are represented by — and — colored lines respectively. For the 20% iBu-POSS
copolymer (top), the iBu-POSS do not crystallize, and they are completely conﬁned
within the polybutadiene phase. The iBu-POSS do not crystallize because they have
good compatibility with (or are soluble in) the polybutadiene block in which they are
grafted. This, along with the fact that the iBu-POSS are noninteracting with polystyrene,
accounts for the preserved polystyrene-polybutadiene interface. Another consequence of
its noninteracting nature is the little or no change in d-spacing (except in the lamellar to
cylindrical morphology change). Noninteracting means the monomeric segregation (x-
parameter) between polystyrene and polybutadiene is unchanged after grafting. The local
and long range order of the morphology does not change (F remains constant). The most
observable consequence of grafting iBu-POSS is the reduction of polystyrene content
which shifts the phase behavior on the xN vs. f phase diagram. This would account for
the changes in Tom, Tom, and the cylindrical morphology for 20% L-series grafted with

iBu-POSS. It is important to remember here that these observations are within the

85

 

 

 

Figure 3.17. Schematic representation of the local morphology of 20% iBu-POSS
grafted copolymer (top), pure SBS (middle), and 20% Ph—POSS. Polystyrene is
represented by — (chain) and the color I, polybutadiene is represented by — (chain) and
the color white, and POSS is represented by O. For 20% Ph-POSS (bottom), — — —
distinguishes the interphase region.

86

context of the experiments. By increasing the grafting content to 30% or 40% may result
in signiﬁcant changes in morphology, transition temperature, and POSS-POSS crystal
formation.

Although the same weight fraction of POSS is grafted in the 20% Ph-POSS
copolymer (bottom), there are remarkable differences from its iBu-POSS counterpart.
The Ph-POSS crystallize because they have poor compatibility with (or are insoluble in)
the polybutadiene block in which they are grafted. To mitigate this enthalpic cost, the
POSS agglomerate to form crystallites. These crystallites are small due to the steric
restrictions imposed by the chemical grating to the polybutadiene chain. The Ph-POSS
interact strongly with polystyrene phase which reduces the monomeric segregation (x-
parameter) between polystyrene and polybutadiene monomers; the Ph-POSS effectively
act as a compatibilizing agent. This results in a smaller d-spacing, a lower Tom, a
disrupted polystyrene-polybutadiene interface (F increases dramatically), and smaller
domain (grain) size. At large grafting fractions, this disruption may be large enough to
create an interphase region (denoted by — — —) where polystyrene, Ph—POSS, and
polybutadiene are present in signiﬁcant amounts and is distinct from the polybutadiene
and polystyrene phases. By increasing the grafting content, it may be possible to disrupt
the morphology so much (and push the Tom— below Tngs) that no thermodynamically

stable, ordered morphology is possible.

87

CHAPTER 4.

DEFORMATION BEHAVIOR OF POSS-GRAFTED SBS:
MECHANICAL PROPERTIES, MORPHOLOGY, AND POSS
N ANOSTRUCTURES

4.1. INTRODUCTION

The morphology of block copolymers plays a principal role in determining the
mechanical properties of the materialg'] 1. The type of morphology and the orientation of
this morphology are among these important factors. The ability to control the size and
shape of the morphology is valuable tool that allows for the precise design of materials.
AS mentioned earlier, SBS is a widely used thermoplastic elastomer. A general feature of
thermoplastic elastomers is a hard block (crystalline or glassy) coupled to a rubbery soft
block. These materials represent a class of multiphase polymers that contain a soft
domain that is in close contact with a hard domain. The soft domain gives rise to
elastomeric behavior of the material, while the hard domain increases the modulus and
enhances the mechanical integrity of the material. In addition, some properties of
thermoplastic elastomers can be tailored based on the ratio of hard to soft segments, but
the range of this ﬂexibility is limited by the constituent blocks. By incorporating
nanostructures, it may be possible to push properties outside these limits.

For SBS, there are several length scales that inﬂuence the material properties. At
the smallest scale are the individual monomers that make up the copolymer: polystyrene
and polybutadiene. On a larger scale, near that of the polymer chain, is the self-
assembled morphology. In the case of a lamellar morphology, the polymer chain is

partitioned between the individual lamellae of polystyrene and polybutadiene. These

88

lamellae stack in alternating layers and extend laterally until they encounter another set of
lamellae with a different orientation, and the boundaries between these regions of
different orientation determine the domain or grain size of the morphology. Within a
grain, the morphology has a ﬁxed orientation. Typically, this grain size is on the order of
one microng’ 10.

The type of morphology plays a large role in the mechanical properties because
each morphology has its own hard to soft segment ratio. The grain size and/or orientation
also play a role11 in some of the properties, especially when there are changes in
continuity of each component (discontinuous A phase vs. continuous A phase).

The work discussed thus far has focused on the equilibrium morphology of this
model polymer-nanostructure system. This has given tremendous insight as to the effects
of nanostructure chemistry on the host polymer. However, outside of WAXS, little has
been discussed about the nature of intra-nanostructure interactions (i.e. POSS-POSS
interactions). The following work attempts to identify the effects of grafted
nanostructure chemistry and content on the mechanical properties of our SBS model.
Studying these effects in combination with the information gathered about the changes in

morphology, it will be possible to reveal information relating to POSS-POSS

interactions.

4.2. EXPERIMENTAL

4.2.]. Materials ,
The host polymer for this study was Vector® 6241 obtained from Dexco

Polymers. According to the manufacturer, it is a pure, linear, symmetric triblock

copolymer containing less than 1% diblock and has 43 wt% polystyrene. The number-

89

average and weight-average molecular weights are 71 kDa and 72 kDa respectively and
were determined by GPC. This gives the SBS respective degrees of polymerization of
approximately 150-750-150. POSS grafting was accomplished via a hydrosilation
reaction in toluene. The procedures used to synthesized the POSS hydrides and the
conditions used for grafting to 1,2-butadiene were identical to our previously reported
work 58. Isobutyl-POSS (iBu) and Phenyl-POSS (Ph) were grafted to SBS in amounts of
5, 10, and 20 weight percent. Samples were prepared in the form of solvent cast ﬁlms of
approximately 0.3 mm thickness. To prepare the ﬁlms, each SBS-POSS copolymer was
dissolved in a toluene, a neutral solvent, in a 3.0 wt% concentration. Approximately 0.1
wt% Irganox® 1010 antioxidant (relative to the polymer) was added to the solution to
reduce polymer degradation at high temperatures. The solvent was then allowed to
evaporate slowly on glass at 20°C over a period of three days. The ﬁlms were removed

from the glass and were then annealed under vacuum at 60°C for seven days.

4. 2. 2. Mechanical Testing

Mechanical testing was performed on a Rheometric Scientiﬁc RSA-III solid
analyzer with a 350 g transducer. SBS-POSS ﬁlms were cut to a width of 3.75mm
(0.3mm thickness), and a gauge length of 5mm was used. Samples were deformed at

30°C and 70°C at 0.001, 0.005, and 0.0505'1 Henky strain rates.

4. 2. 3. X-ray scattering

X-ray scattering experiments were used to characterize multiple features of the
SBS-POSS systems: equilibrium block copolymer morphology, possible POSS
crystallite formation, and morphology changes during deformation. The experiments

were performed at beamline lSID-D (ChemMatCARS) in the Advanced Photon Source

90

(APS) at Argonne National Laboratory. Small-angle X-ray scattering (SAXS) patterns
were collected using a Bruker 6000 CCD X-ray detector, which is a two-dimensional
detector with a 1024 x 1024 pixel array covering an area 94mm x 94mm. The x-ray
beam size was 0.5 x 0.5 mm in size; the wavelength and camera distance varied slightly
for each experiment, as will be discussed. The x-ray radiation was monochromated using
diamond (111) to achieve AE/E z 10“.

Small angle x-ray scattering is ideal for examining the equilibrium morphology of
the SBS-POSS copolymers because it is capable of measuring subtle changes in
morphology by probing a large volume of material in the bulk state. By selecting the
appropriate wavelength and camera distance, one can examine scattering at the length—
scale associated with the block copolymer repeat distance, or d-spacing. For this set of
experiments, the wavelength of x-ray radiation was selected to be 1.500 A with a camera
distance of 1.915 meters. The protocol implemented for the isothermal experiments
included a 10 minute annealing time at the required temperature followed by a two-
dimensional raster of 1 second exposures covering a 3 x 3 mm area of the ﬁlm over a 5
minute time period. The raster protocol was used because it minimizes possible beam
damage to the sample, it allows for greater statistical sampling of the morphology, and it
ensures that the sample has reached equilibrium.

In situ x-ray deformation experiments were also performed using the same x-ray
wavelength and camera distance as the equilibrium morphology measurements because
the same features were being investigated: the morphologies of the block copolymer.
For these experiments, a specially designed tensile stretching device was constructed.

The device had several attributes that were important for this set of experiments. First,

91

 

two co-rotating cylinders were driven by a stepper motor, which allowed for continuous
stretching to an unbounded strain. In addition, the device had an enclosed environment
with Kapton® windows and a forced-air convection heater that permitted deformation
experiments at elevated temperatures. The SBS-POSS copolymers were cut to a width of
3.75mm (0.3mm thickness), and the gauge length in the stretching device is 25mm. For
this set of experiments, a 0.0053'1 Henky strain rate was employed. Data was collected
with 1 second exposures, but consecutive exposures were limited by the detector readout
time of 8 second. Thus, data was collected at approximately 0.045 Henky strain.
Deformation experiments for the lamellar morphology were carried out at 30°C and
70°C.

