n-

.....,~..mu V
m.

,
4?"...Em

i=5.

: 4 e a 3

. an...» . a:
u

to.
. '1‘... u t
€619... t Jud...—

”a

mu
2...... Am 5....

f: I
{3 wi
an: a»;

 

 

 

 

 

 

‘. _
k 1.

“5.13339.
1 ‘ :14. ..

2.1. 1 ... ‘ T

 

 

- :1.=,?ifj:‘.5l;

 

1 Q LIBRARY
2, OOc Michigan State
University

 

 

 

This is to certify that the
dissertation entitled

EQULIBRIUM AND NON-EQUILIBRIUM CONFORMATION
AND MECHANICAL PROPERTIES OF
NANOPARTICLE/LINEAR POLYMER BLENDS

presented by
DAVID ANDREW BOHNSACK

has been accepted towards fulfillment
of the requirements for the

PhD degree in Chemical Engineering

W/W

Major Professor’s Sién’ature
30 x9 Jé- 02 Oo 7

Date

 

 

 

-
o
-
c
I
I
u
n
c
I
I
I
I
n
o
I
I
I
.
I
O
I
I
I
u
I
I
o
I
u
I
l
I
I
I
I
l
u
o
I
u
c

MSU is an affinnafive-action, equal-opportunity employer

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date clue.
MAY BE RECALLED with earlier due date if requested.

 

DAIEDUE

DAIEDUE

DAIEDUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/07 p:/CIRCIDateDue.indd-p.1

 

EQUILIBRIUM AND NON-EQUILIBRIUM CONFORMATION AND
MECHANICAL PROPERTIES OF NAN OPARTICLE/LINEAR POLYMER BLENDS

By

David Andrew Bohnsack

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Chemical Engineering and Materials Science

2007

ABSTRACT

EQUILIBRIUM AND N ON-EQUILIBRIUM CONFORMATION AND
lVflECHANICAL PROPERTIES OF NANOPARTICLE/LINEAR POLYMER BLENDS

By

David Andrew Bohnsack

Fillers with characteristic sizes on the nanometer scale and aspect ratios near unity
are investigated for their potential to enhance the mechanical properties of a linear
amorphous polymer, polystyrene. Four types of nanoparticles with different sizes,
structures, and interactions with the matrix have been investigated to better understand
the particle-polymer interaction and its significance for mechanical property
enhancement. Generally, the particle inclusion increases polymer mobility and free
volume. This is observed through decreases in the glass transition temperature, bulk
modulus, and internal pressure, as well as increases in the free energy anharmonicity, and
strain-to-failure for a sample in tension. The particles behave in a manner similar to a
good solvent, swelling the polymer and increasing chain mobility and sample ductility, an
observation confirmed by neutron scattering. The details of the particle size, loading, and
chemistry introduce other nuances to the polymer-particle behavior. Bulk modulus
increases have been observed for many systems, and a general increase in the energy
dissipation for a sample in tension is observed with nanoparticle addition. The role of the
particles in the orientation of the matrix during uniaxial hot-drawing is studied. In many
cases, it is found that equivalent tensile property enhancement can be achieved under

more moderate processing conditions by the addition of nanoparticles.

I dedicate this work to my Lord and Savior, Jesus Christ. All that I have is from Him, and

all that I do is for Him.

iii

ACKNOWLEDGEMENTS
The work described in this document would not have been possible without the

help and collaboration of a number of people.

I am indebted to those people who provided the nanoparticles that were the basis
for this work. Specifically, I thank Brooke van Horne and Craig Hawker for the synthesis
of the cross-linked polystyrene nanoparticles, Suba Asokan and Michael Wong for the
CdSe nanocrystals, and Guangui Chen and Zhibin Guan for the hyperbranched
polyethylene. I have been especially reliant on the kind and capable staff of the two
neutron sources where I performed experiments. I deeply valued the help of Boualem
Hammouda at NIST and Denis Wozniak, Venky Pingali, and Pappanan Thiyagarajan at
IPNS. Their help in conducting the experiments and suggestions for interpreting the
results have been invaluable.

I consider myself fortunate to have worked under the direction of Prof. Michael
Mackay. I am grateful for the tremendous amount that I learned from him. His
enthusiasm and commitment to his students is apparent and appreciated in both our
professional and personal development. In that vein, he has built a strong research group
of which I am proud to have been a member. I am grateful to the group alumni, R.S
Krishnan, Leslie Passeno, and Anish Tuteja, for helping me to find my way in the lab. I
am also grateful to the newer group members, Jonathan Kiel, Erin McGarrity, Megan
Romanowich, Jonathan Seppala, and Erica Tseng, for their contribution of new ideas and
enthusiasm at a time when both were flagging. I have especially valued my
contemporaries, Tiffany Bohnsack and Melissa Yaklin. Their support as we navigated the

waters of graduate school has made the journey more than bearable, even pleasurable.

iv

I have also benefited greatly from a wonderful group of friends and family who
have supported me throughout my tenure at MSU. In addition to my friends in the
Mackay Group, I am grateful to my other colleagues in the department, Brian Hassler,
Troy Hendricks, Aaron Greiner, and Steven Nartker. I am especially grateful to my
family for their love and support, not only at this time of my life, but for all the years
leading up to this, and those yet to come. I thank my parents, Rich and Kathy, for
encouraging me to set high goals and always assuring me that they were within my reach.
It is the foundation they laid for me that has allowed me to achieve what I have. I thank
my elder siblings, Rob and Carin. Their interest and support in all that I have attempted
has been a source of great encouragement. Finally, I thank my wife Tiffany. Her support
both in and out of the lab has been instrumental in the completion of this work. I am

grateful for her patience, motivation, inspiration, encouragement, perspective, and love.

 

 

 

 

 

m,4 l .

Imt

AILYVV‘V

TABLE OF CONTENTS

List of Tables .................................................................................................................... viii
List of Figures .................................................................................................................... ix
Chapter I: Introduction ................................................................................................. 1
LA. Nanocomposites .................................................................................................. 1
LB. Motivation ........................................................................................................... 4
LC. Equilibrium interactions between particles and polymers .................................. 5
ID. Alignment of neat polymers ................................................................................ 9
LE. Objectives .......................................................................................................... 13
Chapter II: The effect of intramolecularly cross—linked polystyrene nanoparticles on
the thermal and mechanical properties of linear polystyrene ............................................ 14
EA. Introduction ....................................................................................................... 14
11B. Experimental ..................................................................................................... 16
H.C. Results and Discussion ...................................................................................... 21
H.C.l. Equilibrium Thermal Analysis .................................................................. 21
II.C.2. Non-Equilibrium Tensile Behavior ........................................................... 31
[ID Conclusion ......................................................................................................... 36

Chapter 1H: A small-angle neutron scattering (SANS) study of the anisotropic
conformation of linear polystyrene in the presence of intramolecularly cross-linked

polystyrene nanoparticles .................................................................................................. 37
IRA. Introduction ................................................................................................... 37
IH.B. Experimental ................................................................................................. 44
HI.C. Results & Discussion .................................................................................... 45
III.D. Conclusion ..................................................................................................... 53

Chapter IV: The effect of C60 addition on the thermal and mechanical behavior of P855
IV.A. Introduction ................................................................................................... 55
NB. Experimental ................................................................................................. 58
NC. Results & Discussion .................................................................................... 58

IV.C.l. Equilibrium Thermal Analysis .................................................................. 58
IV.C.2. Non-Equilibrium Tensile Behavior ........................................................... 67
ND. Conclusion ..................................................................................................... 71

Chapter V: Dispersion of hyperbranched polyethylene in polystyrene leading to

improvements in stiffness and ductility ............................................................................ 72
VA. Introduction ....................................................................................................... 72
V.B. Experimental ..................................................................................................... 73
V.C. Results & Discussion ........................................................................................ 73

V.C. 1. Equilibrium Thermal Analysis .................................................................. 73

vi

V.C.2. Non-Equilibrium Tensile Behavior ........................................................... 79

VD. Conclusion ......................................................................................................... 83
Chapter VI: Rigid nanoparticle inclusion with polystyrene .......................................... 85
VI.A. Introduction ................................................................................................... 85
VI.B. Experimental ................................................................................................. 85
VIC. Results & Discussion .................................................................................... 86
VI.D. Conclusion ..................................................................................................... 91
Chapter VII: Conclusions ........................................................................................... 93
Appendix A. Notes on PVT Analysis ......................................................................... 95
Appendix B. Additional Tensile Data ...................................................................... 103
References ....................................................................................................................... 104

vii

LIST OF TABLES

Table H-l: Molecular weights and distributions of linear polystyrene and
intramolecularly cross-linked polystyrene nanoparticles .................................................. 17

Table 111-1: Summary of previous work on alignment by hot drawing and their test
parameters. ........................................................................................................................ 39

Table 111-2: Molecular weights and distributions of linear polystyrene and
intramolecularly cross-linked polystyrene nanoparticles .................................................. 44

Table A-1: Values of free volume layer sizes based on the bulk moduli of composites at
200 °C ................................................................................................................................ 97

Table A-2: Tait EOS parameters in the melt state of polymer/nanoparticle blends ......... 98

Table A-3: Simha—Somcynsky EOS parameters in the melt state of polymer/nanoparticle
blends .............................................................................................................................. 100

viii

LIST OF FIGURES

Figure I-l. Typical process for fiber stretching. Extruded fibers pass over rollers that turn
at controlled, increasing speeds. This difference in roller speed induces strain, and
therefore alignment, in the fiber spinning direction. ......................................................... 10

Figure I-2. The room temperature stress-strain curves of unfilled PS 393 kD drawn in
tension at five hot draw ratios. PS processed to a hot draw ratio of 2 or greater exhibits
ductile failure where a less oriented specimen fails by a brittle process ........................... 11

Figure I-3. Schematic depiction of a typical necking process. Regions i and vi are regions
of primarily elastic deformation, while regions ii, iii, iv, and v are regions of primarily
plastic deformation. The initiation of a necked region (ii and iv) and the propagation of
those regions (iii and v) are demonstrated by a series of plateaus in the engineering stress.
........................................................................................................................................... 12

Figure 11-1. Cross—linked polystyrene nanoparticles are synthesized from a random
copolymer of styrene and benzocyclobutene (BCB). When thermally activated, the BCB
groups bond with one another to form an intramolecularly cross-linked particle. ........... 16

Figure 11-2. Change in glass transition with addition of PSNP. At low loadings the Tg is
reduced, contrary to the prediction based on relative weight fraction (indicated by open
symbols and dashed lines), suggesting additional molecular mobility at the particle
interface. Error bars indicate the initiation and completion temperatures of the glass
transition process. .............................................................................................................. 22

Figure II—3. DSC traces for PS, PSNP 78 kD, and a 5% blend of PSNP 78 kD in PS ...... 24

Figure 11-4. Bulk modulus and thermal expansivity of a PS with PSNP 78 kD. The cross-
linked particles tend to decrease the bulk modulus and increase the thermal expansivity
slightly (a). These two effects are suggestive of the introduction of a small region of
unoccupied volume around the surface of the fillers. Similar trends are seen in the bulk
modulus both above (200 °C) and below (50 °C) the glass transition temperature.
Prediction of the bulk modulus with a free volume layer of 1.2 nm provides a satisfactory
fit to the measured bulk modulus at 200 °C (b). The prediction for no free volume is for
an increase in KO, which is not observed ........................................................................... 25

Figure 11-5. Schematic representation of a particle (p) surrounded by a layer of free
volume (f) within a continuous matrix phase (c). The particle has a radius, a, and the free
volume region has a thickness, If ....................................................................................... 27

Figure 11-6. The free volume asymmetry number, and internal pressure as function of
PSNP 78kD volume fraction in PS 393kD. The free volume asymmetry number is
increased with nanoparticle addition, suggesting an increased energetic penalty to
compression as compared to dilation. The internal pressure is decreased by particle
addition, consistent with a decrease in the strength of intermolecular interactions. ......... 28

ix

Figure 11-7. The dimensionless free energy as a function of relative density. The
anharrnonic potential shows an equivalent free energy change for compression or
dilation. The addition of PSNP 78kD is seen to exacerbate the asymmetry of the free
energy profile, with dilation being energetically favored over compression. ................... 29

Figure H-8. Stress-strain curves for unfilled polystyrene and polystyrene filled with three
different PSNP types, each processed to a hot draw ratio of 1.75. The two larger PSNP
species induce ductile failure under conditions for which the unfilled polymer and the
polymer filled with PSNP 41 kD fail by a brittle mechanism at low strains. ................... 32

Figure 11-9. The Young's Modulus (a), strain to failure (b), ultimate tensile strength (c),
and tensile energy to break (d) of hot-drawn PS 393 kD with PSNP as a function of hot
draw ratio. Larger PSNP species have very little effect on Young's Modulus or ultimate
tensile strength, while smaller (41 kD) particles increase these properties for the
unprocessed and slightly processed case. The ductility (b) is increased for all cases at low
draw ratios and at all draw ratios for PSNP 78 kD, which gives rise to an increase in the
material toughness (d). ...................................................................................................... 33

Figure 111-1. The background signal is assumed to be constant at all wave vectors, at
reasonable approximation for the predominantly incoherent scattering observed for
protonated PS. ................................................................................................................... 43

Figure 111-2. The anisotropic SANS pattern of a non-equilibrium, hot stretched PS film
(left). The scattering profiles parallel and perpendicular to the stretch direction are shown
on the right. ....................................................................................................................... 46

Figure III-3. The Lorentzian exponent of PS with and without PSNP addition as a
function of hot draw ratio. The Lorentzian exponent for a Gaussian chain is 2. Swollen
coils exhibit a reduced dependence of I on q at higher wave vectors. .............................. 48

Figure 111-4. The characteristic size development of anisotropic PS with and without
PSNP 78 kD as a function of hot draw ratio. The macromolecular size is calculated
according to either the Debye form factor (a) at all wave vectors, or the Lorentzian
scattering function at high wave vectors. In both cases a discontinuity is observed for the
nanoparticle-laden sample at 7:175, the hot draw ratio at which ductile fracture behavior
is observed in tension. A small increase is observed in the long axis size of the polymer at
the highest draw ratio by both methods of calculation ...................................................... 50