Wide-angle X-ray scattering (WAXS) was performed to observe whether any
POSS crystal structure developed. In order to observe this crystal structure, a camera
distance of 0.549 meters and a wavelength of 0.6199A were used to access a larger q-
range. This allowed investigation from 0.6nm'l to 16.6nm'l (0.38nm to 10.5nm d-
spacing), which is within the diffraction range of POSS crystals. Data was collected at
30°C using 5 second exposures for the undeformed specimens. Deformation was also

performed at this camera length and temperature using 1 second exposures.

4.3. RESULTS AND DISCUSSION

4.3.]. Mechanical Testing
The mechanical properties of the SBS-POSS copolymers can supply further

information about the nature of POSS in the block copolymer system. Uniaxial tensile

deformation was performed on the SBS-POSS copolymers at 70°C and 0.0055'1 Henky

92

 

 

 

   
 

 

  
  

 

 

 

 

 

1.75 I ' l ' l ' I ' I
1.50-
01? .
E 1.25-
53
9 1.001
a
c, 0.75- -
.E
(D
0.50- .
4E: . -<>-Pure 88$
g: —u— 5% iBu-POSS ‘
u.r 0-25~ +10%iBu-Poss t
+20% iBu-POSS .
0.00 . . . . . . . .
0.0 0.2 0.4 0.6 0.8 1.0
Henky Strain

Figure 4.1. Stress-Strain data for isobutyl-POSS copolymers. Testing was performed at
70°C and using a Henky strain rate of 0.005s'l under tensile deformation for SBS-POSS

copolymers.

93

 

 

  
      
 

 

  

-<>— Pure SBS .
—0— 5% Ph-POSS

Engineering Stress (MPa)

 

 

 

 

 

 

0.0 0.2 0.4 ' 0.6 ' 0.8 1.0
Henky Strain

Figure 4.2. Stress-Strain data for phenyl-POSS copolymers. Testing was performed at
70°C and using a Henky strain rate of 0.005s'1 under tensile deformation for SBS-POSS
copolymers.

94

strain rate. Figures 4.1 and 4.2 Show the stress-strain curves for these iBu and Ph-POSS
copolymers respectively. The pure SBS, having a lamellar morphology, exhibits an
elastic response at strains below 0.03-0.04. It reaches a stress maximum near 0.07 strain,
and the stress monotonically decreases at high strains until failure. For discussion
purposes, the maximum supported stress will be noted as the yield stress, but this yield
stress does not necessarily coincide with the onset of plastic deformation. The 5 and 10%
SBS-POSS copolymers have a similar mechanical response, and the general shapes of the
stress-strain curves are akin to the pure SBS. This is not a surprise since there is little
change in the morphology of these systems as discussed previously. There are, however,
trends following both the type and overall fraction of POSS grafted that will be discussed
momentarily.

The mechanical behavior of the 20% POSS is more complicated. The 20% iBu-
POSS has a substantial drop in mechanical response. The chief contributor to these
reductions is the change in morphology from lamellar to cylindrical. The cylindrical
morphology has a lower modulus and does not exhibit a yield stress because it has a
continuous polybutadiene phase (soft/rubbery phase). Thus, the 20% iBu-POSS will be
disregarded in the subsequent yield stress discussions. The 20% Ph-POSS also has an
unusual shape with respect to the other copolymers. In particular it has a reaches its
maximum supported stress at around 0.70 Henky strain or about 1.00 engineering strain;
a nearly ten-fold increase compared to the other materials. The higher supported stress at
high strains is observed on a smaller scale for the other POSS samples as well. Both 5%

iBu and Ph-POSS have a slightly higher supported stress than pure SBS at high strains.

95

For the 10% POSS samples, the reduction in polystyrene outweighs possible POSS
reinforcement.

It is important to note here that the 20% iBu-POSS has a monotonically
increasing stress response in Figure 4.2. The pure C-series SBS of chapter 3, like the
pure L-series Figure 4.1 has a monotonically decreasing stress after yield. The C-series
copolymers have 29 wt% polystyrene, but it is likely that a cylindrical morphology with a
weight fraction of polystyrene equivalent to the 20% iBu-POSS would also have a
monotonically decreasing stress after yield. Thus, there may be a form of iBu-POSS
reinforcement, but a rigorous comparison cannot be made to the 20% iBu-POSS because
an equivalent unmodiﬁed system is not available.

The clearest distinction between the mechanical data for the pure SBS and the
SBS-POSS copolymers is the maximum supported stress, or yield stress. Figure 4.3
shows the yield stress for the iBu and Ph-POSS copolymers. There is a trend of
decreasing yield stress with increasing POSS grafting. This relates to a reduction in
polystyrene content for the SBS-POSS copolymer systems; grafting 10 wt% POSS results
in a 10% reduction of polystyrene by weight. Because TngB << 70°C < T835, the
polystyrene has a significantly higher modulus than polybutadiene and consequently
supports a greater load. The iBu-POSS follow a linear trend almost ideally matching the
polystyrene content. The 5 wt% Ph-POSS yield stress follows the same trend as the iBu-
POSS, almost matching the 5% iBu-POSS. However, there is an additional drop for the
10% Ph-POSS. As seen in other published work9'” and with the 20 wt% iBu-POSS, the
morphology has a critical role in determining the mechanical properties of block

copolymers. The additional yield stress drop is likely related to its slightly disrupted

96

lamellar morphology that was discussed previously in chapter 3. Another anomalous
observation is the increased yield stress for the 20% Ph-POSS relative to the 10% Ph-
POSS. The term yield stress is used rather loosely in reference to the 20% Ph-POSS. As
one can see, the stress-strain curve in Figure 4.2 does not exhibit the same yielding
behavior as the other SBS copolymers. Rather there is an extended region of strain with
nearly constant supported stress, and the maximum of which is around 0.7 Henky strain
or 1.0 engineering strain. The increased yield stress at this temperature is unlikely related
to morphology changes because the 20% Ph-POSS has a more disrupted lamellar
morphology than the 10%. The most likely cause for the increase is some sort of Ph-
POSS reinforcement at higher strain, which will be discussed in more detail later. This
reinforcement is signiﬁcant enough to give the 20% Ph-POSS a higher supported stress
than any of the other copolymers above 0.4 Henky strain.

The elastic modulus is plotted in Figure 4.4. Like the yield stress, the elastic
modulus is strongly related to the polystyrene content and morphology of the block

copolymerg'l '

. As seen with the yield stress, there is a decreasing trend with increasing
POSS grafting due to the change in polystyrene content. However, there are differences
in relative magnitude between the POSS types. For the iBu-POSS, there is a linear trend
for the 5% and 10% grafting, which nearly matches the relative magnitudes of the yield
stress. This observation suggests that the change in polystyrene content is the major
contributor to these mechanical response changes and supports the theory that the iBu-

POSS are noninteracting with the polystyrene. The 20% iBu-POSS has a much lower

modulus due to its cylindrical morphology. The Ph-POSS has a drop in modulus that is

97

 

 

     
    

 

 

 

1 4

1.504 ..

A 1.25- -
(U
o.

E 1.00- 4

CD . .
0)

T9; 075- ..

to . .
'O

E3 0.50- f -

>- 1 70°C, 0.005s'1 -

0.25 - —I-— iBu-POSS -

. +Ph-POSS .

0.00 | F f ' l ‘ l ' I

0 5 10 15 20

Wt% POSS

Figure 4.3. Yield stress for the SBS-POSS copolymers at 70°C using a Henky strain rate
of 0.0053' .

98

 

 

    
 

10 - 70°C, 0.005s;1 4
-I— iBu-POSS
—o— Ph-POSS

Elastic Modulus (MPa)

  
  

 

 

 

0 I 5 ' 10 ' 15 ' 20
Wt%POSS

Figure 4.4. The elastic modulus (or Young’s modulus) for the SBS-POSS copolymers at
70°C using a Henky strain rate of 0.005s].

99

approximately three times greater than that observed for the iBu-POSS in the 5% to 10%
range. There is also a further drop for the 20% Ph-POSS, which differs again from the
yield stress data. The difference between nanostructure chemistry results in this disparity
between POSS types. As discussed earlier, the iBu-POSS has little effect on the host
SBS morphology other than changing the polystyrene content. The Ph—POSS, on the
other hand, has a strong afﬁnity toward the polystyrene domain, which effectively
disrupts the host SBS morphology. The low strain properties that rely on precise
morphological order are undeniably affected. The sharper drop in modulus for the Ph-
POSS implies that the elastic modulus is more directly related to the initial morphology
than is the yield stress, which is expected.

A more subtle difference between the POSS types is revealed in Figure 4.5. For
both the 5% and 10% Ph-POSS, the stress strain curves have an additional drop in
modulus compared to the iBu-POSS, which was shown quantitatively in Figure 4.3. At
low strains, the lamellar morphology has a critical role in supporting the applied stress.
At higher strains, the lamellae get pulled apart and shifted and a preferred orientation
develops. In this higher strain range, the Ph-POSS have a relatively higher supported
stress than the iBu-POSS. This is most easily observed in the 5 wt% copolymers because
of their similar elastic moduli. The two stress-strain curves cross at 0.11 and again at
around 0.70 strain. In this strain range, the Ph-POSS has a greater supported stress than
the iBu-POSS copolymers despite its lower elastic modulus and equal polystyrene
content. This hints that the Ph-POSS act as a greater reinforcement to the SBS, even at

this low grafting fraction. Similar behavior is observed in the 10% systems, but there is a

100

 

   
       
   
 

 

  

 

 

 

 

1.50 . , . , . ,
A I
d.“ 1.25- ' -
é _
a)
(I)
2
O)
.E
5 .
g Q75- —El— 5% iBu-POSS
'5’, - +10% iBu-POSS .
LE -0— 5% Ph-POSS '
. +10% Ph-POSS
0.504 . . . , . , .
0.0 0.1 0.2 0.3 0.4
Henky Strain

Figure 4.5. Stress-Strain data for 5 and 10 wt% SBS-POSS copolymers at 70°C and
using a Henky strain rate of 0.005s'1 under tensile deformation for SBS-POSS
copolymers.

101

larger difference in modulus and yield stress. Nevertheless, one can Observe that the
difference in supported stress between the two 10% copolymers decreases in this same
strain range. In a parallel fashion, one can observe the yield strain for these copolymers.
There is a higher yield strain for the Ph-POSS copolymers. Because Of the lower elastic
modulus, there is not signiﬁcant POSS reinforcement contributing to the initial
morphology. The higher yield strain and period of greater supported stress suggests that
reinforcement is post-yielding at 70°C. This observed greater high-strain reinforcement
for the Ph-POSS is exaggerated in the 20% sample, which hints at high strain
reinforcement of the Ph-POSS.

The mechanical response for the SBS-POSS copolymers at 30°C can be observed
in Figures 4.6 and 4.7. At 30°C and 0.005s'l Henky strain rate, the pure lamellar SBS has
an elastic response at strains below 3%. It reaches a stress maximum near 6-7%, and
again this stress will be noted as the yield stress. After yield, the stress supported by the
copolymer decreases until 40% strain and begins to increase until failure. The lower
temperature deformation results in a lower yield strain and increasing stress to failure
when compared to 70°C. The mechanical responses for the iBu-POSS in Figure 4.6
Show the same trends as 70°C. For 5% and 10%, there is little change in the shape of the
curve, but instead there is a shift in magnitude that results from the reduced polystyrene
content. At 20 wt% iBu-POSS, the morphology has changed from lamellar to cylindrical
and there is a substantial drop in modulus and supported stress. Again, the 20% iBu-
POSS does not have a yield stress, and will be disregarded in subsequent yield stress

discussions. The Ph-POSS has obvious differences than the 70°C data and the 30°C iBu-

102

 

 

 

 

 

   
      
 

 

  
   

 

 

 

 

 

’8 4' ‘
o.
3 W
a 3- +
9
(4;)! -1
E 2'
«T: 1
o
.E J -<>-Pure SBS
o) ‘l . i
c —u— 5% IBu-POSS
UJ 1 +10%iBu-POSS 1

0 + 20% iBu-POSS

. , . T . . . , .
0.0 0.2 0.4 0.6 0.8 1.0
Henky Strain

Figure 4.6. Stress-Strain data for isobutyl-POSS copolymers. Testing was performed at
30°C and using a Henky strain rate of 0.0053'1 under tensile deformation for SBS-POSS
copolymers.

103

 

 

 

 

 

 

 

   
 

 

 

 

 

  

 

’5 -.
o.
g #44?
(I)
w 1
g
a)
.5 2- -
L
02 T .
(D
.E 1 _ -<>- Pure SBS
2’ —o— 5% Ph-POSS ‘
LU . —o— 10% Ph-POSS .

-'lr +20% Ph-POSS

0 ' I ' I ' I ' I '
0.0 0.2 0.4 0.6 0.8 1.0

Henky Strain

Figure 4.7. Stress-Strain data for phenyl-POSS copolymers. Testing was performed at
30°C and using a Henky strain rate of 0.0055'1 under tensile deformation for SBS-POSS
copolymers.

104

POSS data as well. The most noticeable difference is the 10% Ph-POSS in Figure 4.7,
which has a higher yield stress than pure SBS and a sizeable, abrupt drop in stress after
yielding. The 20% Ph-POSS also has an increased yield stress than pure SBS; the highest
yield stress of all SBS-POSS copolymer tested.

Figure 4.8 compares the stress-strain curves of the 5% and 10% SBS-POSS
copolymers. The difference between the 5% iBu and 5% Ph-POSS is barely discemable
outside of the change in magnitude. The 10% iBu-POSS has an additional drop in
modulus and supported stress that is similar to what is observed at 70°C. The 10% Ph-
POSS behavior differs signiﬁcantly from what is seen at 70°C. At 30°C, it shows a large
drop in stress after yielding and a relatively constant post-yield stress. This is consistent
with stable neck formation during deformation. ln polymer systems containing
polystyrene, necking is often connected with the presence of a continuous polystyrene
phase. Block copolymer illustrations of this include a parallel orientation of a single

7. In the lamellar example, the

domain of lamellar morphology11 and the gyroid phase6
single domain parallel orientation has polystyrene lamellae that extend the gage length of
the specimen, but the unoriented gyroid morphology has a continuous polystyrene
network created by the morphology.

It is possible that the Ph-POSS act to create a PS network that extends the length
of the sample in the 10% Ph-POSS copolymer. The SAXS data show that a lamellar
morphology is still present, but the Ph-POSS may act as a bridge between the lamellar

polystyrene sheets. The polystyrene lamellae bridged by Ph-POSS may act together to

complete a three—dimensional network. However, grafting 10 wt% means only about

105

 

 

 

 

 

 

 

 

 

 

 

 

4.0 . r . r ' r
‘ -l]— 5% iBu-POSS ‘
+10% iBu-POSS 4
’5 -O— 5% Ph-POSS .
O. . +10% Ph-POSS .
E 3.5- .
(0 .
(D
g
(D
U) .
.E
E 3.0- 1
(D . 4
.E J
C)
C
LU
2.5 v I ' I ' l '
0.0 0.1 0.2 0.3 0.4

Henky Strain

Figure 4.8. Stress-Strain data at 30°C and 0.0055'1 Henky strain rate for 5 and 10 wt%
SBS-POSS copolymers.

106

13% of the polybutadiene volume is occupied by POSS. It is unlikely that Ph-POSS
bridges could span one entire polybutadiene layer let alone many layers. A three—
dimensional polystyrene network may not necessarily extend via POSS from polystyrene
lamella to lamella directly through the polybutadiene. Instead, it may be through the
domain (grain) boundary. A reduced domain size is anticipated for the disrupted
morphologies of 10% and 20%, and these domain boundaries can connect the polystyrene
lamellae between domains. With the further addition of Ph-POSS to 20 wt%, the same
stable necking does not occur. In this case, the lamellar morphology may be so disrupted
that the polystyrene lamellae disintegrate at low strain. The Ph-POSS may still act to
reinforce or bridge the surviving polystyrene fragments. In both the 10% and 20% Ph-
POSS there would be an expected decrease in yield stress and modulus because of
disturbed morphology, but the observed increase supports the theory of Ph-POSS
contributing to mechanical reinforcement differently at the lower temperature.

The yield stress at 30°C and 0.0055'1 Henky strain rate are shown in Figure 4.9.
Again, the iBu-POSS copolymers show the same trend as 70°C. The 5% and 10% iBu-
POSS are in the range of the ideal 95% and 90% of the pure SBS respectively. For Ph-
POSS, 5% is again on the order of the 5% iBu-POSS; however, the 10% and 20% have
increased in relation to the pure SBS and other copolymers at 70°C. At 70°C, they are
less than pure SBS but are greater than pure SBS at 30°C.

The elastic moduli for the SBS-POSS c0polymers, plotted in Figure 4.10, follow
the yield stress trend but differ in magnitude. There is a decreasing trend with increasing

POSS grafting due to the change in polystyrene content. For the iBu-POSS, there is a

107

4.2 ] ' l ' l ' I r

 

 

 

     
   

 

 

 

4.0-
1:? -
o. 3.8
3
3 3.64
9
5
2 3.4-
.93 .
>- 3 2 30°c,0.005s'1
' ' +iBu-POSS '
—o—Ph-POSS
3.0 I ' | ' l ' I ' I
0 5 10 15 20
Wt% POSS

Figure 49. Yield stress for the SBS-POSS copolymers at 30°C using a Henky strain rate
of 0.0055' .

108

 

 

    
   

  

 

 

 

125-
’«T
g- 1004
‘4’
3 75-
‘U
5
o 50-
g .
— 30°C, 000551
L” 25 +iBu-POSS
+Ph-Poss
O l I 1 ﬁ T l
0 5 10 15 20
Wt% POSS

Figure 4.10. The elastic modulus (or Young’s modulus) for the SBS-POSS copolymers
at 30°C using a Henky strain rate of 0.0055".

109

linear trend for the 5% and 10% grafting, and the 20% iBu-POSS has a much lower
modulus. The difference in modulus trend from 70°C is that the Ph-POSS has a greater
elastic modulus than the iBu-POSS at the lower temperature. The 5% Ph-POSS is greater
than the 5% iBu-POS S, though its difference is on the order of experimental error. There
is a relative jump in modulus for 10% Ph-POSS resembling the yield stress, but 20%
drops to near the 5% Ph-POSS modulus. One would expect that the disrupted lamellar
morphology of the 10% and 20% Ph-POSS would have a lower modulus than their
respective iBu-POSS counterpart, but it is not the case. Again, reinforcement is present
for the Ph-POSS copolymers. The morphology has a greater observable effect on the
modulus, which accounts for the relatively lower 20% Ph-POSS modulus.