Figure III-5. The aspect ratio development of anisotropic PS with and without PSNP 78
kD as a function of hot draw ratio. The aspect ratio is calculated according to either the
Debye form factor (a) at all wave vectors, or the Lorentzian scattering function at high
wave vectors. In both cases a discontinuity is observed for the nanoparticle-laden sample
at 7t=l.75, the hot draw ratio at which ductile fracture behavior is observed in tension.
The dashed line represents the aspect ratio for a chain that deforms affine to the bulk
sample, the maximum attainable orientation in the absence of an additional driving force.
........................................................................................................................................... 52

' .1159

:n_

 

.vrfi'

 

 

Figure IV-l. Change in glass transition with addition of C60. Extremely low
concentrations - corresponding with an interparticle half-gap of similar size to the
statistical Kuhn segment length of polystyrene - of C60 show an increase in Tg that
corresponds to a reduction in polymer mobility. Higher, but still homogeneously
dispersed, loadings show a T g reduction. .......................................................................... 59

Figure IV -2. Bulk modulus and thermal expansivity of a
polystyrene/buckminsterfullerene blend. At very low volume fractions for which the
interparticle gap is greater than the statistical segment length of the matrix polymer, the
bulk modulus is reduced and the thermal expansivity is increased. At higher loadings, the
C60 is spaced closer than the Kuhn segment length of polystyrene and the bulk modulus is
increased and the thermal expansivity is decreased. Similar trends are seen in the bulk
modulus both above (200 °C) and below (50 °C) the glass transition temperature.
Prediction of the bulk modulus with a free volume layer of 0.26 nm provides a
satisfactory fit to the measured bulk modulus at 200 °C (b). The prediction for no free
volume is for a much greater increase in KO than is observed experimentally. ................ 62

Figure IV-3. The free volume asymmetry number, and internal pressure as function of
C60 volume fraction in PS 393 kD. The free volume asymmetry number goes through a
maximum before decreasing with increasing particle loading. The internal pressure is
decreased by particle addition, consistent with a decrease in the strength of
intermolecular interactions. ............................................................................................... 64

Figure IV -4. The Young's Modulus (a), strain to failure (b), ultimate tensile strength (0),
and energy to failure ((1) of hot drawn PS 393 kD with buckminsterfullerenes as a
function of hot draw ratio. The modulus (a) and ultimate tensile strength (0) are
unchanged for the undrawn case and increased by C60 inclusion at low draw ratios for
both loadings. At higher loading (2.5v%) the modulus and ultimate tensile strength are
reduced at draw ratios greater than 2.5. The ductility (a) is increased for both loadings at
moderate (1.75 to 2.5) draw ratios. At higher draw ratios the samples with low loading
(lv%) are similar to unfilled PS while the higher loading (2.5v%) is much less ductile
than the neat polymer. ....................................................................................................... 68

Figure V-l. DSC traces of pure PELP and blends of PELP with linear PS. Phase
separation becomes apparent in the DSC trace for the 5% blend. .................................... 75

Figure V-2. Bulk modulus and thermal expansivity of a polystyrene/hyperbranched
polyethylene nanoparticle blend. The PELP decreases the modulus and increases the
thermal expansivity as expected for a system with little chemical interaction. Similar
trends are seen in the bulk modulus both above and below the glass transition
temperature. ....................................................................................................................... 76

Figure V-3. The free volume asymmetry number, and internal pressure as function of
PELP volume fraction in PS 393 kD. The free volume asymmetry number is increased
with nanoparticle addition, suggesting an increased energetic penalty to compression as
compared to dilation. The internal pressure is decreased by particle addition, consistent
with a decrease in the strength of intermolecular interactions. ......................................... 78

xi

Figure V4. The Young's Modulus (a), strain to failure (b), ultimate tensile strength (c),
and tensile energy to break ((1) of hot-drawn PS 393 kD with 3v% PELP as a function of
hot draw ratio. All four key tensile properties are increased at draw ratios less than five.
At higher draw ratios, the behavior of the matrix dominates and the composite follows
the tensile properties of unfilled polystyrene. ................................................................... 80

Figure V-5. Stress-strain curves for polystyrene with (green diamonds) and without
(black circles) PELP, each processed to a hot-draw ratio of 1.5. The PELP induces ductile
failure under conditions for which the unfilled polymer fails by a brittle mechanism at
low strains. ........................................................................................................................ 82

Figure VI-l. The Young's Modulus (a), strain to failure (b), ultimate tensile strength (c),
and tensile energy to break (d) of hot-drawn PS 393 kD with IV% CdSe-pyr as a function
of hot draw ratio. The modulus and tensile strength are both increased at all draw ratios
less than five. The strain to failure and tensile energy are increased at moderate (2 to 2.5)
draw ratios but unchanged from the unfilled polymer under other processing conditions.
........................................................................................................................................... 88

Figure VI-2. TEM micrograph of CdSe-pyr in PS. The wrinkles in the film are a familiar
artifact of ultramicrotomy, reflecting imperfections in the knife edge. The particles are
oriented perpendicular to these striations, suggesting that the particles are disturbed
during the microtomy process and deposited intermittently as the knife moves across the
sample ................................................................................................................................ 91

Figure VII-l. The calculated free volume layer size (a) and free volume fraction relative
to particle volume fraction (b) for nanoparticles for four different sizes. The free volume
thickness associated with the particle addition increases with particle size. With the
exception of the extreme case of C60 (a = 0.38 nm), the ratio of free volume to particle
volume is independent of particle size. ............................................................................. 94

Figure A-l. The measured specific volume (a) of polystyrene-nanoparticle blends.
Blends of polystyrene with nanoparticles follow close to a rule-of-mixtures type trend for
specific volume. The deviation from that trend is apparent in the Excess Free Volume (b)
for which a positive value represents the presence of free volume in the blend. It must be
noted that the measurement technique is very subject to environmental variations and
small changes in free volume may not be apparent in specific volume measurements. . . .95

Figure A-2. The Simha-Somcynsky statistical hole fraction for blends of PS 393 kD with
four different nanoparticle types ................................................................ 102

Figure B-l. The Young's Modulus (a), strain to failure (b), ultimate tensile strength (c),
and tensile energy to break (d) of hot-drawn PS 393 kD with PSNP as a function of hot
draw ratio. Blends of 1% PSNP are represented by open symbols while blends of 5%
PSNP are represented by closed symbols. Larger PSNP species have very little effect on
Young's Modulus or ultimate tensile strength, while smaller (41 kD) particles increase
these properties for the unprocessed and slightly processed case. The ductility (b) is

xii

increased for all cases at low draw ratios and at all draw ratios for PSNP 78 kD, which
gives rise to an increase in the material toughness (d) ........................................ 103

xiii

Chapter I: Introduction

LA. Nanocomposites
The development of techniques to create well-defined structures with

characteristic dimensions less than 100 nm has led to new possibilities for structural
enhancement of polymers. The general strategy for the formulations of these
nanocomposites is similar to traditional composites; a material of higher modulus and
aspect ratio is incorporated into the weaker matrix material with the objective of
concentrating stress on the higher modulus material, thereby strengthening the composite.
A number of types of nanoparticles which have a multitude of properties have received
particular attention. In contrast to this traditional mode of enhancement, we hypothesize
that the small characteristic length scale of these additives and their close proximity to
one another presents the opportunity to alter the structure of the matrix material itself,
thereby strengthening it directly.

The development of characterization techniques suitable for probing length scales
in the nanometer range has given momentum to the design and characterization of
nanocomposites. Microscopy techniques which are different, but complementary to one
another, allow visualization of particles and structures with feature sizes on the order of 1
nm. While microscopy can be used to visualize local features, scattering methods provide
an avenue for evaluating the overall, average, morphology of a given system.

Scanning electron microscopy (SEM) facilitates visualization of surface
topographies and limited compositional information based on Z-contrast. A key obstacle
in the use of this technique is the need for the sample to be electrically conductive. This

requirement can be circumvented by coating the sample with a thin layer of conductive

material, often gold. Unfortunately, this coating layer may obscure the smallest
topographical features. Environmental SEM (ESEM) can also be used to characterize
insulating samples without the need for a conductive layer. This is achieved by
immersing the sample in a conductive environment, generally water vapor, rather than the
high vacuum used in traditional SEM.

Transmission electron microscopy (TEM) and atomic force microscopy (AFM)
allow the visualization of particles and structures with length scales close to 1 nm. TEM
samples must be sufficiently thin so that the number of scattering events per electron is
close to one. Contrast is achieved in TEM imaging through Z contrast and, to a lesser
degree, mass density. Where sufficient natural contrast is not present, it can be enhanced
through the use of TEM-specific stains. Heavy metal compounds such as 0304 or RuO4
will preferentially bind to certain chemical environments, especially unsaturated carbon-
carbon bonds. This allows Z-contrast to be induced where previously only chemical
differences were present. AFM relies on the physical interaction between a probe having
a radius of curvature less than 20 nm and the sample surface. Primarily used for
profilometry, AFM can also be used as a relative measure of sample stiffness, as regions
of different modulus cause the cantilever tip to oscillate at different frequencies. While
the vertical resolution attainable by AFM is close to 1 nm, the lateral resolution is limited
by the probe tip radius and is often an order of magnitude greater than the vertical
resolution.

In addition to microscopic techniques, scattering methods provide a means to
understand the average size and structure of a particular species. The variety of scattering

methods available — light, x-ray, neutron — ensures that a suitable technique will likely be

available based on the type of contrast that is available for a given sample. A key
advantage of scattering methods is that an average measurement is made over billions of
scatterers, in contrast to microscopy methods with which at most order of one hundred
objects are characterized. While scattering and microscopy are the key methods for
visualizing or deciphering nanostructures, the range of bulk characterization methods also
reveal nanoscale features such as the strength of interaction at nanoscale interfaces or the
presence of free volume.

A number of length scales that are significant in a filled system are affected
greatly by the reduction in the filler size. One such length scale is the interparticle half-
gap, h, which is determined by the particle radius, a, the particle volume fraction, (p, and
the maximum random packing fraction, (pm, for the particle geometry in question.

Eq. 1 Ma = (tom/W —1
For the case of a colloidal (1 pm radius) particle versus a nanoscale (5 nm radius) particle
the reduction in radius at constant volume fraction results in a reduction of the
interparticle half-gap from ~1300 nm to ~7 nm at a modest loading of 5v%. When
included in a matrix of moderately high molecular weight (500 kD) polystyrene, the
interparticle half-gap of the colloidal system is nearly 70 times the radius of gyration (Rg)
of the host polymer, while the half-gap in the nanosize system is only one third of the
polymer’s R3. This geometric evaluation makes it clear that a polymer chain of this
molecular weight could not reside between neighboring nanoparticles without becoming
distorted from its equilibrium conformation. Systems for which the interparticle half-gap

is less than the matrix polymer’s Rg are referred to by us as confined, and have been

 

III

de
Till
as

sol
mu

[hes

cred

shown to display behavior that is substantially different than that of the neat polymer or
of a traditionally modeled system.

A decrease of the individual particle size at constant volume fraction naturally
also increases the number concentration of particles. For the present example of a
colloidal versus nanoscale particle, the number concentration is increased by a factor of
8 x 106, which obviously increases the surface area for interaction. If one assumes that
the polymer within a certain layer thickness, 1, is directly affected by the presence of the
particle, then the increase in surface area will also increase this volume of interaction. In
fact, if one assumes that the thickness of the interaction is similar to the Kuhn segment
length of the polymer - 1.8 nm for polystyrene — then for the present example of the
colloidal versus nanoscale filler the interaction volume increases by a factor of 240 for
the nanoscale filler over the colloidal filler and can represent ~3 % of the volume for the

nanoscale system.

LB. Motivation

Much effort has been devoted to mimicking the hierarchical structures
demonstrated by natural systems which often exhibit key features in the nanometer size
range. The controlled liquid crystallinity of silkworm1 and spiderz'4 silk has been studied
as a potential route to high modulus synthetic fibers5 and the layered structure of hard and
soft components in nacre has been studied6 in hopes of achieving a similarly strong
material through structural control of synthetic composite materials. The recognition that
these naturally occurring systems that exhibit desirable end-use properties rely heavily on
the structures and interactions that occur over nanometer length-scales lends further

credence to the importance of controlling these behaviors in synthetic systems.

One product area that is especially appealing for the application of
nanocomposites is protective materials, especially body armor. The ability to produce
synthetic fibers with very high modulus supports the development of woven fabrics that
can be used as body armor. Kevlar, for example, has been used to achieve extremely high
modulus predominantly through strong interchain hydrogen bonding between the
polyaramid chains which is enhanced by the polymer chain alignment.7 Ultra—high
molecular weight polyethylene (UHMWPE), sold commercially as Dyneema or Spectra,
owes its very high impact strength to the extreme length of its chains and their high
parallel orientation (up to 95%).

In addition to high modulus materials, flexible fibers that effectively dissipate
energy prior to failure are needed as restraints. These restraint and cushion materials must
deform to gently bring their cargo to a stop in the event of a sudden impact or change in
velocity.

It has been found that, in some cases, the addition of nanoparticles to a polymer
can reduce the polymer’s viscosity,8' 9 resulting in a reduction of energy needed for
processes like extrusion and injection molding. While this is beneficial from a processing
standpoint, in order to be industrially viable the additives must, at the least, not diminish
the end use properties of the product. Particles that also provide an improvement to the

end use properties in addition to facilitating processing would be particularly desirable.

I.C. Equilibrium interactions between particles and polymers
The ability to uniformly disperse nanoparticles within a linear polymer matrix is

significant for the development of functional polymer composites, as well as a new route

to enhanced processing or end—use properties through nanoparticulate additives. While

the phase stability of these blends has been studied,10 the filler-particle interaction of the
binary system is insufficiently understood. Some effort has been devoted to the
interactions of nanocomposites of inorganic fillers with high aspect ratios.”14 These
studies often involve melt-compounded clays with high surface energy and a strong
attractive interaction with the polymer melt. Due to the strong van der Waals forces
present between individual clay sheets, adequate exfoliation of the sheets and subsequent
intercalation of the polymer between the sheets is often problematic. Once these obstacles
are overcome, the frequent result is a tendency towards adsorption of the polymer on the
clay surface, resulting in the “hairy clay platelet” structure which has an abnormally high
polymer density at the clay surface.