The inﬂuence of temperature on the yield stress and elastic modulus is shown in
Figures 4.11 and 4.12, respectively. In Figure 4.11, temperature has the same effect on
yield stress for pure SBS, 5% and 10% iBu-POSS, and 5% Ph-POSS. The 10% and 20%
Ph-POSS copolymers show a signiﬁcantly higher yield stress ratio, which means there is
greater reinforcement for this property at lower temperatures relative to the pure SBS.
The modulus data in Figure 4.12 show a slightly different trend. For the iBu-POSS there
is a relatively small decrease in the elastic modulus ratio with increasing POSS showing
little temperature effect. The Ph-POSS modulus, on the other hand, is strongly affected
by temperature.

Both yield stress and elastic modulus data show that reinforcement effects for Ph-
POSS are more signiﬁcant at lower temperatures (if the reinforcement was equal at both

temperatures, the data would match pure SBS). It is important to note that both yield

110

 

 

 

 
   
   

  

 

 

 

I I I T j I
3 - -
.0
O
Na
of ri
\
.0
8 2 . _
>5
b
0.0059;1
+ iBu-POSS l
—o— Ph-POSS
1 | T l ' I ' I r I
0 5 10 15 20

Wt% POSS

Figure 4.11. The ratio of the yield stress, try, at 30°C to the yield stress at 70°C for a
0.0055'1 Henky strain rate.

111

 

 

 

 

   
      

 

 

 

Lu” 1 -1
+ +
2 - ~E-
0.005s‘1
+ iBu-POSS .
+ Ph-POSS
0 I I l ' I l I
0 5 10 15 20
Wt% POSS

Figure 4.12. The ratio of the elastic modulus at 30°C to the elastic modulus at 70°C for a

0.0055'1 Henky strain rate.

112

stress and elastic modulus are low strain properties. The variation in trends between
yield stress and modulus likely arises from the different strain ranges the two properties
cover: elastic modulus s 3% and yield strain z 7%. The elastic modulus, in the lowest
strain range, is principally affected by the initial morphology of the copolymer. As strain
increases to the yield stain, the morphology begins to deform, so larger effects of POSS
reinforcement begin to emerge. Additional reinforcement is possible at higher strains as
observed by the 20% Ph-POSS yield strain at 70°C, but it is difficult to ﬁnd a
comparable, quantitative material property at these high strains.

The effects of yield stress on strain rate at 30°C and 70°C are shown in Figure
4.13. The plot shows the yield stress, oy, normalized to temperature for pure SBS, 10%
iBu and 10% Ph-POSS. Three strain rates of 0.001, 0.005, and 005051 are plotted. The
vertical shift between the temperatures shows that the yield stress is temperature
dependent. The nonzero slope of the lines connecting each material indicates that the
yield stress is also strain rate dependent. The slope for each line is approximately equal
indicating that the strain rate dependence is the same for each material at both
temperatures.

In order to correlate the effects of temperature and strain rate to the yield stress,
one can use Eyring’s model of the ﬂow of solids“. The model begins from a molecular
foundation, where an atom, molecule, or polymer segment must pass over an energy
barrier in moving from one position to another within the solid. Without an applied
stress, this jumping is infrequent and random. Under an applied stress, the energy barrier

for jumping decreases in the direction of applied stress. A consequence of this reduced

113

 

1.5x104

 

 

 

 

 

1.0x10‘4
g - J
(U
9., .
I; 50x10‘SJ ‘
b ' . .
0.0 ., . . . . . .
10* 10'2
Strain Rate (5")
30°C
0 Pure SBS

I 10% iBu-POSS

O 10% Ph-POSS
70°C

0 Pure SBS

D 10% iBu-POSS

O 10% Ph-POSS

 

 

Figure 4.13. Yield stress data normalized to temperature (Kelvin) for three strain rates
(0.001, 0.005, 0.0505") and two temperatures (30°C and 70°C). Data is shown for pure
SBS, 10 wt% iBu-POSS, and 10 wt% Ph-POSS.

114

energy barrier is a faster jumping rate in this direction resulting in an observable strain.

Eyring’s equation is as follows:

0' £3
__y_=_2_* L“ +an J— (4.1)
T V T 80

where 0y is the yield stress, T is the temperature, V* is the activation volume in which the

polymer segment (in this case) acts, AH is the energy barrier for jumping, R is the molar

gas constant, éy is the applied strain rate, and 50 is a constant. The slopes of the lines

in Figure 4.13 are used to calculate V*. AH can be calculated by comparing oy /T at

constant éy or by comparing éy at constant oy /T.

Table 4.1 lists the calculated values for V* and AH for the three materials in

Figure 4.13. V* is slightly greater for the 10% grafted systems, but the difference is on
the order of experimental error. The interpretation of this in terms of the Eyring model is

that the interaction volume for segmental jumping during deformation is increased after

the grafting of POSS. An increase in V* is reasonable considering that POSS are being
added to the butadiene backbone in the grafting process. The difference in enthalpy
barrier between the pure and POSS copolymers is on a comparably larger scale. The
10% iBu-POSS has a AH similar to the pure SBS, but the 10% Ph-POSS has a AH
greater. From the viewpoint of the Eyring model, the increased AH signiﬁes that the Ph-
POSS grafting has created a greater energy barrier for segmental jumping. The electronic
properties of the POSS nanostructures apparently have a greater role in determining the

energy barrier rather than they do the interaction volume. Ph-POSS at or near the

115

Table 4.1. Values are calculated using Eyring’s model on the ﬂow of solids. V. is based
on the data at 70°C and AH is calculated using the data from the 0.0055" Henky strain

rate .

 

 

Material V. V. error AH AH error
(m3/mol) (m3/mol) (kJ/mol) (kJ/mol)

Pure SBS 0.0233 :1: 0.0011 236.8 d: 6.9

10 wt% iBu-POSS 0.0253 :1: 0.0017 231.8 :1: 11.3

10 wt% Ph-POSS 0.0243 :t 0.0022 289.8 i 3.9

116

polystyrene-polybutadiene interface may be the cause for the greater AH. The presence
of POSS crystallites, as Observed by WAXS, may be another contributor for the higher
AH. Analysis of the SBS-POSS copolymer microstructure can assist in the discernment

of how Ph-POSS acts to reinforce the grafted copolymers.

4. 3. 2. Small Angle X-ray Scattering

During tensile deformation of block copolymers, changes in morphology can be
observed using SAXS. Figure 4.14 shows a two-dimensional SAXS pattern at 70°C for
pure SBS (a) before deformation and (b) at 0.3 Henky strain. Because the diffraction
plane normal is c0planar with the incident and diffracted beam, the intensity of the
diffraction pattern is a direct expression of the morphology in a given orientation. By
qualitatively examining the diffraction pattern in Figure 4.14, one can see that the
morphology is coupled to the strain ﬁeld: dilating in the tensile direction (q‘ decreases)
and compressing in the transverse direction (q‘ increases). There is also a change in the
overall orientation of the morphology from random (isotropic intensity) to a preferred
orientation (anisotropic intensity).

A more quantitative analysis of the morphology is preformed by examining slices
of the diffraction pattern in directions of interest. For instance, integrating along the
stretching direction :1: 5° can yield information about the morphology of lamellar sheets
oriented orthogonal to the stretching direction (lamellae normal coincident with the
stretching direction). Likewise, integrating perpendicular to the stretching direction can
yield information about the morphology of lamellae oriented along the stretching

direction. The hexagonally packed cylindrical structure has two-dimensional order, so

117

 

 

 

Intensity (A.U.)

Figure 4.14. Two-dimensional SAXS patterns (through view) for (a) undeformed, pure
SBS and (b) SBS deformed to a Henky strain of 0.3. Deformation was at a rate of
0.0055"l in the stretching direction Shown (SD) and at 70°C. Intensity is in arbitrary
units.

118

there is not a one-to-one correspondence to the one-dimensional lamellar order. As a
result, the 20% iBu-POSS will be omitted from the following analysis, so that only a
comparison between lamellar morphologies is required.

The SAXS experiments for this study used an x-ray beam with a cross-section
measruing 0.5mm x 0.5mm. This method gives diffraction data from a small fraction of
the material gage length during deformation. Thickness variations along the length of the
sample can lead to a difference between the macroscopic strain and local strain ﬁeld. In
order to insure proper interpretation of SAXS information, the data will be plotted vs. the

local strain as measured by SAXS. The local Henky strain, 810w], was be calculated as:

d
a = ln SD (4.2)
local d0

where dSD is the d-spacing in the stretching direction measured by integrating i 5° from

 

the stretching direction and do is the undeformed d—spacing.

As mentioned earlier, peak width, F, is a quantitative measure of the morphology
and is correlated to the local order of the morphology. Figure 4.15 plots F in the
stretching direction (F59) normalized to the undeformed F for each SBS-POSS
copolymer at 70°C and a rate of 0.005". Because the q-range changes signiﬁcantly
during deformation, F was calculated in terms of real-space units instead of q-space. For
pure SBS, FSD increases during deformation. This corresponds to a decrease in the
morphological order as the lamellae sheets are pulled apart. The iBu-POSS copolymers
have nearly identical behavior to the pure SBS. This is because the iBu-POSS is

noninteracting with polystyrene and merely changes the polystyrene content of the

119

10

 

I

 

. -<>- Pure SBS

—El— 5% iBt—POSS
8 _ +10% iBt—POSS
—0— 5% Ph-POSS
i -O— 10% Ph-POSS
+ 20% Ph-POSS

   
  
 
 

 

  

I‘SD/l"0 (real space)
it
‘5

 

 

 

0.0 ' 0.2 ' 0.4 ' 0.6

8
local

Figure 4.15. The normalized peak width in the stretching direction is plotted vs. the
local strain, elm], for all lamellar morphology copol ers. Tensile deformation was
performed at 70°C using a Henky strain rate of 0.0055' . To obtain the values of F39, the
2-D diffraction pattern is integrated :t 5° along the stretching direction. From the
subsequent plot of I vs. q, F is correlated to real-space measurements and is then
normalized to the undeformed peak width for each individual copolymer.