The situation of a filler particle with an aspect ratio approaching unity and a
characteristic length on the nanometer scale is much different, as it lacks the large smooth
surface that leads to a concentration of van der Waals forces. A considerable amount of
theoretical and simulation work has been devoted to understand the conformation and
behavior of a polymer chain confined near a spherical surface.”'19 In molecular dynamics
simulations of a rigid spherical particle in a polymer matrix, Brown et al.20 showed that
the polymer can orient parallel to the particle surface, leading to radial density
fluctuations very close to the particle surface. This interphase region has a reduced bulk
modulus due to the distortion of the melt structure and regions of low density. Very high
loadings of the nanoparticle result in a high volume fraction of this interphase which
reduces the total bulk modulus to a value less than that of the neat polymer.
Papakonstantopoulos et al.18 studied the effect of the polymer-particle interaction force,

finding that attractive polymer-particle interactions lead to the formation of a glassy

ill

Sig

interphase layer around the particle, increasing the shear and Young’s moduli. Repulsive
particle-polymer interactions, on the other hand, produced an interphase region with a
modulus less than the bulk, surrounded by a region with modulus greater than the bulk.
The net effect of this is reduction of the overall modulus and glass transition temperature
of the composite system. These simulations are computationally difficult, however,
especially because the time scale of large polymer relaxation is much greater than the
time scales that can generally be probed by molecular dynamics simulations.” 22 The
alternatives to rigorous simulations of long chain polymers include limiting simulations
to oligomeric systems which may overlook entanglement or entropic effects,18 or
simulating only a few phantom chains by attempting to mimic the behavior of a single
chain in a continuum melt.l7

While simulation efforts have shed light on the problem, there is less
experimental work devoted to this situation of spherical fillers with radii less than or
equal to the R8 of the matrix polymer.23 In one case described by Merkel et al.,23
spherical fumed silica particles were incorporated into a membrane material of glassy,
amorphous poly(4-methyl-2-pentyne). The result was an increase in the gas permeability
and an increase in the size of one type of free-volume void as observed by positron
annihilation lifetime spectroscopy (PALS). By performing similar tests with particles of
varying size but constant volume fraction, it was concluded that smaller particles cause
greater disruption to the polymer matrix, likely due to their increased surface area. The
maximum particle size that affected a change in the free volume or permeability for this

system was found to be 50 nm.

The glass transition temperature (Tg) is an indicator of polymer chain mobility in
amorphous polymers. More mobile chains require less thermal energy to initiate the
Brownian motion of 20 to 50 carbon atoms that is characteristic of a material above its
Tg.24 This transition is sensitive to the polymer’s chemical structure and molecular
weight, as well as the environment in which it is located. Studies have shown that placing
a polymer in a thin film, pore, or other confined geometry alters its conformation
sufficiently to change the Tg.25'27 Studies of the effect of nanofillers on the glass
transition temperature have shown that they can increase or decrease Tg by as much as
30 °C.28

In a study of PDMS networks filled with 10 nm silica particles, Fragiadakis et
al.29 found that the Tg was not significantly changed, but the shape of the calorimetric
step change was altered with the particle addition. Dielectric measurements confirmed the
presence of a second slower (rt-relaxation indicative of the restricted motion of polymer
chains near the particle surface.

Bansal et al.30

studied the effect of wetting behavior on Tg of nanocomposites by
grafting oligomeric polystyrene chains onto silica spheres in a polystyrene matrix. By
increasing the molecular weight of the matrix polymer, the system transitions from
wetting to dewetting behavior. In the case of the low molecular weight, wetting system,
the strong interface reduced chain mobility and increased the Tg by as much as 4 0C. The
high molecular weight, dewetting system showed a T8 reduction of as much as 4 °C,
caused by the introduction of a free interface that increased chain mobility at each

particle surface. This behavior is similar to the behavior observed for T1; changes in thin

polymer films.31 In similar work, Rittigstein and Torkelson32 prepared nanoparticle filled

films and observed the change in both Tg and physical aging rate. For poly(2-vinyl
pyridine) filled with 47 nm alumina particles which had an attractive wetting interaction
the Tg increased by 16 °C and the rate of physical aging, another measure of molecular
mobility, decreased by a factor of 17. A non-wetting system of alumina particles in
poly(methyl methacrylate) showed a Tg reduction of 5 °C and the same particles in
polystyrene had a wetting, but not attractive interaction, causing the TS to be unchanged
by the particle addition.

Another method of nanoparticle inclusion is grafting particles directly onto
polymer chains as random copolymers, a method often employed with polyhedral
oligomeric silsesquioxane (POSS). Xu et al.33 studied the thermal effect of POSS
inclusion with poly(acetoxystyrene) (PAS). Their study revealed competing and adverse
effects on Tg; at low POSS concentration, the POSS disrupted the dipole-dipole
interaction of the PAS chain, decreasing the Tg. At higher POSS concentration the Tg
increased as dipole-dipole interactions between POSS and polar PAS moieties became

more significant.

LD. Alignment of neat polymers

Introducing global alignment to otherwise amorphous materials is known to
increase their tensile strength in the direction of alignment.“ 35 This has been
demonstrated for linear polymers by introducing axial strain to a sample above its Tg,
then quenching it well below Tg, locking the polymeric chains in their nonequilibrium
anisotropic conformation. This process is representative of typical polymer processing
methods that consist of fiber formation by either melt or gel spinning, followed by hot-

stretching which is controlled by passage over rollers that move at progressively

increasing speed. The process is completed by cooling the sample through immersion in a

low temperature bath and optional cold—stretching below Tg (Figure H).35

W“— Extruder
1 Sir I h. R ll
Idler Rolls (— e 0 mg 0 S
_SnUbbl1
'9 o—o
.. . Rolls if \\

 

 

 

 

 

.................

.................

 

 

': - Cooling
" Rolls

-...
IIIII

  

 

 

 

 

 

 

. u
4.. ..
.- . -
... ..

. .. . ....

. ..- .. ...

.. .. . .... .

._ ’._. . .-.'. p

I III la au- .59.

. .. . .... e

. ... .. ...

‘. .'.’. .‘. '.'.'.'

. .. . .-..

- III II III UIII

..‘..’ .'.'..°. '..'.‘. .‘_'. .'.’.‘.'.‘ '.'.'.'

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

.. ... ......... '. '- .2. . . ..‘..'.'-‘. -'.‘.‘.

.... .... ..... ............ . ...

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

....................... ............-......-..,.............

L L .
Hot Bath Quenching Bath

Figure I-l. Typical process for fiber stretching. Extruded fibers pass over rollers that turn
at controlled, increasing speeds. This difference in roller speed induces strain, and therefore
alignment, in the fiber spinning direction.

 

 

 

 

In addition to a simple increase in tensile modulus or ultimate tensile strength,
chain alignment by hot-stretching has been shown to increase the material’s strain—to-
failure. At low draw ratios, this is manifested as an incremental increase in the strain-to-
failure, while still fracturing by the brittle mechanism that is expected for amorphous
polymers below their Tg. At higher draw ratios, a change is typically seen in the failure
mechanism as the sample begins to exhibit ductile fracture behavior. The stress-strain
curves for PS 393 kD are shown in Figure 1-2 for samples processed to a number of hot
draw ratios. Ductile failure initiates after a maximum in the stress-strain curve after
which the sample cross—section decreases locally, creating a “neck” in the sample which

propagates along the sample in the stretch direction as plastic deformation proceeds.

10

 

 

 

 

 

 

 

 

' l ' l ' .
10‘ J "3 "r. f." ..
D. . I. "f' ..... -
E ;. ... ~ ’ " -
(D ' 4 o-
co #3- l :
U) '1 ..
.5 30 hi' l +
L 4‘ | T
a .1: .
. ..' l '
'EC'» 20 I l l -
c 5:. i -e— =
”J A; f g "B” A. = 1 5
10 H“ l +—x=175
{“0 ll 7 ”‘ 7‘ = 2
‘ ' + =
. :3 ’3 LT] I 1 ! 1*, A: 2 5
0.0 O 2 0.4 O 6

Strain

Figure [-2. The room temperature stress-strain curves of unfilled PS 393 kD drawn in
tension at five hot draw ratios. PS processed to a hot draw ratio of 2 or greater exhibits
ductile failure where a less oriented specimen fails by a brittle process.

The origin of ductility and necking — a schematic illustration of the morphological
changes and corresponding stress-strain response is depicted in Figure I-3 — in aligned
samples is attributed to an increase in the ability of the sample to distribute stress along
the length of the sample.36' 37 Whereas an isotropic sample concentrates stress at sample
flaws or cross-sectional area minima, a sample with axial orientation can distribute stress
along the polymer chain backbone which is aligned in the stress direction. This more
even distribution of stress means that regions of the sample with sufficient local freedom
to deform can do so, relieving stress from those regions without sufficient mobility to

deform without fracturing.

11

 

 

 

 

 

 

><JE§

 

 

 

 

 

 

 

 

 

 

 

Figure [-3. Schematic depiction of a typical necking process. Regions i and vi are regions of
primarily elastic deformation, while regions ii, iii, iv, and v are regions of primarily plastic
deformation. The initiation of a necked region (ii and iv) and the propagation of those
regions (iii and v) are demonstrated by a series of plateaus in the engineering stress.

12

LE. Objectives

In the present work, blends of linear polystyrene with four primary types of
nanoparticles are investigated. The blends are investigated in their equilibrium state by
DSC and PVT. The tensile properties of the blends are also measured in both their
equilibrium state and in their non-equilibrium state following chain alignment by uniaxial
hot drawing. In some cases, the conformation of the polymer chain following this
alignment process is evaluated by small angle neutron scattering. Cross-linked
polystyrene nanoparticles (PSNP) are used as an enthalpically simple system with
moderate particle stiffness. Buckminsterfullerenes (C60) are rigid, high modulus particles
with a size scale much smaller than PSNP. Hyperbranched polyethylene macromolecules
(PELP) are a low modulus filler with an unfavorable interaction with PS. Finally,
pyridine stabilized cadmium selenide nanocrystals are rigid particles with a size scale

comparable to PSNP.

13

Chapter II: The effect of intramolecularly cross-linked
polystyrene nanoparticles on the thermal and mechanical
properties of linear polystyrene.

ILA. Introduction

A key factor in any study of composites is the enthalpic interaction between the
host matrix and the filler particle. In the case of traditional composites with macroscopic
fillers this interaction is largely responsible for the filler-matrix bonding that dictates how
well stress will be transferred across the interface. Poor interaction leads to poor stress
transfer, weakening the material. The issue of chemical compatibility becomes even more
important as the filler size is reduced, increasing the interfacial area and decreasing the
interparticle gap at equivalent volume fraction as well as increasing the particle mobility.
An unfavorable interaction will cause the filler and matrix to phase separate, leading to
an inhomogeneous dispersion and the reduction of mechanical properties. In addition to
the thermodynamics, the average interparticle gap is important to any analysis of a
system filled with nanometer-scale particulates since small gaps can lead to depletion
flocculation. The gap, 2h, is given by the equation

Eq. 2 Ma = (com/w)“ —1
and depends on the particle radius, a, the particle volume fraction, (p, and the maximum
packing fraction for the particle geometry, (pm.

The unfavorable interaction state is often ameliorated by chemically attaching a
species that interacts favorably with the matrix to the exterior of the filler particle. In the
case of polymer nanocomposites, the stabilizing species is often an oligomeric chain of
the matrix polymer. This strategy is often successful for enhancing the stability of the

system but, in addition to adding a synthetic obstacle, this strategy complicates analysis

14

by introducing a third, often ill-defined phase. Furthermore, the stabilizing ligand
generally does not possess the desired reinforcing character of the filler particle, thereby
acting against the desired effect of composite formulation.

One way to circumvent the practical difficulties of ligand stabilization is to
synthesize a nanoparticle that is itself chemically similar to the matrix polymer. Harth er
al.38 demonstrated a method for preparing cross—linked nanoparticles with well defined
sizes that are chemically similar to polystyrene (PS). This is accomplished by producing a
random copolymer of styrene with benzocyclobutene (BCB). The butyl group on the
BCB moiety can be thermally activated for potential cross-linking, leading it to bond with
a similarly activated group located elsewhere on the same chain. By activating the
reaction under ultra-dilute conditions it can be assured that each copolymer chain will
cross-link only with itself, producing an intramolecularly cross-linked nanoparticle that
has a well-defined size and is chemically similar to polystyrene. The degree of cross-
linking, and therefore the extent to which the macromolecule behaves in a manner more
consistent with a particle than a Gaussian chain, is controlled by the relative proportion of
BCB to styrene. While the ideal reaction cross-linking reaction is one in which two
identical cross-linking groups bond with one another, this is not the only possible
outcome. The activated cross-linking moiety may also capture a styrene backbone
hydrogen and bind at this newly activated site along the backbone. While this does not
functionally change the resulting product - an intramolecularly cross-linked structure is
created in either case — it should be noted that the structure may vary from the idealized

scheme, a representation of which is shown in Figure ILL

15

:IQUZIO

Crosslinking group

 

*-

A

Linear Chain Precursor Nanoparticle

Figure 11-1. Cross-linked polystyrene nanoparticles are synthesized from a random
copolymer of styrene and benzocyclobutene (BCB). When thermally activated, the BCB
groups bond with one another to form an intramolecularly cross-linked particle.

In the present study, the nature of the polymer-particle interaction is studied by
equilibrium DSC and PVT measurements. These complimentary techniques are used to
elucidate the system mobility and the introduction of free volume to the system by PSNP
addition.

The addition of the polystyrene nanoparticles (PSNP) to linear PS has been shown

. -4
prevrously39 2

to decrease the viscosity of the melt, aiding processing. Evidence that
these particles don’t diminish the mechanical performance of the polymer, or that they
even improve it, would lend additional credence to the application of these particles as
processing aids. To this end, the solid-state mechanical properties of the PS/PSNP blends
in tension are also examined. Specifically, a hot drawing scheme that approximates an

industrial fiber spinning process is used to understand how the PSNP influences the non-

equilibrium alignment of PS chains.

II.B. Experimental

Polystyrene standards were purchased from Scientific Polymer Products (Ontario,

NY). Intramolecularly cross-linked polystyrene nanoparticles were synthesized according

16

to the process described by Harth er al.9 The particles contained potentially cross-linking
benzocyclobutane (BCB) groups randomly distributed along the chain in a ratio of 4
styrene monomers: l BCB. Particle molecular weight values and distributions were
measured by an HPLC system with a Wyatt Technologies (Santa Barbara, CA) DAWN
EOS static light scattering detector, and an Optilab Rex refractive index detector.
Samples for HPLC were prepared in tetrahydrofuran and filtered through 0.02 pm filters
prior to characterization.

Table 11-]: Molecular weights and distributions of linear polystyrene and
intramolecularly cross-linked polystyrene nanoparticles

 

 

 

Sample Name Mw (g/mol) Mn_(_g/mol) PDI Rfl (nm)*
PS 393,400 339,140 1.16 17.3
PSNP 4lkD 42,520 41,090 1.04 2.5
PSNP 78 kD 89,020 77,830 1.14 3.1
PSNP 211 kD 278,400 211,200 1.32 4.3

* R3 for the linear polymer is based on molecular weight of PS. Radii for particles are
based on the bulk density of PS

Linear polymer/nanoparticle blends were made by dissolving both the linear
polymer and nanoparticle in a mutual solvent, toluene. The solution was then dripped into
a mutual non-solvent, methanol, where the polymer and nanoparticles rapidly
precipitated, forming an intimately mixed, homogeneous dispersion of nanoparticles in
the linear polymer.43 After removing the majority of the liquid from the sample by
decanting and vacuum filtration with copious methanol rinsing, the blend was dried for a
week in an oven at 50 °C and under rough vacuum.

Differential scanning calorimetry measurements were conducted using a TA
Instruments (New Castle, DE) Q-1000. The instrument was fully calibrated using indium

and sapphire standards. All tests were conducted using the modulated DSC (MDSC)

17

V0

dez

heat-only test type with a modulation period of 40 s and an overall heating rate of 5 °C
min'1 under a nitrogen atmosphere. Each sample was heated three times to erase the
thermal effects of processing and measurements were taken from the third heating. The
glass transition temperature is reported as the inflection of the step change in reversible
heat flow as a function of temperature. The onset and offset points of the transition are
indicated in the figure as bars above and below the point.

Pressure-Volume-Temperature measurements were conducted using a Gnomix
(Boulder, CO) bellows type PVT apparatus.44 This automated, programmable instrument
was used to measure the change in specific volume to within 0.0001 cm3 g'1 as a function
of pressure and temperature in an operating range of 10-200 MPa and ambient to 400 °C.
A hydrostatic pressure is achieved by immersing the sample in an inert confining fluid
(mercury), which is contained in a steel sample cell at one end of which is a steel bellows
of known cross-sectional area. The sample is prevented from adhering to the side of the
sample cell — which would result in only a quasi-hydrostatic pressure — by placing the
sample in a flexible Nickel foil cup. Expansion of the sample, confining fluid, and sample
cup are translated to the bellows, which deforms linearly, allowing quantitative
observation of the change in sample volume as a function of pressure and temperature in
both the solid and melt states. The measured quantity is the change in sample specific
volume, AV. The actual specific volume, V, is the sum of the measured AV and the
specific volume at the initial test condition, Vo_ Because the minimum test pressure is 10
MPa, an extrapolation of AV to zero pressure was used to ascertain the true specific
volume under ambient conditions. The sample specific volume at zero pressure was

determined based on the buoyancy of the sample in water, according to a procedure

18

 

110

Re

Cat

Inn

Sub.

adapted from ASTMD792. Prior to data collection, the sample was allowed to anneal
within the PVT cell for one hour at 150 °C to ensure that all measured properties were
equilibrium properties, and not influenced by processing conditions. Data were collected
using isothermal run cycles from 10 to 200 MPa and distributed at 10 °C increments from
30 °C to 200 °C; isothermal run cycles were used to prevent sample degradation at high
test temperatures from influencing subsequent runs.

Samples for PVT analysis were made by compression molding 200 - 400 mg
cylinders under vacuum to ensure that air was not incorporated into the sample. All
samples were annealed at 180 °C under no pressure for an hour or more to ensure that
polymer chains had sufficient time to relax and equilibrate prior to testing. A sufficient
number of cylinders were pressed to make the total sample size 1 g, the standard size for
PVT measurement.

Samples for mechanical testing were prepared by compression molding a void-
free pellet under vacuum. All samples were annealed at 180 °C for one hour or more to
ensure that polymer chains had sufficient time to relax prior to the next processing step.
Thin (ca. 0.3 mm) sheets were made by pressing the pellet in a sheet press at 160 °C
under a load of ca. 1 ton. Sheet thickness was dictated by placing steel shim stock
between the press plates. Sheets were annealed after pressing at 160 °C for two hours.
Rectangular strips were cut from the subsequent sheet using a razor blade with the sample
carefully positioned on a hard cutting surface to prevent any torsional stresses during
trimming. Dog bone shaped specimens were avoided, as they would unduly complicate

subsequent processing.

19

ft

r)
(‘1

str

Pll

Uniaxial processing was conducted using TA Instruments (New Castle, DE) RSA
3. Rectangular samples were affixed to the rectangular film sample geometry and heated
to the processing temperature (115 °C, ca. Tg + 10 °C) and allowed to equilibrate for 8
min. After heating, the gap was increased to take up slack in the sample caused by
thermal expansion of the tool and sample. The sample was then subjected to a constant
Hencky strain rate of 0.1 s'1 (8n = L‘1 (dL/dt». The draw ratio 0. = 111.0) was
predetermined by setting the sample deformation time. Once the deformation was
complete the sample was cooled using the instrument’s forced air environmental control
unit followed by exposure to ambient lab air. Cooling to below Tg generally occurred in
less than 15 s, with cooling to ambient temperature happening within 3 min. During this
time, the grips were held in place to prevent gross chain retraction. Samples were
removed from the instrument and measured to determine the minimum deformed cross-
sectional area. While the deformation surfaces were not uniformly parallel, a region in
the midsection of the sample usually had parallel surfaces, and this was the region used
for subsequent tensile testing.

Mechanical testing was carried out using a TA Instruments (New Castle, DE)
RSA 3 at ambient conditions and a constant Hencky strain rate of 0.01 3". Strain values
were corrected for the measured compliance of the instrument and Young’s modulus was
computed from the slope of the low strain linear region of the stress-strain curve. Many
stress-strain curves exhibit a toe region at low strains that is not indicative of any material
property, rather it is due to the take-up of sample slack at the test start. This deviation
from zero strain is corrected by extrapolating the linear portion of the stress-strain curve

to zero stress and setting this point as the strain origin. Tensile Energy to Break was

20

computed as the numerical integral of the stress-strain curve from the corrected strain
origin to the breaking strain. All mechanical properties are computed as the average of

three to five samples with error bars indicating the standard error between measurements.

II.C. Results and Discussion

II.C.1.Equilibrium Thermal Analysis
The glass transition temperature (Tg) is an indicator of polymer chain mobility in

amorphous polymers. More mobile chains require less thermal energy to initiate the
Brownian motion of 20 to 50 carbon atoms that is characteristic of a material above its
Tg.24 This transition is sensitive to the polymer’s chemical structure and molecular
weight, as well as the environment in which it is located. Studies have shown that placing
a polymer in a thin film, pore, or other confined geometry alters its conformation
sufficiently to change the Tg.25'27 One possible route to increase chain mobility is an
increase of free volume. As obstacles to motion are reduced, especially by the
introduction of unoccupied area (free volume), the thermal energy needed to initiate free
motion of the amorphous chains is decreased, leading to a reduction in the glass transition
temperature.

The effect of three PSNP sizes on the glass transition temperature (Tg) of
polystyrene is shown as a function of particle volume fraction in (Figure H-2). In all three
cases the TS is decreased by nanoparticle addition at low (1%) loadings. At higher
loadings the glass transition temperature increases, eventually surpassing that of the neat
polymer. The glass transition temperatures of the PSNP particles themselves are 15 to 20
°C greater than polystyrene. A general, rule of mixtures, approach to the T8 of the

polymer-particle blend would suggest that the glass transition temperature of the blends

21

 

Ex)
(1

C0:

fill:

should increase in a linear fashion between the Tg of polystyrene and the Tg of the pure

particles as a function of the volume fraction, (p, of the particle.

 

 

  
   

 

 

 

 

 

 

 

 

 

 

 

 

 

4 _ j I I l I l d
. r
2 l— ”—1
b -l
P
O ;
8 t 5 -
or '2 — i q
l- ’ -
4 ' 1
- ‘- .JL. -. L
-4 — .- I l
r L + PS 393kDa, PSNP 41kDa T
‘ + PS 393kDa, PSNP 78kDa ‘
-6 f +- PS 393kDa, PSNP 211kDa :
_ Open symbols with dashed lines .
i are predictions.
_ I J I 1 I 1
0.00 0.04 0.08 0.12

Volume Fraction Particle
Figure 11-2. Change in glass transition with addition of PSNP. At low loadings the T: is
reduced, contrary to the prediction based on relative weight fraction (indicated by open
symbols and dashed lines), suggesting additional molecular mobility at the particle
interface. Error bars indicate the initiation and completion temperatures of the glass
transition process.

Eq- 3 Tg(<p) = (l - (p) x Tg(<p=0) + (p x Tg(q>=l)
This expected behavior is shown in the figure for comparison.
In this enthalpically simple case of PSNP in PS the Tg decreases slightly (ca.
2 °C) at 1v% loading, then increases as the loading increases. While the samples are
confined (h < Rg) even at 1v%, the interparticle half-gap is greater than the radius of the

filler particle (h > a). At loadings for which the Tg increases to PS’s unfilled value, the

22

interparticle half-gap has been reduced to be less than the nanoparticle radius (h < a),
suggesting that a rogue nanoparticle would be hindered in its attempt to diffuse freely
though the polymer/nanoparticle medium. Previous measurements45 of the diffusivity of
nanometer-sized CdSe nanocrystals have shown the nanoparticles to diffuse anomalously
fast. If particle diffusion plays a significant role in the overall mobility of the system,
then this critical “jamming,” which occurs at (p Z 8%, would understandably contribute to
a reduction of system mobility and an increase in T8 when h < a. While this condition
serves as a helpful benchmark, interparticle interference to diffusion may become
operable at loadings even less than that.

The DSC traces of the individual species and blends of the two also shed light on
the quality of dispersion. Figure 11-3 shows the DSC traces of PS 393 kD, PSNP 78 kD,
and a blend of 5% PSNP 78 kD in PS 393 kD. The step change in the reversible heat flow
that is indicative of the glass transition is clearly visible for all three samples between 100
and 135 °C. The step change of the PSNP trace is more broad, and an endothermic
melting peak is seen near 20 °C. The trace for the PS-PSNP blend shows a single Tg and
no apparent melting peaks, suggesting phase stability. Phase separated samples, on the
other hand, often show the distinct features of the constituent species. While the DSC

trace is not a guarantee of phase behavior,46 it is a good indicator.

23

 

811'
an;
0b,
bch
Hm

 

    

r I I I

        
 

 

 

 

— P8393 kD l
----- PSNP 78 kD -
A '0'6 - - ,PS. PSNP 78kD, 5% "j
3 L : i :
g '0.8 ---;\ ., '_
a - i
E -1.0 7' ~5 ~ .—
4d ...‘ \
to ~ ; ~
0) ' ; \ .
I -1.2 :. ............ J. ‘1 s. ; ‘ __
9 - ' -:
.o - ..... .
'55 -1.4 - .. ._
L— - ‘~ -
m - d
5 - _
m -1I6 l..— -:
-1.8 :1-m ...__._....... f........"f:_~
l I A I -
0 50 100 150

Temperature (°C)
Figure 11-3. DSC traces for PS, PSNP 78 kD, and a 5% blend of PSNP 78 kD in PS.

The overall compressibility of the system and its volumetric response to changes
in temperature and pressure are sensitive to internal structure and the presence of void
space. Engineering properties of interest that can be derived from PVT data are the bulk
modulus, K = —V(6P/6V)T, and the coefficient of thermal expansion,47 or = V"(6V/6T)p.
In the case of the bulk modulus, changes brought about by particle addition result from
the interplay of two competing factors. Due to their intramolecularly cross-linked
structure, the PSNP are expected to have a bulk modulus greater than that of the
analogous linear polymer. This tendency toward more rigid, solid-like behavior has been
observed through the elevated T8 of the particle compared to PS and through their flow
behavior,48 exhibiting a yield stress rather than acting as a simple viscoelastic fluid.

However, the presence of free volume at the particle surface in the blend, as suggested by

24

 

(Iii—LS!) -4

HI

Fig
Iin
Sli;
Uni
m0
of I
me;
in l

the reduction of Tg, simultaneously reduces the bulk modulus of the nanocomposite. In
the case of PSNP 78kD in PS it appears that these two factors are well-balanced, resulting
in a modest reduction in K0, the bulk modulus extrapolated to zero pressure, at 200 °C
(Figure 11-4). In fact, while PVT measurements are only strictly valid in the melt state,
where pressure is uniformly hydrostatic, similar trends are also observed for the solid
state bulk modulus, measured at 50 °C (Figure II-4a). The reduction of the bulk modulus
provides strong evidence in support of an increase in free volume caused by PSNP
incorporation; if there were no additional free volume introduced, K0 would certainly be

increased by the addition of these semi-rigid macromolecules (Figure II-4b).