120

copolymer. The Ph-POSS, on the other hand, has a more remarkable behavior during
deformation. The 5% Ph-POSS has little apparent change from the pure SBS and iBu-
POSS copolymers. The increased grafting of the 10% Ph-POSS shows a striking change
compared to the unmodiﬁed systems. In the 10% Ph-POSS copolymer, the peak width
has a smaller change during the deformation. The 20% Ph—POSS has an even more
dramatic difference compared to the other systems. This implies that the 10% and 20%
Ph-POSS copolymer morphologies are better preserved during the deformation process.
The preserved peak width and morphological order should not be confused with
the overall morphological order because there is a large difference in peak width between
the undeformed pure SBS and 20% Ph-POSS. Figure 12 shows that the Ph-POSS
morphologies are better preserved relative to the undeformed morphology during
deformation. Figure 13 shows the real-space peak width in the stretching direction for
the pure SBS and Ph-POSS copolymers. The peak width for the Ph-POSS copolymers is
initially greater than the pure SBS, which is indicative of the disrupted morphology. The
copolymer morphologies are strained at an equivalent rate, but the pure SBS morphology
becomes more disordered earlier than the Ph-POSS copolymers. At even a modest
morphology strain of 0.15, the 20% Ph-POSS has a similar morphological order (as
observed by peak width) to the pure SBS. Upon further deformation, the Ph-POSS peak
width is narrower than pure SBS for all Ph-POSS grafting. The same analysis can be
extended to primary peak intensity, and analogous conclusions are drawn. All three of
the Ph-POSS copolymers collapse onto a similar peak width trend that is narrower than

the pure SBS.

121

 

 

    
   

 

 

 

 

 

 

15 . r . u
.4
O
G) O fﬁr/
(CI? 10 1 . I / / d
9) q . ‘ ’0 /
T“ -1
9
E q l
5 5 l
8 J -<>- Pure SBS .
L. _ —O— 5% Ph-POSS '
‘ '1" +10% Ph-POSS ‘
‘ +20% Ph-POSS ‘
O T | I I r
0.0 0.2 0.4 0.6

8
local

Figure 4.16. The real-space peak width in the stretching direction is plotted vs. the local
strain, slow, for pure SBS and Ph-POSS copolymers. Tensile deformation was performed
at 70°C using a Henky strain rate Of 0.005". To obtain the values of FSD, the 2-D
diffraction pattern is integrated :1: 5° along the stretching direction. From the subsequent
plot of I vs. q, F is correlated to real-space measurements.

122

The peak width in Figures 4.15 and 4.16 are slices of the 2-D diffraction pattern
that look at the lamellae whose normals coincide with the stretching direction. These
ﬁgures are essentially a l-D slice of a 3-D morphology structure. As seen in Figure 4.14,
the SBS lamellae develop a preferred orientation during deformation. By quantitatively
examining the preferred orientation of these patterns, one can gain a better understanding
of the changes in the morphology in three dimensions. The overall orientation of the

morphology is best represented by Herman’s orientation function, f, given by Equation

 

 

4.3:
)
aqz
l 1 1(q. y) (12 (0082 #)(8in #ldq d4:
f=(3<cos ,u>—1)/2= 2 —— (4.3)
”‘12 2 2
l l 1(q. .104 (sin #)dq 61/1
K 0 ‘11 2

 

where I(q,,u) is the intensity of the two-dimensional diffraction pattern as a function of
scattering vector q and azimuthal angle Tu. The equation relates the diffraction intensity,
which is assumed to be proportional to the number of diffracting planes, to the lamellae
orientation, whose planes are normal to the direction of diffraction intensity. f —> 0 for a
random orientation, f —> 1 for lamellae perfectly aligned in the stretching direction
(lamellae normals orthogonal to the stretching direction), and f —> -0.5 when the lamellae
are oriented orthogonal to the stretching direction (lamellae normals in the stretching
direction). A more detailed discussion of Herman’s orientation function can be found in

the Appendix.

123

 

0.4. 4 , , . . ..

 

 

 

 

 

I
I A._’__—,:..I,-t
I _ ,3 '-
0.3- T _T,,'/' 4
I ’I./” - ‘
I.;- - -
0.2- / 2
“N ’z’ ‘
,1; -
011 ../
0.0 - . e. , . , .
0.00 0.25 0.50 0.75 1.00
glocal
-<>-PureSBS

   
 
 
   

-[l— 5% iBt—POSS
—E— 10% iBt-POSS
-0- 5% Ph-POSS
—O— 10% Ph-POSS
+ 20% Ph-POSS

 

Figure 4.17. Herman’s orientation function, f, is plotted vs. the local strain, 810“], for the
lamellar morphology SBS-POSS copolymers under tensile deformation at 70°C using a
Henky strain rate of 0.0055". The Herman’s orientation function was calculated by
integrating over the primary scattering peak q-range.

124

Herman’s orientation function, f, is plotted vs. the local strain for the pure SBS
and SBS-POSS copolymers at 70°C with a Henky strain rate of 0.0055'1 in Figure 4.17.
For unmodiﬁed SBS, the lamellae become oriented along the stretching direction as
observed by an increase in f with strain. The rate of orientation change is greatest at low
strains, levels off, and reaches a maximum lamellae alignment at higher strains. For the
iBu-POSS copolymers, there is little difference from pure SBS. This can again be
attributed to its noninteracting nature with the polystyrene phase, and in that sense is
similar to the peak width data. The Ph-POSS again show behavior different than pure
SBS. For the 5% Ph-POSS copolymer, there is a greater orientation change compared to
the unmodiﬁed system. The 10% and 20% show a restricted orientation change. The
restricted orientation change at high Ph-POSS loadings is similar to the peak width data
in that there is a better preserved morphology during the deformation process, i.e. the
strained morphology better resembles the undeformed morphology. In case of orientation
change, it is more understandable that the Ph-POSS are acting to network the
morphology. This network is possible because of the favorable enthalpic interaction of
Ph-POSS with itself and the polystyrene domains. The Ph-POSS network bridges the
polystyrene domains, and during deformation may act to preserve the order of the
morphology and restrict orientation changes. The 5% Ph-POSS, at ﬁrst glance, seems do
deviate from this in Figure 4.17 by having greater orientation change.

There may be several contributing factors which stem from the fact that only a
small fraction of Ph-POSS are grafted. First, unlike 10% and 20%, the 5% Ph-POSS has
a better preserved morphology; the intensity and peak width are on the order of pure SBS

and the iBu-POSS copolymers. The preserved morphology and lower fraction of POSS

125

suggest fewer POSS at the polystyrene-polybutadiene interface. As a result the POSS
will play a slightly different role then in the 10% and 20% copolymers where these POSS
disrupt the morphology and the polystyrene-polybutadiene interface. Another contributor
to this anomalous behavior may be how f is deﬁned in Equation 4.3. Intensity is assumed
to be proportional to the number of diffraction planes. Intensity in particular directions
(for instance the stretching direction) can decrease because the lamellae disintegrate and
order is lost or because lamellae are tilted away from the diffraction condition (change
orientation). Thus, reduced diffraction intensity in the transverse direction or preserved
diffraction intensity in the stretching direction have the same effect on f This would
mean that the observed increase in f for the 5% Ph-POSS can be the result of preserved
diffraction intensity from lamellae oriented along in the stretching direction, i.e. lamellae
normals orthogonal to the stretching direction for 5%. To accompany these possible
explanations, it has also been observed that lightly cross-linked SBS above Tgps show a
greater increase in f with deformation. The intensity observation and lightly cross-linked
theories are supported by the previously stated hypothesis of a Ph-POSS network.

The peak width for the 30°C deformation data is shown in Figure 4.18. As in
Figure 4.15, F in the stretching direction is normalized to the undeformed F for each
SBS-POSS copolymer. Peak width increases faster at the lower temperature, so there is a
lower strain at which the diffraction peaks are stretched beyond reliable ﬁtting. For pure
SBS, FSD increases during deformation. The increase in FSD is mild in the elastic range
before reaching the yield stress. Above the yield stress, FSD increases signiﬁcantly. The

iBu-POSS copolymers have nearly identical behavior to the pure SBS. This is similar to

126

 

 

5 I I f I I I I I I
-‘_ -
1 _/‘.’

4.. if ‘ -
A
.. . / -
8 .
a /' -
_ 31 .
. /
(D
L. d
v -1

o -» ‘
b I
521 -
h /
1 t -
A"
1 -

 

 

I I I I I I I I I I I I I
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
glocal
-<>-Pure SBS
—£l— 5% iBu-POSS
—B— 10% iBu-POSS
—O— 5% Ph-POSS
+10% Ph-POSS
+20% Ph-POSS

  
   
   
   

 

Figure 4.18. The normalized peak width in the stretching direction is plotted vs. the
local strain, £1003], for all lamellar morphology copol mers. Tensile deformation was
performed at 30°C using a Henky strain rate of 0.0055' . To Obtain the values of F51), the
2-D diffraction pattern is integrated 5: 5° along the stretching direction. From the
subsequent plot of I vs. q, F is correlated to real-space measurements and is then
normalized to the undeformed peak width for each individual copolymer.