 

 

 

K0 (GPa) —e—

 

i 1.08 -
" 75-6 — I,-1.2mn \
. : ; 5 "w h-Onm \
l J l 1 l I _l
l . l i r

000 002 004 0065-5 1‘05 '
. - - - 0.00 0.02 0.04 0.06

 

 

 

 

 

 

 

 

Volume FraclJon ofParticle Volume Fraction of Particle

Figure 11-4. Bulk modulus and thermal expansivity of a PS with PSNP 78 kD. The cross-
linked particles tend to decrease the bulk modulus and increase the thermal expansivity
slightly (a). These two effects are suggestive of the introduction of a small region of
unoccupied volume around the surface of the fillers. Similar trends are seen in the bulk
modulus both above (200 °C) and below (50 °C) the glass transition temperature. Prediction
of the bulk modulus with a free volume layer of 1.2 nm provides a satisfactory fit to the
measured bulk modulus at 200 °C (b). The prediction for no free volume is for an increase
in K), which is not observed.

If an estimate of the bulk modulus for the nanoparticles is assumed, a relative

amount of free volume present in the sample can be computed based on a volumetric

25

average of the moduli of the three components: the continuous PS (0), particulate PSNP
(p), and free volume (f).
Eq.4 1=tpc+tpp+tpr
Eq.5 Ko=<ppKo.p+<pcKo.c
The known bulk modulus of the composite, K0, and the nominal volume fraction of filler,
(pm, p, can be used to calculate the free volume fraction.
Eq. 6 (pa, p=Vp/(Vp + V)
Eq. 7 cm = 1 — Kot(1-<p.,.)Ko,. + «p... . K0, .1"
If one assumes that the free volume is concentrated in an even layer around the particle,
with a radius a, the free volume layer thickness, If, can also be calculated.
Eq. 8 If: a me. + q») «ppz )‘B/wp) — 1]

It is likely that the presence of cross-linking increases the bulk modulus of the
particle beyond that of simple PS, so the pure polymer’s bulk modulus of 1.13 GPa is
used as a lower bound on the bulk modulus of PSNP. One might estimate that the
modulus scales as the coordination number. Monomers of the unfilled polymer have an
average coordination number of 2, while the monomers of the cross-linked particle have
an average coordination number of 2.2, based on 20% of the monomers having a nominal
coordination number of 3. This leads to a scaled estimate of the particles bulk modulus of
1.24 GPa which serves as a conservative upper-bound. Based on these values, the
average thickness of the excluded volume shell (Figure 11-5) around each particle is
between 0.65 and 1.8 nm. Volumetric estimates of the bulk modulus based on a PSNP
bulk modulus of 1.24 GPa and free volume layer thickness of 1.2 nm lie within the

experimental error of the bulk modulus measurements of the PS-PSNP blends (Figure

26

II-4b). A similar free volume size can be calculated from the solid state bulk modulus and

values of this calculation are tabulated in Appendix A.

 

 

/ ‘ , .
r/_,' ‘ /, - /
// / 0 C L , ..
, ,- /_. / _. / ., /

/ / l / r‘ f /- /; ’ ./ ,
1 1 ’ 711‘1111 '1'1//1// ”/1 ’1 /1 ’1' 1 11 ’ "-‘1

' , 1‘. ’I/ ’1 /
.I ,/
. . ‘ Ar /
.1 '1',
./ ,r 9
f

 

 

(I > ’ , I
1/141 ”4111/

 

Figure “-5. Schematic representation of a particle (p) surrounded by a layer of free volume
(1') within a continuous matrix phase (c). The particle has a radius, a, and the free volume
region has a thickness, If.

The calculation of increased free volume according to the bulk modulus is
supported by the observed increase in the thermal expansivity (Figure H-4a), which has
been attributed to an increase in the overall free volume of a sample.”52

In addition to the value of bulk modulus at zero pressure, it is instructive to
measure the slope of the bulk modulus as a function of pressure close to zero pressure, K1

(Figure 11-6). For PSNP 78kD in PS 393kD at low loading (1% to 2.5%) the value of K;

27

appears to change little compared to the unfilled polymer. However, at a volume fraction

of 5% the value of K1 increases by ca. 10%.

 

 

: I . l . I . 1 320
13.2 5 z ‘ ‘
: , — 300
12.8 E . _ 280
4) : ’ .1!
A E - 2602
g 12.4 F g
g t -240 I
1- " A
X : I
12.0 _-_-- - 220
E — 200
11.6 _— . E : ~
F I 1 I 1 I 1 I 180

 

 

 

0.00 0.02 0.04 0.06

Volume Fraction of Particle
Figure II-6. The free volume asymmetry number, and internal pressure as function of PSNP
78kD volume fraction in PS 393kD. The free volume asymmetry number is increased with
nanoparticle addition, suggesting an increased energetic penalty to compression as
compared to dilation. The internal pressure is decreased by particle addition, consistent
with a decrease in the strength of intermolecular interactions.

The quantity, K1, is related to the shape of the free energy minimum and is
referred to as the free energy anharrnonicity.53 A K1 value of five is equivalent to a
harmonic potential, for which compression and dilation are equally favorable processes.
However, intuition and experience suggest that K; is generally greater than five,
consistent with a material for which dilation is favored relative to compression. Typical

K. values for polymeric materials are 11.0 i 1.5.53 It has been shown through the

28

reduction of Tg and K0 that the addition of PSNP introduces a driving force towards free-
volume expansion within the nanocomposite. This driving force is also manifested in an
increase in the free-volume anharmonicty, K, as the system becomes increasingly biased
towards dilation over compression. The shape for of the dimensionless free-energy as a
function of relative density is shown in Figure II-7 for three value of K1, the harmonic
potential, and the values for unfilled PS and PS filled with 5% PSNP 78 kD. The free

energy contour illustrates the increasing bias towards dilation compared to compression.

 

0.04 _ r r r

t --------- PS 393kD: K, = 11.8

: - - - PS 393kD w/ PSNP 78kD 5%: K1 = 13.0 i

.. : 3 I;

0.03 ;

l- I."

C ,1;

: ._,.='

l- 1.:
~ :
S 0 02 ......... ..'.-.-.
“‘ :

   
    

4-

0.01

rlllllITIlll{.1[lll
I
LL11|1111|11111111

 

 

 

0.00
0.8 0.9 1.0 1.1 1.2

Relative Density (p)

Figure Il-7. The dimensionless free energy as a function of relative density. The anharrnonic
potential shows an equivalent free energy change for compression or dilation. The addition
of PSNP 78kD is seen to exacerbate the asymmetry of the free energy profile, with dilation
being energetically favored over compression.

 

In addition to the shape of the free energy well, the sensitivity of internal energy

to volumetric changes can be calculated from PVT data. This sensitivity is defined as the

29

internal pressure, Pi.“ The internal pressure is not a direct measure of the magnitude of
intermolecular interaction energy, but rather a measure of the response of this energy to a
change in volume.52 The direct measure of the interaction energy between molecules is
the Cohesive Energy Density (CED) which is defined55 as
Eq. 9 CED = UN

In the past, the difference between CED and P,- has sometimes been wrongly neglected
and values of Pi have been used for CED. While not strictly correct, it was shown by
Hildebrand et (11.56 that the ratio, n, of P,- to CED is approximately one for low molecular
weight liquids. In further analysis Sauer and Dec55 showed for a number of polymeric
materials that n is between 0.88 and 1.35.

The internal pressure is strictly defined as the response of the internal energy to a
change in volume:

Eq. 10 P13 (6U/6V)T
Eq. 11. P,- = T (6S/6V)r - P
The internal pressure can also be written as the difference between the thermal pressure
(TdK) and the system pressure (P).
Eq. 12 P, = TaK - P

As free volume is increased in a system, additional regions are introduced for stress relief
in the event of a change in volume. This diminishes the system’s energetic response to
changes in volume, and therefore reduces P,-. This effect is observed for the PS-PSNP
78kD system. Similar to the change in T8, at extremely low loadings (1%) the mobility of
the system is maximized, reflected by a nearly 30% decrease in P1. Much like the trend

seen in Tg, this reduction becomes less drastic at higher particle loadings, increasing

30

slightly compared to the 1% blend. This confirms the notion that optimum mobility
enhancement occurs at very low particle loadings for which free volume introduction

dominates, prior to particle crowding effects becoming more significant.

II.C.2.Non-Equilibrium Tensile Behavior

The observed increase of free volume with PSNP addition has consequences for
the tensile behavior of the nanocomposite material. The presence of nanometer sized
voids that increase polymer mobility in a material encourages plasticization of the matrix.
51' 57’ 58 The even distribution of stress across the sample may prevent the stress
concentration at a specific larger flaw that otherwise leads to stress concentration and
failure.59’ 60 This increase in ductility may manifest itself as an incremental change in the
strain-to-failure, 8f, or it may result in a shift in the failure mechanism. In concert with the
stress distribution brought about by the small, homogeneous regions of low density (free
volume), alignment of the matrix polymer has been shown to promote stress propagation
in the direction of orientation. In its unprocessed state, unfilled PS 393kD fails by the
low-strain brittle mechanism that is typical for amorphous polymer below their Tg. When
sufficiently oriented (1.22 for the processing conditions of the current study) by a hot
drawing process, PS undergoes ductile failure characterized by neck formation and
failure at higher strain values.

Studying the solid state stress-strain curves of the nanocomposites reveals that
blends of PS with the two larger PSNP types fail by the ductile mechanism at a lower
draw ratio (1:1.75) than the unfilled system (Figure II-8). While stress-strain curves are
only shown for 1% loading, PSNP 78kD and PSNP 211kD also exhibit ductile failure at

7.21.75 for 5% loading. The transition to ductility occurs when the stress to flow initiation

31

is less than the stress to failure. This shift may be due to an increase in alignment, the
added stress distribution facilitated by the particle-induced free volume increase, or a

combination of the two.

 

   

 

 

 

 

 

: I -e— PS 393k kDa, neat

80 _ I“ -V - PSNP 41 kDa, 1% vol

A ; -a- PSNP 78 kDa, 1% vol
act-l ‘V. -a-PSNP211kDa,1%voI
a ’ i
b 60 Vi)? —_
«a?! . -
a)" 1:75! ,3; 1.32-girl... ................ 1 ...... 1 a';,'(.'.‘.’,'.,.‘.‘.'.‘.‘.‘.‘.’.’.‘.‘.‘.‘& 03:99:11; 1
(0’)) :I'I'II"::IIIII"'IHII:"il'wri1::1, 1|~~, l;i:.:‘.IL-V'.!1"'"‘ E

h m. 1 1 - ,
III-I. V'- ', l :
m 40 fit I' [31. 2'
a z .1 :.
'2 1"» 1 1'. ‘ :
g :t?’ : g l :
C 20 1""! I :1 .1
'— Ir: | . d
C} 9'1, ‘ | r ‘1
C '- .1 -
LU “" K. II ;
I I 1' :
V ‘ -
- v
... ',.:::::::;:;.;); H

l l 1 1 l l

0.00 0.10 0.20 0.30
Strain, s

Figure 11-8. Stress-strain curves for unfilled polystyrene and polystyrene filled with three
different PSNP types, each processed to a hot draw ratio of 1.75. The two larger PSNP
species induce ductile failure under conditions for which the unfilled polymer and the
polymer filled with PSNP 41 kD fail by a brittle mechanism at low strains.

In addition to the shift in fracture mechanism to increase ductility, 8f is increased
for the particle blends at low to moderate draw ratios (Figure II-9b). From the stand-point
of material design, this increase in ductility also increases the Tensile Energy to Break
(TEB) (Figure II-9d). This is an attractive benefit for the design of safety devices that

need to effectively dissipate energy before failure. The increases in toughness and

32

ductility are primarily applicable for low to moderate (k5) draw ratios. At higher draw
ratios, the polymer chain is oriented to such a degree that stress is being applied more
directly along the chain back-bone.“ 35 In this case, stress relief by increased mobility

can do little to ameliorate the strain being applied directly to the rigid covalent bonds.

 

 

_a
n

 

8,, Strain t0 Failure

   
   

Young's Modulus (GPa)

 

—e—P8393Ir0.neat
-a-PSNP41kD1v%
-9—psupmomt

. PSNP211kD1V5$ Q 1 . . .1 l‘ PSNPWWM"
1 1 1 1 1 1_11L In t l
2 3 4 s 5 7091 ‘

, -B-PSNP «Home _
-s-PSNP moms

 

 

 

 

 

 

L l
2 3456789
10

 

 

   

Ours» Ultimate Tensile Strength (M Pa)
Tensile Energy to Break (XI 08 Jlma)

 

 

 

 

 

 

11

—e—P8393kD,neat - ' +PS3Q3:D,neal 5

«3435111: 41110 was _ -a-:SS::;18:3.11;6W:I ;

-<.>-PSNP 7811mm ‘ , -1.- w _

‘1 PSNP 2111011715 i PSNP211KD1%vol
'IL 1 1111111 10'31 11111111
< 2 3 4 s s 789 s 2 3 4 5 s 789
1 10 1 1

nun, 1t=L/LD

Figure “-9. The Young's Modulus (a), strain to failure (b), ultimate tensile strength (c), and
tensile energy to break (d) of hot-drawn PS 393 kD with PSNP as a function of hot draw
ratio. Larger PSNP species have very little effect on Young's Modulus or ultimate tensile
strength, while smaller (41 kD) particles increase these properties for the unprocessed and
slightly processed case. The ductility (b) is increased for all cases at low draw ratios and at
all draw ratios for PSNP 78 kD, which gives rise to an increase in the material toughness

(d).

33

Also, it should be noted that the most substantial increases in ductility occur for
the 1% blend of PSNP 78kD in PS. The low loading, 1% blend was also shown by
changes in T8 and P,- to be most effective at improving system mobility, a key factor in
enhancing ductility. Higher loadings, which were previously associated with the
development of interparticle interference effects, show a reduction in TEB relative to
PSNP 78kD 1% (Appendix B).