127

the 70°C data because the iBu-POSS is noninteracting with polystyrene and merely
changes the polystyrene content of the copolymer. The Ph-POSS again has a more
remarkable behavior. The 5% Ph-POSS has a slightly higher relative peak width than
pure SBS and iBu-POSS copolymers. The increased grafting of the 10% Ph-POSS shows
a striking change compared to other copolymers. In the 10% Ph-POSS copolymer, the
peak width has a smaller change during the deformation. The 20% Ph-POSS has an even
more dramatic difference compared to the other systems. This implies that the 10% and
20% Ph-POSS copolymer morphologies are better preserved during the deformation
process.

Figure 4.19 plots f vs. the local strain at 30°C with a Henky strain rate of 0.0055".
For unmodiﬁed SBS, the lamellae become oriented along the stretching direction as
observed by an increase in f with strain. The rate of orientation change is greatest at low
strains, and f reaches maximum lamellae alignment at higher strains. For the iBu-POSS
copolymers, there is little difference from pure SBS. This can again be attributed to its
noninteracting nature with the polystyrene phase, and in that sense is similar to the peak
width data. The Ph-POSS again show behavior different than pure SBS. Like 70°C, the
5% Ph-POSS copolymer has a greater orientation change, and the 10% and 20% show a
restricted orientation change compared to the unmodiﬁed system.

The magnitude of f has also changed; f30oc <f70oc. At temperatures farther below
TgTPS, the polystyrene lamellae are more brittle and tend to break up during deformation
rather than shift orientation. This is evident in the lower strain to peak disappearance and

lower f. 20% Ph-POSS has a negative f meaning little or no change in lamellae

128

 

0
(JO
1
d
\
at
1

lﬁO

0.2 .1 ‘ ‘ /I- -1
-1 I J'O’V

 

 

 

 

: . - -:
. /-.‘.
0.0 - 5" -
. l
.1 J
T .
'01 I I I I I I I I I 77—1—
000 005 0.10 015 020 1.0
glocal
-<>- Pure SBS

   
   
 

—[l— 5% iBu-POSS
+10% iBu-POSS
—O— 5% Ph-POSS
—O— 10% Ph-POSS
+ 20% Ph-POSS

 

  

Figure 4.19. Herman’s orientation function, f, is plotted vs. the local strain, elm], for the
lamellar morphology SBS-POSS copolymers under tensile deformation at 30°C using a
Henky strain rate of 0.0055". The Herman’s orientation function was calculated by
integrating over the primary scattering peak q-range. fat 1.0 Henky strain is measured at
the command strain. ’

129

orientation. The intensity of the 2-D diffraction pattern in the stretching direction is well-
preserved showing almost no change, while the intensity in the normal direction
diminishes. This is associated with lamellae that are stronger (i.e. retain their character
more) when their normals are coincident with the stretching direction compared to when
their normals are orthogonal to the stretching direction. To be certain of what exactly
causes the negative fat 70°C, a detailed look at the deformation mechanisms of oriented
copolymers is necessary. The f data also show the same temperature trends as the yield
stress and modulus data where 10% and 20% Ph-POSS copolymers have more signiﬁcant

reinforcement (f is relatively lower) at 30°C compared to 70°C.

4. 3. 3. Wide-angle X-ray Scattering (WAXS)

The nature of the Ph-POSS crystallites during deformation was examined in
further detail using deformation experiments. Figure 4.20 shows the Ph-POSS crystallite
diffraction peaks in 20% Ph-POSS at selected strains during deformation. These
deformation experiments were performed at a stretching rate of 0.0055" at 30°C. The
intensities in Figure 4.20 are normalized to constant incident and transmitted intensities
in order to compensate for differences in thickness, which decreases as the ﬁlm is
stretched. There are several features of the ﬁgure that are worthy of mention. The
intensity of the diffraction peaks decrease with strain, and the width at half maximum
increases concurrently. The intensities of the diffraction peaks are well-preserved in
comparison to the morphology. The POSS crystallite diffraction intensity falls to 70% in
the stretching direction at a Henky strain of 1.22, but the pure SBS morphology intensity

falls to 70% at 0.04 at the same temperature. Crystalline diffraction peak broadening is

130

 

I
“5)»
r

 

 

Intensity (A.U.)

 

 

 

4 mm")

 

Henky Strain
+ 0.00

+ 0.17
+ 0.42
+ 0.67
—>— 0.92
+ 1.22

   
 
 
 
   

 

Figure 4.20. X-ray scattering data is plotted over a q-range of crystalline Ph—POSS
during the deformation of 20% Ph-POSS. Intensity is in arbitrary units and is normalized
to constant incident and transmitted intensities to compensate for thickness changes
during deformation. Deformation was performed at 30°C using a Henky strain rate of
0.0055". Data has been integrated 360° azimuthally.

131

generally caused by either a nonuniform strain or a decreasing crystallite size. By
examining the diffracted intensity in the stretching and transverse directions, there is no
observable change in d-spacing which if present would indicate strain. It is difficult to
rule out nonuniform strain completely because there may be changes in strained
crystallite orientation similar to that seen with the block copolymer morphology. It is
likely that decreasing crystallite size is contributing to the peak width changes as well.
As the SBS-POSS copolymer is deformed, crystallite structures may be pulled apart due
to the chemical attachment of Ph-POSS to the polybutadiene block.

The differences between the diffraction data for the Ph-POSS crystallites and the
block copolymer morphology during deformation generate information about the relative
strength of POSS-POSS interactions and morphology stability. Figure 4.21 shows the
local Henky strain for the morphology and crystallites of the 20% Ph-POSS copolymer
along with the local morphology strain of pure SBS for comparison. The morphology
strain is closely coupled to the command strain, as expected. The crystallites are strained
to a maximum of 0.006. Figure 4.22 compares peak width in the stretching direction,
F51), for the 20% Ph-POSS morphology and crystallites to the pure SBS morphology.
Unlike the d-spacing, FSD increases continuously, but its increase is at a much slower rate
than the pure SBS and 20% morphologies.

The Ph-POSS crystallites have preserved intensity, minute d-spacing shift, and
little broadening, all of which indicate that the crystallite POSS-POSS interaction is
stronger than the SBS morphology. This is to be expected since the bond strength in

crystals is Often greater than in liquids or amorphous materials. The possibility of

132

0.8 I I I ' ﬁ ' l
Pure SBS

-<>- Morphology
20% Ph-POSS

0-6 ‘ —O— Morphology
+ Ph-POSS c

 

 

 
  
   

 

  

 

 

 

_ 0.41 -
8
0
To.
0.2 4 -
0.0 -
0.0 0.2 0.4 0.6 0.8
Command aHenky

Figure 4.21. The local Henky strain of the morphology and Ph-POSS crystallites (as
deﬁned by Equation 4.2) is plotted vs. the command Henky strain. Data are plotted for
the morphologies of pure SBS and 20% Ph-POSS along with crystallite data in the 20%
Ph-POSS copolymer. Tensile deformation was performed at 30°C using a Henky strain
rate of 0.005".

133

 

 

  
 
 
    

 

 

 

 

5- -
78‘
co 4 - -
Q.
‘1’
g Pure SBS
: 3 " -<>- Morphology -
If 20% Ph-POSS
\9 -O— Morphology
LI” 2 . + Ph-POSS c stallite _
1 _
I ' I ' l ' I ' I ' l
0.0 0.2 0.4 0.6 0.8 1.0

Command 8
Henky

Figure 4.22. The normalized peak width in the stretching direction is plotted vs. the
local strain for the morphologies of pure SBS and 20% Ph-POSS along with crystallite
data in the 20% Ph-POSS copolymer. Tensile deformation was performed at 30°C using
a Henky strain rate of 0.0055". To obtain the values of FSD, the 2-D diffraction pattern is
integrated :t 5° along the stretching direction. From the subsequent plot of I vs. q, F is
correlated to real-space measurements and is then normalized to the undeformed peak
width for each individual copolymer.

134

crystallite formation has two main criteria: ungrafted (and ultimately the grafted) POSS
nanostructures must be able to crystallize and the POSS cannot be soluble in (or have
favorable interactions with) the phase which it is grafted to. Both iBu-POSS and Ph-
POSS have the ability to crystallize in their ungrafted form. However, the iBu-POSS is
soluble within the polybutadiene phase and does not form crystallites. The Ph—POSS is
insoluble in the polybutadiene phase and forms crystallites. Ph—POSS, as stated
previously, has an afﬁnity to and is soluble in the polystyrene domain, but complete
phase separation is impossible because of the attachment to the polybutadiene block.

The presence of Ph-POSS crystallites is certainly a contributing factor to the
reinforcement of the 20% Ph-POSS copolymer morphology. The relative strength and
stability of these crystallites offer opportunity for reinforcement even at higher strains.
Thus, these POSS-POSS connections are the main reinforcement mechanism for the high
strain behavior of the 20% Ph-POSS in Figure 4.2. The Ph-POSS crystallites are similar
to a crosslink junction for the polybutadiene. In the same way, POSS-POSS interactions
are likely responsible for the reinforcement seen in the lower Ph-POSS loadings
compared to the iBu-POSS in 4.5.

The contribution of possible POSS reinforcement mechanisms differ between
30°C and 70°C because of the glassy nature of the polystyrene at lower temperatures.
This allows for a greater contribution from the small grain size reinforcement
mechanism. At 30°C, polystyrene is stiffer, and in Figures 4.6 and 4.7 the high strain
POSS crystallite reinforcement is not as noticeable; partly because when the morphology
is broken apart at higher strains the residual polystyrene segments serve the same

function as the crystallites.