It was suggested earlier that the increase in ductility may be due to either an
increase in free volume or chain alignment. Choi, Spruiell, and White“63 studied the
orientation development developed in PS by a hot drawing process and correlated the
optical birefringence — a measure of monomer orientation — with tensile property
changes. The authors found that of the tensile properties studied, 8f is the most sensitive
to chain orientation, but Young’s modulus, E, and the ultimate tensile strength, OUTS are
also dependent on orientation. In the case of PSNP 78kD and PSNP 211kD in PS,
however, there is no discernible trend of either of these other properties (Figure II-9a, c)
with PSNP inclusion. The absence of an observed increase in Young’s modulus or
ultimate tensile strength may indicate that no significant change is occurring to the chain
orientation. However, the weaker dependence of E and OUTS on orientation demonstrated
by Choi, Spruiell, and White, also suggests that the increase is more subtle than the
resolution of measurement. From the present data, it is unclear whether changes in tensile
behavior brought about by PSNP inclusion are due to increases in free volume or chain
orientation.

It should also be noted that, while no specific increase is observed for E or oUTs,

no significant decrease is observed either. Traditional plasticizers increase ductility at the

34

expense of reduced stiffness. This ability to increase ductility without reduction in E or
OUTS shows that the nanoparticle inclusion may provide a more attractive route to
ductility and toughness enhancement than traditional additives.

The exception to the trend of strict ductility enhancement is the blend of 1%
PSNP 41kD in PS. This system shows moderate ductility increase relative to unfilled PS
at low draw ratios and notable increases in strength and modulus at low draw ratios.
Contrary to the previously described PSNP behavior, this is consistent with a view of
enhanced orientation. However, the stiffness increase is not due solely to orientation
development. The fact that E and Ours are increased for even the undrawn (1:1) sample
shows that the PSNP 41kD imparts some inherent stiffness to the system. The deviation
from the behavior observed for the larger particles may reflect a size dependence of the
PS-PSNP interaction. The measured radius of the PSNP 47kD is 2.8 nm, which is less
than twice the statistical segment length of polystyrene, 1.8 nm. This presents a challenge
to polymer to efficiently pack in the vicinity of the particle. This is consistent with a view
of free volume introduction around the periphery of the particle as suggested by the
reduction of TE (Figure II-2), but reflects the strained nature of the polymer near the
particle.

The processing space for which most property enhancement has been
demonstrated is for low to moderate draw ratios (l.<5). These draw ratios are well below
the extremely high elongations utilized in fiber spinning applications but these effects
are, nonetheless, significant. Other polymer materials production processes lead to the
moderate orientation of polymer chains. Injection molding is one such application for

which there may be room to exploit the illustrated particulate enhancement effect.

35

 

proc
if n;

prod

nano
mobi
pant
fined
bthu‘
mOdL
from
Unpor
azer.

H"Cini

Injection molding, however, is often limited by a poor ability to carefully control the
chain alignment, and the stresses often vary widely across a given part, based on the mold
geometry. In biaxially oriented polystyrene, on the other hand, the stresses are well-
controlled and uniform, but much lower than for fiber spinning. This manufacturing
process could be benefit from the reduced neat for processing to achiever similar results
if nanoparticles similar to those utilized in the present work are incorporated into the

production feedstock.

II.D. Conclusion
When added to linear polystyrene, intramolecularly cross—linked polystyrene

nanoparticles are shown to increase free volume and mobility. The increase in polymer
mobility is the greatest at low loadings, for which free volume has been introduced at the
particle surface, but at sufficiently low loadings that particle-particle crowding does not
interfere with overall system mobility. For larger particles, this leads to plasticizing
behavior and tendency toward ductility, but it doesn’t necessarily diminish Young’s
modulus. It is difficult to disambiguate the additional mobility caused by free volume
from the plasticizing effect of orientation enhancement. The smaller particles reveal the
importance of filler size in determining mechanical properties. The similarity of the filler
size to the persistence length of the matrix polymer creates an obstacle to packing in the

vicinity of the particle and a stiffening behavior.

36

Chapter III: A small-angle neutron scattering (SANS) study
of the anisotropic conformation of linear polystyrene in the
presence of intramolecularly cross-linked polystyrene
nanoparticles

III.A. Introduction

Introducing global alignment to otherwise amorphous materials is known to
increase their tensile strength in the direction of alignment. This has been demonstrated
for linear polymers by introducing axial strain to a sample above its Tg, then quenching it
well below Tg, locking the polymeric chains in their nonequilibrium anisotropic
conformation. This process is representative of typical polymer processing methods that
consist of fiber formation by either melt or gel spinning, followed by hot-stretching
which is controlled by passage over rollers that move at progressively increasing speed.
The process is completed by cooling the sample through immersion in a low temperature
bath and optional cold-stretching below Tg (Figure I-l).

The effect of uniaxial processing strain on fiber properties has been studied for
neat polystyrene under a number of processing conditions and the induced alignment has

been observed by optical birefringence measurements“ 65

and small angle neutron
scattering (SANS).""5 Optical birefringence was the first experimentally feasible method
for evaluating the orientation of amorphous polymers. However, birefringence
measurements often present a misleading understanding of the chain’s orientation. In the
case of polystyrene, it is the large, flat phenyl rings that dominate the optical character of
the polymer. Consequently, an aligned chain has phenyl rings oriented perpendicular to

the chain backbone, resulting in a negative birefringence. The alignment being probed,

therefore, is that of the individual chain segments, rather than the entire chain.

37

Dominated, as these short segments are, by extremely short relaxation times they are not
a good indicator of the overall orientation of the chain backbone, which has a total
relaxation time orders of magnitude larger than the segmental relaxation time. Indeed, it
is the long scale orientation that has been shown to be most important for determining the
solid state mechanical properties of a polymer system.10

While a great deal of work has been conducted towards understanding the strain-
induced alignment process, very little agreement exists regarding appropriate processing
methods or parameters. So while general trends can be observed and confirmed or
disputed, quantitative comparison is often impractical. A summary of some existing work
and the disparate processing and evaluation methods employed is presented in Table
III-l. Especially noteworthy is the inconsistency between definitions of the time
dependence of the sample strain. While some groups have processed their material by
imparting a constant strain rate, many researchers process their samples based on a
constant cross-head speed, resulting in a strain rate that diminishes exponentially during
the process. The latter method makes lesser demands on instrumentation, but convolutes
the experimental conditions, as most material properties are rate, rather than speed,
dependent. A constant-rate process is also more consistent with industrial application of

the process than a constant-speed process.

38

Table III-l: Summary of previous work on alignment by hot drawing and their test

parameters.

First Author

Cleereman35

Cheatham34
Ender67
Picot64
Tanabe"8

Boue69
Choim’ 63

Choim’ “3

Ramzi65

Pellerinm

Bent71

Stendahl37
De

Francesco72

Theodorou73

Yokouchi74

Dvoranek7S

Han76

Embery'f’6

Draw
Temperature (°C)

99 — 132
145

115

110 — 130
197

113 — 134
110

120
134

120
170
108

105 - 130

105
105
225 - 265

100 -115
113, 148

Drawing

Draw
Ratio
50% -
1200%

S 12000%
1.

NS

S 4.5
NS

3
1.6-2.5
3-7.2
1.2-3
2

NA
250%,
1000%

2,4,6
NS
57,5
NS
2-5

1-5

Initial Draw
Rate (s'l)

NS
NS
NS
0. 18
NS

0.06 — 0.189
0.0833

0.0767
NS

0791*
01-30

0.00654*

0.0119*

0.00333*
NS
NS

.0048-.0033*
NS*

Tensile Testing
Initial Testing
Rate (s‘l)

NS

1.6x10'5 — 0.167
NS

NA

0.0167 *

NA
NA

0.00328*
NA

NA
NA
NS*
10'4
NA

.0029 - 230
0.00242*

NA
NA

*: Sample was deformed at a constant cross-head speed. The instantaneous strain
rate was determined from the cross-head speed and the initial gauge length.

1': Draw ratio was determined by the change in the cross-sectional area

NS: Not clearly specified
NA: Not applicable, the specified process was not conducted

39

While the orientation of high aspect ratio nanoparticles for use as composite filler
has been studied, little work has been conducted to understand the orientation of the
surrounding matrix, especially in the case of fillers that have an aspect ratio approaching
unity. Work has been conducted to quantify the equilibrium conformation of linear
polymers surrounding spherical nanoparticles. It has been shown through previously

20
I.

described (I.C) simulations by Brown et a that polymer chains orient in layers

perpendicular to the particle surface. Mackay et al.77

have demonstrated that the presence
of certain nanoparticles leads to an increase in the radius of gyration (R3) of the matrix
polymer. It is believed that this swelling behavior may make the linear polymer more
susceptible to the strains that lead to orientation under uniaxial processing conditions.

A key factor in any study of composites, and especially a study of the matrix
conformation, is the chemical (enthalpic) interaction between the matrix polymer and the
filler species. In the case of traditional composites with macroscopic fillers this
interaction is largely responsible for the filler-matrix bonding that dictates how well
stress will be transferred across the interface. A poor interaction leads to poor stress
transfer, which weakens the material. The issue of chemical compatibility becomes even
more important as the filler size is reduced and the particles gain mobility within the
system. An unfavorable interaction will cause the filler and matrix to phase separate,
leading to an inhomogeneous dispersion and the generally negative effects on the
mechanical properties.

The unfavorable interaction state is often ameliorated by chemically attaching a

species that interacts favorably with the matrix to the exterior of the filler particle. In the

case of polymer nanocomposites, the stabilizing species is often an oligomeric chain of

40

the matrix polymer. This strategy may be successful for enhancing the stability of the
system but, in addition to adding a synthetic obstacle, this strategy complicates analysis
by introducing a third, often ill-defined phase. Furthermore, the stabilizing ligand
generally does not possess the desired reinforcing character of the filler particle, thereby
acting against the desired effect of composite formulation.

One way to circumvent the analytical, as well as practical, difficulties of ligand
stabilization is to synthesize a nanoparticle that is itself chemically similar to the matrix

polymer. Harth et al.38

demonstrated a method for preparing cross-linked nanoparticles
with well defined sizes that are chemically similar to polystyrene. This is accomplished
by producing a random copolymer of styrene with benzocyclobutene (BCB). The butyl
group on the BCB moiety can be thermally activated for potential cross-linking, leading it
to bond with a similarly activated group located elsewhere on the same chain. By
activating the reaction under ultra-dilute conditions it can be assured that each copolymer
chain will cross-link only with itself, producing an intramolecularly cross-linked
nanoparticle that has a well-defined size and is chemically similar to polystyrene. The
degree of cross-linking, and therefore the extent to which the macromolecule behaves in a
manner more consistent with a particle than a Gaussian chain, is controlled by the relative
proportion of BCB to styrene.

Small angle neutron scattering (SANS), allows characterization of a broader range
of molecular length scales78 than optical birefringence measurements. It is especially

well-suited to evaluating macromolecular feature sizes, including the RE of a polymer

chain. The general equation for the scattered intensity, (62/60), as a function of wave

41

vector, q (q = 471/71,, sin(®/2) where O is the scattering angle and A." is the neutron
wavelength), is given by Eq. 13
Eq. 13 (ax/ac) (q) = W (Am2 an 501) + B
The incoherent background scattering is defined as B. The number fraction of scatterers,
N, their individual volume, V, and the scattering length density contrast, Ap, are
independent of wave vector and are often grouped together and referred to as the scale
factor, or the intensity at zero wave vector, 10.
Eq. 14 10 =1vv2 (Ap)2
Information about the size and shape of an individual scattering center is given by the
form factor, P(q), while the long range order of scatterers is defined by the structure
factor, S(q), both of which tend towards unity at low values of q. For very dilute,
amorphous systems, the structure factor can be set to one at all wave vectors, leaving
only the parameters of the form factor to be determined. Form factors have been
determined for a number of scatterer geometries and one of particular interest to polymer
science is that of the Debye distribution of a Gaussian.
Eq. 15 P (q) = 2 (exp (4211.2) + qugz — 1) (qZRgzrz

In addition to simplifying the filler-matrix interaction, using a filler with a similar
chemical structure to the matrix simplifies the neutron beam contrast. The scattering
length density, p, depends only on the chemical composition and the bulk density of the
scatterer. As these two quantities are similar for the PS and PSNP, scattering from a
composite of the two can be reasonably approximated as a constant intensity regardless

of wave vector.

42

The conformation of individual matrix chains can be studied by substituting a
small fraction (2v%) of the protonated matrix polymer with a deuterated chain of the
same size and type. It is then a simple matter to subtract a measured background
scattering signal for the purely protonated sample. Alternatively, the largely incoherent
scattering of the background can be treated as a constant background value and estimated
from the plateau at high values of the scattering vector. This is found to be a satisfactory
assumption (Figure 111-1) for the scattering of the background and it avoids the error

propagation that accompanies background sample scattering subtraction.

 

 

 

mgzl I I. I I I I .I I I..I...I. I ll 1 I I. I:
1 ‘13»..3. '7 ,. i. ..:
- ' lll.“’.§"§.11- ”fig E
A , "’r'i r: . f, T -' '7‘ '.I
I ,I il ., u -—I
5, 0.1 El
L" ~ ~' E 77.1.»:in
0.01 V ~ . ~ . -- 5|

' f ‘ . . , Mll'l

0 Background 1 ll

0 Sample minus background i 1

11111111111 11111111 1

6 8 2 4 6 8 2
0.01 0.1

-1
q (A )
Figure III-1. The background signal is assumed to be constant at all wave vectors, at
reasonable approximation for the predominantly incoherent scattering observed for
protonated PS.

 

l

0 001 q- Sample ...... “I I I
' . ' l
l

 

 

43

IH.B. Experimental

Protonated polystyrene (PS) was purchased from Scientific Polymer Products
(Ontario, NY) and deuterated polystyrene (dPS) was purchased from Polymer Source
(Montreal, QC). Linear polymer/nanoparticle blends were made by dissolving the linear
polymer(s) and nanoparticle in a mutual solvent, toluene. The solution was then dripped
into a mutual non-solvent, methanol, where the polymer(s) and nanoparticles rapidly
precipitated, forming an intimately mixed, homogeneous dispersion of nanoparticles in
the linear polymer.43 After solvent removal by decanting and filtration the blend was
dried for a week in an oven at 50 °C and under rough vacuum.