135

4.4. CONCLUSIONS

The deformation studies supplement the previous ﬁndings regarding the
equilibrium morphology, and they also give further information on the nature of POSS—
polymer and POSS-POSS interactions. The grafting of POSS nanostructures causes a
reduction in the polystyrene content. This inherently reduces the low strain mechanical
properties of the copolymers. For iBu-POSS, the reduction in mechanical properties
(elastic modulus and yield stress) was consistent with this simplistic model because the
iBu-POSS are noninteracting with the polystyrene block. This was observed at both low
(30°C) and high (70°C) temperatures. The Ph-POSS behavior is more complex. With
increasing Ph-POSS, the morphology becomes more disrupted which causes an
additional drop in mechanical properties (elastic modulus and yield stress). At larger
concentrations of Ph-POSS, crystallites form which can act to reinforce the copolymers.
The disrupted morphology Of the 10% and 20% Ph-POSS results in a smaller domain
(grain) Size, which together with the POSS crystallites reinforce, or network, the
morphology. The networked morphology has better preserved morphology order (F) and
a reduced orientation change during deformation (f). At high temperatures (but still
below TgTPS), the drop in mechanical properties from the disrupted morphology order
outweighs the low strain reinforcement effects. Some reinforcement is still observed at
these higher temperatures due to POSS-POSS effects. There is a comparatively higher
supported stress for the Ph-POSS copolymers. The 5% and 10% have subtle changes
compared to their iBu-POSS counterparts. The 20% Ph-POSS shows the highest
supported stress at strains above 0.40 Henky strain. In fact it has a yield strain of

approximately 0.70 Henky strain.

136

CHAPTER 5.

CONCLUSIONS AND RECOMMENDATIONS

5.1. CONCLUSIONS

The objective of this research was to develop a fundamental understanding of how
block copolymers are affected by the attachment of functionalized nanostructures. To
accomplish this, a model nanostructure and copolymer were chosen. Polyhedral
oligomeric silsesquioxanes (POSS) was chosen as the model nanostructure because it has
a precise, well-deﬁned structure and organic groups can be chosen to effectively tune its
surface chemistry. Polystyrene-block-polybutadiene-block-polystyrene copolymer (SBS)
is the model polymer host primarily because it offers a reaction site (1,2-butadiene
segments), but also because it is available in narrow molecular weight. The chemical
reaction scheme for grafting the SBS-POSS copolymers allows for reproducible grafting
reactions that can be performed to produce a wide range of nanostructure grafting
fractions.

The effect of grafting four sterically similar, yet electronically different POSS
derivatives onto the polybutadiene phase of a lamellar SBS triblock was investigated in
order to examine how nanostructure chemistry plays a role in a host copolymer. It is
concluded that the POSS derivatives affect the SBS in two ways: by changing the overall
content of the polystyrene and by altering the styrene-butadiene segregation. Order-
disorder transition temperature and d-spacing data show clear trends that follow POSS
nanostructure chemistry: Ph > Cye > Cy > Cp. Here, grafting Ph-POSS results in greater
changes when compared to the ungrafted SBS block copolymer. The reason for this is

that the phenyl chemistry has the largest contrast to the block in which it is grafted

137

(polybutadiene) while simultaneously having the largest afﬁnity toward the ungraﬁed
block (polystyrene). Cp-POSS has the smallest effect after grafting because it is most
similar to the block in which it is grafted while simultaneously having the smallest
afﬁnity toward the ungrafted block. Nanostructure chemistry must be considered when
they are to be incorporated into a homopolymer, polymer blend, or block copolymer.

iBu-POSS was investigated in order to observe the effects of incorporating a
noninteracting nanostructure. Two host morphologies were examined with POSS
grafting at 0, 5, 10, and 20 wt% to compare noninteracting (iBu) and strongly interacting
(Ph) POSS nanostructures. The morphology and phase behavior observed for
noninteracting POSS is consistent with simply changing polystyrene content with no
noticeable change in x. The local and long-ranged order of the morphology is well-
preserved. The interacting nanostructures reduce x and disrupt the local order of the
morphology, which is equivalent to a compatibilizing effect. With this knowledge
grafting can be used to shift the host block copolymer morphology to attain different
morphologies.

The deformation studies supplement the previous ﬁndings regarding the
equilibrium morphology, and they also give further information on the nature of the
interactions between POSS nanostructures and the host polymer and interactions between
the POSS nanostructures themselves. The mechanical properties (elastic modulus and
yield stress) of the grafted copolymers inherently drop because nanostructure grafting
reduces the polystyrene content. For the noninteracting iBu-POSS, the reduction in
mechanical properties was consistent with this simplistic model because the

nanostructures do not qualitatively change the morphology and are noninteracting with

138

the polystyrene block. This was observed at both low (30°C) and high (70°C)
temperatures. The interacting Ph-POSS behavior is more complex. With increasing Ph-
POSS, the morphology becomes more disrupted which causes an additional drop in
mechanical properties (elastic modulus and yield stress). At larger concentrations of Ph-
POSS, crystallites form which can act to reinforce the copolymers. The disrupted
morphology of the 10% and 20% Ph-POSS results in a smaller domain (grain) size,
which together with the POSS crystallites reinforce, or network, the morphology. The
networked morphology has better preserved morphology order (smaller change in F
during deformation) and a reduced orientation change during deformation (f is smaller).
At high temperatures (but still below Tgys), the drop in mechanical properties from the
disrupted morphology order outweighs the reinforcement effects. An exception to this

can be made for the 20% Ph-POSS yield strain.

5.2. RECOMMENDATIONS

This work has established a base of knowledge in the area of grafted
nanostructured materials. Based on the results of this work, there are several
recommendations for future research that can advance this knowledgebase:

1. To develop a complete picture of the role that POSS nanostructures, it is
necessary to examine the deformation mechanisms. The work would require the
analysis of single grain copolymer samples in selected orientations.
Supplemented with the unoriented deformation ﬁndings in chapter 4, valuable
knowledge can be gained in role of POSS-POSS interactions and POSS in both

the polybutadiene and polystyrene phases.

139

2. This study examined 5%, 10%, and 20% grafting by weight, but maximum
possible grafting fractions can be pushed higher. Higher iBu-POSS grafting may
lead to greater POSS-POSS effects due to the increased conﬁnement. The L-
series grafted with 20% iBu-POSS may be on the cusp of this threshold as seen in
the d-spacing and deformation data.

3. It would be advantageous to graft to an SBS with a higher polystyrene content to
widen the window of available POSS grafting fractions for the lamellar
morphology. The 43 wt% polystyrene faction was on the edge of the lamellar-
cylindrical border in the morphology phase diagram. By selecting a polystyrene
fraction > 50%, it may be possible to graft more than 20% iBu-POSS.

4. The temperature range investigated in this study is well above the glass transition
temperature of polybutadiene. At temperatures near or below Tg,p3, the
nanostructures may behave differently. In particular, the iBu-POSS may act as a
reinforcement rather than maintain a noninteracting nature.

5. A complement study to the current polybutadiene grafted systems would be
grafting POSS to polystyrene. Likewise, extending this scheme of grafting
nanostructures to other polymer systems would also complement the current

work.

140

APPENDIX

14]

APPENDIX

Calculation for the Volume Fraction of Polystyrene

The volume percent polystyrene, ﬁns, was calculated using bulk densities of 1.05

and 0.887 g/cm3 for polystyrene and polybutadiene respectively. The density of the iBu-

POSS hydride was estimated to be 1.15 g/cm3 based on measurements of Larsson69’ 70.

 

 

 

,0

fps = g WPS (A-l)

pPS
p, = 1 (A2)

WPS /pPS + WPB /pPB + WPOSS /pPOSS

l

p = (A3)
3 (1‘ WPOSS XWPSo /,0p5 +(1- WPSo )/ pPB )+ Wposs /pposs

VP WPSo (1 " WPOSS )/ 1’ PS (A. 4)

 

S = (1‘ WPOSS XWPSO /PPs +(1_WPSo)/pPB)+ WPOSS /Pposs
where pps, ppg, pposs, and pg are the densities for polystyrene, polybutadiene, iBu-POSS
hydride, and the SBS-POSS grafted system, respectively. ng, ng, and Wposs are the
weight fractions for polystyrene, polybutadiene, and iBu-POSS hydride for a particular
SBS-POSS grafted system. The expression can be made more general by using the
densities and the polystyrene weight fraction of the original SBS, WPSO, and the weight
fraction of POSS grafted, Wposs. It is important to note that the above calculations
assume no change in volume upon mixing and do not take into account differences in

thermal expansion. Calculated ﬂag for the C-series and L-sen'es copolymers can be found

in Table 3.2.

142

Calculations for N

The parameters and notation used in the calculation of N are the same as those

1.65

used by Owens et a N was normalized to constant monomer volume according to the

geometric average by the following relations:

l/n
... n
p =[I1 pi] (A5)
i=1
b*—b / * A6
* ... 2
N. =N.(b./b.) (A.7)
l l l l

where p,- is the monomeric density of the ith component, ,0. is the average monomer
density, b is the statistical segment length, and N is the degree of polymerization. The
monomeric density for polystyrene and polybutadiene used in the calculations are based

on bulk densities of 1.05 and 0.887 g/cm3 respectively (to achieve 10,100 and 16,400

mol/m3 respectively).