Table III-2: Molecular weights and distributions of linear polystyrene and
intramolecularly cross-linked polystyrene nanoparticles

 

 

 

Sample Name Mw (g[mol) Mn_(g/mol) PDI
PS 393,400 339,140 1.16

dPS 420,200 373,200 1.26
PSNP 41 kD 42,520 41,090 1.04
PSNP 78 kD 89,020 77,830 1.14
PSNP 211 kD 278,400 211,200 1.32

Samples for neutron scattering were prepared by the method described in section
11.3. Measurements of orientation were made ex situ, after the drawing process was
completed and the sample was cooled to ambient conditions.

Small angle neutron scattering tests were conducted using the NG7 30-m Small
Angle Scattering Instrument at the NIST Center for Neutron Research (Gaithersburg,
MD). The instrument is a variable geometry instrument with a sample to detector distance
of 1.0 to 15.3 m and an associated wave vector range of 0.0008 to .7 A”. The source to
sample distance is also variable, but was held constant in the present work at 15m. The

detector is 640 x 640 mm with 5 x 5 mm resolution.

HI.C. Results & Discussion
Primary SANS studies were conducted for two sample compositions: 98% PS, 2%

dPS and 97% PS, 1% PSNP 78kD, 2% dPS, each measured in the solid state, below their
glass transition temperature. For each sample, background samples were measured for
which the dPS was replaced by PS and processed by the same conditions. In light of this
it was found to be preferable to assume a constant value for the background based on the
high-q plateau. Each sample was evaluated at a number of hot draw ratios in order to
quantify the development of orientation in the matrix polymer.

The data analysis method for isotropically scattering samples includes averaging
of points with the same scattering vector, regardless of their azimuthal angle. In the case
of non—equilibrium, oriented films, the scattering is asymmetric and this circular
averaging would be invalid. Instead, the 2-dimensional scattering profile can be divided
into angular regions parallel and perpendicular to the direction of stretch (Figure 111-2) and
these regions can be treated separately, averaging the individual data segments at each q—
value and generating two intensity profiles for each sample. The process of separating the
data azimuthally involves a trade-off between attaining sufficient counting statistics to
provide an adequately high quality signal, and capturing the direction specific size scale
that is brought about by the hot drawing process. For the present study azimuthal sections

were analyzed with a width of 40°.

45

 

r ritrili] r it!

  
   
 

1 iiiiiil

1(0) tan“)

lllllll

 
 

 

   

 

 

2 8
Stretch Direction 0.01 0.1
> Q (K‘)
Figure 111-2. The anisotropic SANS pattern of a non-equilibrium, hot stretched PS film

(left). The scattering profiles parallel and perpendicular to the stretch direction are shown
on the right.

 

 

Even with care taken to select a sufficiently large wedge size to provide high
quality data, difficulties arise for this type of analysis. The applicable q-range for a given
feature size is based approximately on the inverse of the characteristic length scale to be
measured. A high molecular weight was selected for this study of orientation because
higher molecular weight chains are more sensitive to orientational flow than lower
molecular weight chains, due to their longer relaxation times. This presents a challenge to
the low-q resolution of the instrument, a challenge which increases as the size of the
chains’ long axis is increased by the extensional flow. Consequently, the short axis -
perpendicular to the draw direction — data are easier to interpret and less error prone for
low to moderate q-range analyses.

To simplify the fitting procedure and reduce the number of degrees of freedom for
analysis, the intensity at zero wave—vector, Io and often referred to as the scale factor, was

held constant for all samples and draw ratios. 10 is dependent on the volume of the

46

scatterer, its number fraction, and the scattering length density contrast between the
scatterer and background. As none of these quantities are expected to change with draw
ratio or PSNP inclusion, this is viewed as a reasonable assumption. The value of Io was
determined from the fit of the undrawn PS-dPS scattering profile to the form factor for a
Gaussian chain.

A useful and accurate method for interpreting the collected scattering profiles is
by fitting to a previously derived form factor that is appropriate for the shape of the
scatterer under investigation. For the system in question, the expectation is that the chains
will conform to the form factor of a Gaussian chain in each direction. This would allow
determination of the R8 in the directions parallel and perpendicular to the stretch
direction. In order to confirm the suitability of the proposed Debye form factor for the
system in question, the low and high q intensity profiles can be analyzed to ensure
consistency with the limits of the form factor. The low-q trend can be checked by the
Guinier approximation, for which a plot of ln(I(q)) versus q2 should tend towards a
straight line in the range of q Rg < 1. Due to the aforementioned limitation on the low-q
data, the Guinier analysis is not feasible for the present system. In the high-q range
(q > 5 Rg'l), the scattering profile of a Gaussian chain can be treated with the Kratky
approximation, reaching a plateau at IoRg'2 when plotted as qu versus q. Rather than
simply looking for a plateau in the Kratky plot, the high-q data can also be fit to the
Lorentzian function

Eq. 16 1(q) = Io/(1+qn L“)
and values of the Lorentzian exponent and screening length determined. For a Gaussian

chain the exponent is equal to 2 and the screening length is equal to the radius of

47

gyration. For a swollen coil in a good solvent, the value of the exponent is less than 2,65’
79 decreasing with increasing solvent quality. The screening length is a characteristic size
of the polymer, but not strictly equivalent to the radius of gyration. The values of the
Lorentzian exponent determined from fits of the high-q scattering profiles to Eq. 16 are

shown in Figure III-3 as a function of the hot draw ratio.

 

 

 

 

 

 

 

 

2.0 _*_-~ ‘_

.. 1.9 ~ ~-
3 ' 3
s E '
o. 1.8 -- “i
x : :
UJ q r
c . ..
g 1.7 C" "T
c : I
e __ ..
o . - ‘
_. 1 6 _ . 2 . , g . ‘ ‘ .
- +PS,neatJ. Q‘x‘ I

- - + PS, PSNP 78kD 1% 1 * q

: -A - PS, PSNP 78kD 1% || 5 I

- l I I l ‘

 

1 2 3 4 5
Hot-draw Ratio (A)
Figure 111-3. The Lorentzian exponent of PS with and without PSNP addition as a function

of hot draw ratio. The Lorentzian exponent for a Gaussian chain is 2. Swollen coils exhibit a
reduced dependence of I on q at higher wave vectors.

The results of the hot drawing process are largely dependent on the initial state of
the material before drawing. To this end, the high-q dependence of the scattering
intensity provides a measure of the conformation of the unperturbed system. The

nanoparticle laden system is seen to have a slightly lower value of the Lorentzian

48

exponent than the unfilled polymer. This is consistent with the view of the nanoparticle
swelling the linear polymer, as has been demonstrated in previous studies of the
dependence of Rg on nanoparticle addition.10 This also sheds light on the particle-
polymer interaction, suggesting that the polymer may partially wrap around the particle,
rather than simply confining the particle to a space between isolated polymer chains. The
observed decrease of the Lorentzian exponent suggests that the chain adopts a swollen
coil conformation, which is expected to increase the radius of the polymer chain. This
increase in radius is observed as a small increase in the Lorentzian screening length for
the undrawn sample (Figure HI-4b). If the scattering from the nanoparticle-laden chains is
treated as a Gaussian chain and fit to the Debye form factor (Eq. 15), disregarding the
high-q deviation, the R3 is also seen to increase by ca. 1% (Figure III-4a), consistent in
magnitude with the results of Mackay et al.10 for a high molecular weight chain blended

with a similar size and type of nanoparticle at a low loading.

49

a b

 

 

    

 

 

 

 

 

I I I T I l

60: 100 E-o-PSJIeau I i
I E E-o-P8.neat|| E
_ C : +98. PShP78kD1%L :
50 '— ‘-' E-L-PS.PSt~P78k01%|| g
"‘ 5 80: ‘ I’ 1
h 8‘ l: .’ :
- a) E ’4 ’x' E
A 40: _l : v o’ :
E - g) 60:— " ,' '0' —:
E : E E I, i, E
a 30— a) '- I 0’ —1
'- Q) : I 'a :
0: i b I I .' :
: U) 40.— 6,’ 1
-.-. c : 2
2 ............ g E :
I 5 +- Z
; '0- PS, neatJ. : 20 ~__-_ i'd .5
10l- -0-PS.PSNP78kD1v%L e ; I“ | __.. 2
: +P8,neat|| 3 E‘ .I. E
: +PS,PSNP 78k01v%|l : E
0 l 1 l 0- r l m l 1 .

1 2 3 4 5 1 2 3 4 5

Hot-draw Ratio (1) Hot-draw Ratio (71.)

Figure 111-4. The characteristic size development of anisotropic PS with and without PSNP
78 kD as a function of hot draw ratio. The macromolecular size is calculated according to
either the Debye form factor (a) at all wave vectors, or the Lorentzian scattering function at
high wave vectors. In both cases a discontinuity is observed for the nanoparticle-laden
sample at 1:1.75, the hot draw ratio at which ductile fracture behavior is observed in
tension. A small increase is observed in the long axis size of the polymer at the highest draw
ratio by both methods of calculation.

In studying the drawn samples by this high-q approximation it is important to
consider the quality of data. The assumptions for the high-q trends in the scattering
profile are generally considered valid for values of q > 5 Rg". Based on instrumental
limitations, however, scattering data is rarely reliable beyond a value of the scattering
vector of 0.5 A'l. This means that for a larger scatterer, or data for a chain parallel to the
draw direction, there is a wider range of high-q data available for analysis than for a
smaller scatterer, or data for a chain perpendicular to the draw direction. Also, separating
the scattering profiles into separate sections parallel and perpendicular to the draw
direction reduces the quality of the data. While the Lorentzian scattering function may

provide a more accurate representation of the non-Gaussian chain behavior, the additional

50

degree of freedom introduced by the unknown Lorentzian exponent increases the
possibility of an errant fit to noisy data. With this is mind, it is worthwhile to consider the
results based on both the Lorentzian function (Eq. 16) and the Debye form factor (Eq.
15).

Analysis of the Lorentzian exponent with increasing draw ratio shows that the
exponent for both filled and unfilled PS decreases for the data parallel to the draw
direction as the hot draw ratio increases. This is reasonable behavior and has been shown

previously,“ 65

showing that the chain is drawn to a size greater than its equilibrium,
Gaussian, distribution. The Lorentzian exponent for the data perpendicular to the stretch
direction also decreases with l, reflecting the perturbed shape of the coil in both
directions. Very low draw ratio behavior is similar for the samples with and without
particles, as their exponents are nearly the same at a draw ratio of 1.5. At a draw ratio of
1.75, however, the exponent of the particle filled system is greater than the unfilled
system. At higher draw ratios, this trend reverses, as the exponent of the filled system
exceeds the unfilled system. The screening length in the parallel direction also increases

with It and shows trends similar to the dependence of the exponent with 9..

Perhaps more illustrative than the individual length scales, is the ratio of these
length scales (Figure III-5). This provides a molecular aspect ratio, §=LI/L-J-, of the
overall chain and measure of orientation. As a reference for the extent of orientation, the
affine limit of the aspect ratio can be calculated, which scales as é = A”. This is the
maximum aspect ratio that is to be expected for the given draw ratio. 5 increases with hot
draw ratio, adhering closely to the affine limit at low draw ratios, but deviating

substantially at 7t = 5. For the draw ratios of 1.5, 2, and 5, the aspect ratios calculated

51

from the Lorentzian Screening Lengths of the dPS chain in the particle filled system are
greater than the unfilled system, but not beyond the range of error for the measurement
(Figure III-5b). According to the Debye fit, the aspect ratios at these draw ratios are

essentially unchanged by nanoparticle addition.

 

 

  

         

 

 

 

 

 

 

3.0 if I l E I I
A - _ O E E
‘I "" r- '1
a __ . 4..-

m :. J
“g 2 5 P d a 5 ' 2
ea 1 - g s E
O l" - : :
g - « 313 4 E 3
tr ' - E : :
tr 2.0 - ~ 3 E 3
0 a - o : I
Q __ _ £2 3 :- ':
<03 - - ° : :
L .. d
2 - - E E E
8 1.5 — -~ 0 5. j
9 - -1 m 2 .. .-
o . +P8, nod . 2. E -o— P8. neat E
2 + P8. PSNP 78k01v9b . am : + PS, PSNP 78k01% :
- - - Mocham Mm Detomfion- 5 - - . Affhe defamation rm;

1 2 3 4 5 1 2 3 4 5

Hot—draw Ratio (7t)
Hot-draw Ratio (7t)

Figure III-5. The aspect ratio development of anisotropic PS with and without PSNP 78 kD
as a function of hot draw ratio. The aspect ratio is calculated according to either the Debye
form factor (a) at all wave vectors, or the Lorentzian scattering function at high wave
vectors. In both cases a discontinuity is observed for the nanoparticle-laden sample at
L=1.75, the hot draw ratio at which ductile fracture behavior is observed in tension. The
dashed line represents the aspect ratio for a chain that deforms affine to the bulk sample,
the maximum attainable orientation in the absence of an additional driving force.

At the intermediate draw ratio of 1.75, however, there is a significant difference
between the two systems, the PSNP-filled system showing a lower aspect ratio than the
unfilled system. It has been shown previously (Chapter II:) that PSNP-filled PS
undergoes tensile failure by a ductile mechanism accompanied by neck formation when
processed to a hot draw ratio of 1.75, while unfilled PS fails by a brittle mechanism under
the same conditions. The primary obstacle to polymer chain orientation in a flow field is

the relaxation of the polymer from its strained state; for example, low drawing

52

temperatures have been shown to enhance orientation by increasing the relaxation time of
the polymer chain. This decrease in the aspect ratio for the PSNP-filled system suggests
that the relaxation time of a polymer chain is decreased by the presence of nanoparticles.
This is consistent with previously described observations of increased chain mobility by
PSNP addition as measured by a decrease in the equilibrium Tg and an increase of the
strain-to-failure for nanoparticle filled samples tested in tension. The decrease of the
relaxation time decreases the orientation, and therefore 9;, at k=l.75. However, the lower
relaxation time also improves chain mobility which leads to ductile failure when stressed

in tension

[II.D. Conclusion
Small angle neutron scattering has revealed a number of key features about the

influence of PSNP addition on the polymer conformation of both isotropic, equilibrium
chains, and anisotropic, non-equilibrium chains. The polymer chain is shown to swell to a
form that is larger than a simple Gaussian distribution, as reflected by the reduction of the
Lorentzian exponent. This chain swelling relative to the unfilled polymer is also seen at
higher draw ratios, accompanied by an increase in the chain aspect ratio at high draw
ratios. In mechanical studies of tensile behavior, a transition to a ductile fracture
mechanism after processing to a hot draw ratio of 1.75 was observed for the PSNP filled
system. This has been corroborated by a reduction in the matrix chain aspect ratio at this
processing condition, reflecting a decrease in the relaxation time of the matrix, decreasing
orientation but also increasing the mobility of the chain. The increased chain mobility,

coupled with the swelling of the polymer conformation shows that the cross-linked

53

nanoparticles act as a solvent for the PS matrix. This solvent-like behavior is unusual for

a material with a cross-linked structure, high modulus, and Tg greater than PS.