Calculations for the Form Factor Minima:

The cylindrical morphology of the C-series SBS is modeled as an arrangement of
polystyrene cylinders aligned in a hexagonally packed manner. The hexagonal packing
(interparticle order) yields the typical allowed intensities for the structure factor of a
cylindrical morphology (1, \/3, ‘14, \17, \19, ...). The polystyrene cylinders themselves
also contribute to the scattering proﬁle through particle scattering or the form factor. The
particle scattering for a cylindrical or rod-like particle, F (q), where the length of the rod
is much larger than the radius and in scattering directions orthogonal to the cylindrical

axis scales by the relation”’ 60:

143

J 1 (qu
qR

 

F(q)~

(A.8)

where J; is the Bessel function of the ﬁrst kind of order 1, q is the magnitude of the
scattering vector, and R is the cylinder radius. In block copolymers, the cylinders have an
interfacial thickness which contributes to an additional damping factor which does not
contribute to the position of the scattering minima. Based on the Born approximation,
observed scattering intensity scales as F2(q)S(q), where F (q) is the form factor and S(q) is
the structure factor. The minimum intensity in this form factor can be found when J1(qR)
= O for values of q > 0. If we denote S, as a solution to the equation J1(x) = 0, then the q
at which the form factor is at a minimum (denoted here as qm) is related to the cylinder
radius by:

S.
= —L A.9
q... R ( )

The volume fraction of polystyrene, fps, can be related to the cylinder radius, nearest

neighbor cylinder distance (a = d] 00), and the d-spacing of the primary scattering peak, dt.

2
-2}? . dbl/3a (A.10)

flat-£217, 2

J57: R2 2d3f
fps=——2 :17; R: T5: (A.11)

The form factor minimum, qm, is most easily compared to the morphology structure

factor by the dimensionless ratio qn/q'.

qm=S.,/ ‘6” ; q’l' =S,.,/ ‘5 (A.12)
Zd'fps ‘1 84f)“

 

 

 

144

The solutions, 8,, to J1(x) = 0 are approximately 3.83171, 7.01559, 10.1735,... Values
for the ﬁrst two solutions of qn/q‘ can be found in Table 3.2.

In the case of the L-series, the structure amplitude for lamellae, or ﬂat particles,
whose in-plane dimensions are much greater than the thickness and spacing dimensions

scales by59’ 62:

~ sin(qT/Z)
F(q) —————qT/2 (A.13)

where q is the magnitude of the scattering vector, T is the thickness of the lamellae.
Observed scattering intensity scales as F2(q). The minimum in this form factor can be
found when sin(qT/2) = 0 for values of q > 0. The solution to this equation takes the
form qT/2 = 7m where n is a positive integer (for q > 0). The relationships of qm and
q,,/qt to fps are:

qm=2—ﬂn= 2” n; q’i’ 1

=—n
T fPSD q fps

 

 

(A.14)

Values for the ﬁrst two solutions of qn/q. can be found in Table 3.2, and a plot of
the form factor for the pure C-series and L-series SBS is displayed in Figure A. l.

The calculations relating fps to the polystyrene cylinder radius and lamellae
thickness assume that the entire volume of iBu-POSS is conﬁned within the
polybutadiene domain. In practice, the polystyrene cylinders and lamellae possess a size
distribution, interfacial curvature, and interfacial thickness rather than existing as
monodisperse hard particles. In addition, the orientation of the particles (cylinders and
lamellae) is random in the plane of the ﬁlm. Consequently, the form factor minima will
not result in complete destructive interference, but it will result in reduced intensity for

the allowed diffraction of the structure factor.

145

 

 

Pure SBS
+ Cylindrical
+ Lamellar

 

 

 

1%) (A.U.)

 

 

 

Figure A.1. Plot of the form factor for the pure C-series and L—series SBS.

146

 

Herman ’s Orientation Function

For a quantitative examination of how the orientation changes, one can observe
the intensity as a function of azimuthal angle, a, which is deﬁned as the angle from the
direction perpendicular to the stretching direction. The direction diffracted intensity is
coplanar with the incident beam and diffraction plane normal. In addition, diffraction
intensity is approximately proportional to the number of diffracting planes, so it is
possible to correlate intensity in a particular direction and the number of diffraction plane
normals oriented in that direction. Equation A.15 calculates the angular dependence of
the diffracted intensity, 101)“, and Equation A.16 represents the normalized orientation
distribution function, N(,u). However, they require the assumption or limitation of a

random texture or wire texture along the stretching direction.

‘12
1m): I 1(q, #04qu (AIS)
‘11

q
N(#)=1(#)/7f 1210140612 sin/qud/J (A.16)
0 q1

It is difﬁcult to compare the 10:, 8”) quantitatively for various POSS-grafted
systems. It is possible to summarize 1(a) as a scalar by calculating the average cosine
squared of the diffracting intensity (<coszw) from the normalized orientation distribution
function, N(,u). The degree of orientation can be more straightforwardly represented as a
scalar by the Herman’s orientation function or second-order orientation factor, f7 1. f is
related to the N01) through (0052p) by Equations A.17- A.19. For a random microdomain

orientation represented by a uniform intensity ring, f —-> O. In the case of lamellae, f —-> 1

for lamellae perfectly aligned in the stretching direction (lamellae normals orthogonal to

147

the stretching direction), and f —> -O.5 when the lamellae are oriented orthogonal to the

stretching direction (lamellae normals in the stretching direction).

2 7‘ 2
<cos p>EIcos pN(p)sinydp (A.17)
0

f = (3(a)? y) —1]/ 2 = %[iN(p) (sin ﬂ)(cos2 u) du — 31,-] (A18)

 

0
K
”‘12 2 2 . N
I l 1(q,#)q (cos #](Sln#)dqd#
Oq
f=(3<cosz,u>—1)/2= 3 1 J (A.19)
2 ﬂqz 2 2
I I 1(q,#)q (sin#)dqd#
\ Oql /

 

 

The procedures for calculating f in this document begin with the 2D SAXS image.
The diffraction pattern is integrated to get SAXS proﬁles of 1(q) for 91 angular slices (of
2° each) from -1° to 181°, where 90° coincides with the stretching direction (Figure A.2).
Each angular slice represents a value of ,u. Each of these patterns is subsequently
integrated numerically in the form of Equation A.15 over a q-range of the primary
diffraction peak to obtain 1(a) for 2° increments of ,u. This data is then integrated with sin
,u to obtain the denominator in Equation A.16, and N01) is calculated. Another numeric

integration is performed to obtain <coszu> and is f is calculated arithmetically.

Tensile Device for In-Situ Deformation Experiments using SAXS

In-situ stretching was performed using two co-rotating cylinders driven by a
stepper motor. A schematic of the setup is shown in Figure A.2. The setup allows for

continuous stretching to an unbounded strain. The motor for the stretching device is

148

90° - Stretching
Polymer Direction

Film
\A Detector

. > \QN
Incrdent

X-ray

Beam
\ Stretching Device

Figure A.2. A schematic of the experimental setup for in situ deformation experiments
using small angle x-ray scattering.

 

 

 

0° - Transverse
Direction

 

 

 

 

149

directly connected to the bottom cylinder. The two cylinders are geared together so that
they rotate in the opposite directions. When the motor is driven at a constant angular
velocity, the polymer ﬁlm experiences tensile deformation at a constant Henky strain
rate. To facilitate an equal comparison, mechanical testing was also performed at a

constant Henky strain rate.

Experimental Calculations for Stretching Device Strain

The calculations for strain are not straightforward because the ﬁlm is no longer
stretched when it is drawn up onto the cylinders, as seen in Figure A.3. If the entire

length of the ﬁlm was continuously stretched, the strain, 6 (engineering), is

a = — (A.20)

where AL is the change in length of the ﬁlm and L0 is the initial length of the ﬁlm. AL
can be related to the rotation of the co-rotating cylinders by:

A1. = 2R6 (A.21)
where R is the cylinder radius and 6 is the rotation of the cylinder in radians. A factor of I

2 is needed because both cylinders rotate. Combining Equations A20 and A22:

 

e = 2R6 (A22)
1’0
To obtain the differential change in strain, d8:
213:3.19 (A23)
Lo

where d6 is the differential change in 6. Up to this point, the calculations are considered

for when the entire length of the ﬁlm was continuously stretched. Only the length

150

 

 

 

R

 

Figure A.3. A schematic of the mechanical portion of the stretching device.

151

between the cylinders, L0, is deformed in this setup. Thus, the actual strain will be larger
than equation A.22 since the gauge length is a subsection of the total length. To account
for the difference in strain, the effective length, Leff, must be considered. L4; is the length
of the ﬁlm if the entire ﬁlm were deformed with the same strain that the center region of
the ﬁlm experiences. The effective strain, 8e17, will represent the actual strain that the

center region of the ﬁlm experiences. Correcting the differential form of Equation A.23:

L
dew. = LIZ—R d6 (A24)

0 0
L917 can be related to 69);, so Equation A.24 becomes:

dam = (1+ 5,, )2;- d8 (A25)

0
Integrating Equation A.25 will result in the equation of the actual engineering
strain, 85 at rotation angle 6. The initial conditions are such that Eeﬁ': 0 at 6 = 0.

55 6

 

 

d
j 8"” = [35cm (A26)
0 (new) 0 L0
1n(1+e,,)= 31:9 (A27)
Lo
3, =exp[2R9]—l (A28)
L0

The equation for the actual strain can be simpliﬁed when expressed in terms of

Henky strain, 8”.

 

85 = exp(£H)—1; 8H = ln(55 +1) (A29)
8,, = 2R6 (A.30)
L0

152

In terms of the actual stretching device, R = 3/16 inch and L0 = 1 inch, then:

_ﬁ_7rw

e —— A.31
” 8 480 ( )

where a) is the angular change in degrees for the motor (or one of the cylinders since the

motor is directly connected directly inline with one of the cylinders).

 

153

 

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