54

Chapter IV: The effect of C60 addition on the thermal and
mechanical behavior of PS

IV.A. Introduction

Fillers with high aspect ratios such as carbon nanotubes”84

and clay particles15 ' 39'

4" 83‘ 85’ 86 are popular fillers for creating aligned nanocomposites. Work has even been

3942 and the

conducted to evaluate the ability to induce orientation of the filler particle
effect this has on mechanical properties.

Miaudet et al.,‘4’0 for example, showed that the hot drawing of wet-spun fibers
containing poly(vinyl alcohol) (PVOH) and multi-walled carbon nanotubes (MWNT) or
single-walled nanotubes (SWNT) increases a number of desirable end-use fiber
properties, including energy absorption at low strain and moisture resistance. These
property enhancements were attributed to the alignment of the polymer and nanotube
moieties. The hot drawing process was shown to increase the alignment of PVOH from
i27° from the fiber axis for the as-spun fiber to 143° and :6.3° for the hot drawn fibers
containing SWNT and MWNT, respectively. The nanotubes had a similar limited
orientation in the as-spun case, but hot drawing improved the orientation of the SWNT to
i9° and the MWNT to -_t-ll°. The hot drawing process was also found to increase the
PVOH crystallinity.

Minus et (11.86 also studied PVOH fibers with SWNT formed in the presence of a
shear flow. They found that the nanotube increased PVOH crystallinity and templated
polymer orientation parallel to the nanotube axis, which was parallel to the fiber axis. In
the case of poly(acrylonitrile) (PAN), the same group85 found that PAN orientation was

also enhanced by the addition of SWNT. However, they found that while the average

crystalline size was increased, the total crystallinity is reduced. Contrary to the findings

55

of Miaudet et al.,40 this group found that the nanotube is more oriented than the
surrounding polymer.

Dror et al.41 measured the alignment that developed during electrospinning
nanofibers of poly(ethyleneoxide) (PEO) with MWNT. They found that the converging
flow geometry led to alignment of the MWNT with the fiber axis. The PEO chains were
also found to align, but the presence of the MWNT diminished the alignment of the PEO.

Weon and Sue83 examined the significance of filler aspect ratio and orientation on
a composite of nylon-6 and silicate clay. They found that the composites modulus, tensile
strength, and distortion temperature all increased with increasing clay aspect ratio and
orientation. The opposite dependence on aspect ratio and orientation was observed for
composite toughness and ductility.

The development of buckminsterfullerenes (C60) in 198587 and carbon nanotubes
(CNT) in 199188 ushered in a new era in composite research. The well-defined molecular
structure, potentially high mechanical stiffness, appealing electronic character, and
nanoscopic dimensions of these materials made them extremely attractive for use in
myriad applications. Buckminsterfullerene has been found to have a truncated
icosohedral structure,87 with an average radius of gyration equal to 3.82 A.89 This third

90-92

crystalline form of carbon has been studied theoretically as well as experimentally93'

97 in order to determine the bulk modulus at zero pressure, K0, of individual particles, as
well as crystalline assemblies of C60. The values for K0 that have been suggested range
from 6.8 GPa97 for an fcc crystal to 20 GPa92 for an individual particle. While these

values are high, they are less than the bulk modulus of diamond at zero pressure (442-433

GPagS), which is one of the hardest known materials and another allotropic form of

56

carbon. At pressures greater than 70 GPa, however, buckminsterfullerenes come into hard
sphere contact with one another and the bulk modulus reaches 600 to 700 GPa”92
exceeding that of even diamond, making C60 the hardest currently known substance,
under certain conditions.

In addition to its high modulus, C60 deserves special attention as a filler for
polymeric materials due to its very small size. The radius of the particle (0.38 nm) is
much less than the Kuhn segment length, 1K, of polystyrene (PS), ca. 1.8 nm. The Kuhn
length has been identified as the size scale on which a polymer chain can bend 180°
relative to itself, and is ca. 8-9 monomers for PS.99 This small size of the particle relative
to the chain flexibility limit suggests the potential for the particles to occupy space that is
otherwise inaccessible to the polymer due to the chains’ limited flexibility. While the
fullerene cage is open and has a hollow interior, it is unlikely that a polystyrene chain
would be able to access the void space. The openings within the C60 cage structure are the
same size or smaller than the pendant phenyl rings along the PS backbone, creating an
obvious steric obstacle to penetration and leaving C60 to be reasonably considered as a
hard, impenetrable sphere.

In the present study, the effect of C60 addition to polystyrene will be studied with
regard to developing an understanding of the polymer-particle interface and how this
impacts solid state mechanical properties. Of particular interest is the ability for these
spherical fillers to perform with respect to a processing environment that imparts
alignment to the polymer matrix by aligning the polymer in the melt state, followed by

rapid cooling to lock the chains in an anisotropic, non-equilibrium state.

57

IV.B. Experimental

Polystyrene standard was purchased from Scientific Polymer Products (Ontario,
NY) with MW: 393,400 Da and Mw/Mn=l.16. Buckminsterfullerenes were purchased
from Term—USA (Moscow, Russia). Linear polymer/nanoparticle blends were made by
dissolving both the linear PS and C60 in a mutual solvent, toluene. This ternary solution
was then dripped into a mutual non—solvent, methanol, where the PS and C60 rapidly
precipitated, forming an intimately mixed, homogeneous dispersion of C60 in the linear
PS.43 After removing the majority of the liquid from the sample by decanting and vacuum
filtration with copious methanol rinsing, the blend was dried for a week in an oven at
50 °C and under rough vacuum. Sample processing and characterization techniques were

identical to those described in section 11B.

[V.C. Results & Discussion
IV.C.l. Equilibrium Thermal Analysis

The effect of buckminsterfullerene inclusion on the glass transition temperature of
polystyrene is shown in Figure IV-l. The glass transition temperature is often used as an
indicator of polymer mobility, and therefore free volume. As obstacles to motion are
reduced, especially by the introduction of unoccupied areas, the thermal energy input
required to initiate rapid motion of the amorphous chains is decreased, leading to a
reduction in the glass transition temperature. In the case of C60 added to PS, the glass
transition temperature is seen to decrease relative to the T8 of unfilled PS at loadings
greater than 1v%. Extremely low loading of C60 (O.5v%), on the other hand, brings about

an increase in Tg of the same magnitude as the decrease at 1-2v%.

58

 

 

N
IIT—lfil
fl
‘1

IIILA

 

 

 

 

 

 

 

ATQ (°C)

ITIIIIIIIfIIIII

'8': """ l-v-PS393kDa,C60|mé """
- i i i i

o 20 4o 60 80x10”3

 

 

llllllLLllllll'lll

 

 

 

 

Volume Fraction Particle

Figure IV-l. Change in glass transition with addition of C60. Extremely low concentrations -
corresponding with an interparticle half-gap of similar size to the statistical Kuhn segment
length of polystyrene - of C60 show an increase in T11 that corresponds to a reduction in
polymer mobility. Higher, but still homogeneously dispersed, loadings show a T3 reduction.

An important parameter to consider in the study of any nanoparticulate filled

system is the interparticle gap, 2h, given by Eq. 17.
El 17 Ma = (¢m/¢)l/3 - 1

At equivalent volume fractions the interparticle gap scales with the particle radius, a. For
particles with extremely small radii, such as C60, this gives rise to very small interparticle
gaps into which the polymer chain is confined. In fact, for the concentrations at which the
glass transition temperature is reduced, the interparticle half-gap is less than the Kuhn
segment length, IX, of polystyrene, 1.8 nm. It is likely that the difference between having

an interparticle half-gap that is less than 1K and one that is greater than [K is sufficient to

59

delineate two separate regimes of packing and polymer conformation. In the limit of h 2
1K, the polymer is able to pack a full segment or more lengthwise between neighboring
particles. It is possible to consider this to be a sort of critically percolated packing state in
which the C60 limits the polymer mobility.

In the other regime, h < 1K, the C60 particles are forced into closer proximity with
one another. The fact that this space is smaller than that into which PS can freely pack
suggests that the C60 are relegated to regions that are inaccessible to the polymer, or that
the matrix expands to accommodate the particles. The results from DSC suggest that the
latter mode of packing is operable. The PS matrix expands to accommodate the ever-
encroaching fullerenes, leading to an increase in the overall system mobility and,
potentially, free volume.

PVT analysis is a sensitive test of the internal structure and potential presence of
free volume within polymeric materials. Engineering properties of interest that can be
directly calculated from PVT data include the bulk modulus, K = —V(6P/6V)T, and the
coefficient of thermal expansion,47 or = V’1(6V/6T)p. The bulk modulus is of particular
interest in the case of C60 because it reflects the cumulative result of two competing
effects. As mentioned previously, both simulation and experiment have shown C60 to
have an extremely high bulk modulus at zero pressure, K0, ranging from 6.8 to 20 GPa.
While this is a very broad range, it reflects the broad range of forms and interactions that
C60 can assume and the values are sufficiently high compared to PS (1.13 GPa) as to
justify the treatment of C60 as a rigid particle. In addition to the rigidity of the particle, the

volumetric response of the material will also be influenced by any free volume that may

60

be introduced to the system. This free volume will act in opposition to the reinforcing
effect of the high modulus particle, reducing the modulus of the nanocomposite.

The effect of C60 addition to PS on K0 is shown in Figure IV-2. In fact, while PVT
measurements are only strictly valid in the melt state, where pressure is uniformly
hydrostatic, similar trends are also observed for the solid state bulk modulus, measured at
50 °C. Similar to the discontinuity seen in the T8 at (p = 0.5%, the bulk modulus is
reduced by more than 10% for this very low loading. Further addition of C60 leads to an
increase of K0 in excess of the value for unfilled PS. The thermal expansivity, a, shows
the opposite behavior, increasing by ca. 8% for the O.5v% blend before decreasing to a
value that is less than the unfilled polymer and remaining nearly constant with increasing

volume fraction.

61

 

 

   

 

 

 

 

 

 

3 5 '- I I T l I I I 6.4 I Y ‘ I
: . _' ‘ _ 1 4 — !,= 026an .-
30; -62 - i
4) 2.5 :- gl-snf; + 1.3~ —
.. 5 r I 8
g 2.0,. ’ ¢—5.a : g
g : . 0;. o 1.2 _ —
f 15} .. was ‘7 ,2
: y A
1.0:— -~-,-5.4 1'1" _
" 200'0
l r l 1 l r l 5.2 1 a l ‘ l J 1 l
0 00 0.02 004 0 06 0.00 0.02 0.04 0.06
Volume Fraction of Particle Volume Fraction of puma.

Figure IV-2. Bulk modulus and thermal expansivity of a polystyrene/buckminsterfullerene
blend. At very low volume fractions for which the interparticle gap is greater than the
statistical segment length of the matrix polymer, the bulk modulus is reduced and the
thermal expansivity is increased. At higher loadings, the C60 is spaced closer than the Kuhn
segment length of polystyrene and the bulk modulus is increased and the thermal
expansivity is decreased. Similar trends are seen in the bulk modulus both above (200 °C)
and below (50 °C) the glass transition temperature. Prediction of the bulk modulus with a
free volume layer of 0.26 nm provides a satisfactory fit to the measured bulk modulus at 200
°C (b). The prediction for no free volume is for a much greater increase in K, than is
observed experimentally.

Contrary to the Tg observations made by DSC, these PVT quantities suggest an
increase in free volume for the 0.5v% case and a decrease at higher loadings. However,
the types of mobility being probed by the two techniques are not precisely equivalent.
DSC results are based on the thermal energy required to initiate motion to transition from
the glass to melt state. PVT results, on the other hand, are based on the volumetric
response of a material, already in the melt state, to changes in pressure and temperature.
This means that PCT is a more direct measure of internal voids, while Tg changes
observed by DSC are indicative of mobility, which is a possible result of changes in void

space. Furthermore, while the K0 and a values indicate a reduction in the effect of free

62

volume at higher C60 loadings, they do not preclude the possibility that free volume is
still greater than for the unfilled polymer. Recalling that K0 for pure C60 is much higher
than for unfilled PS, the addition of 2.5v% C60 would be expected to increase the value of
K0 for the blend to 1.27 GPa, based on the lowest estimates of the modulus of C60 asigure
IV-Zb). This is much higher than the observed value of 1.18 GPa and suggests that highly
compressible void space is being introduced with the C60.

If the void space is considered to have an infinite compressibility (Ko") and based
on the known range of moduli for C60 and unfilled PS then the bulk modulus of the
composite can be used to estimate the amount of free volume in the sample based on a
volumetric average of the bulk moduli of the PS, C60, and free volume (see section
II.C.l). For the very low concentration system that showed a stark drop in K0, the free
volume fraction, (Pf is 0.18 to 0.13 and the free volume to C60 volume ratio ((pf/(pC60) is
43.47 to 30.32. At the higher (1v% to 5v%) loadings of C60, (pf/(p030 becomes essentially
constant at 3.5 i 0.5 to 14.8 i 0.7. If one assumes that the free volume introduced by C60
is located in a layer of constant thickness around the perimeter of the particle, then a
value for that layer thickness may be calculated. For the very low concentration system,
the free volume layer thickness, If is 0.98 to 0.83 nm. At the higher (lv% to 5v%)
loadings of C60 If is 0.25 i 0.03 to 0.58 i 0.01 nm. Volumetric estimates of the bulk
modulus of PS-C6o blend based on a free volume layer thickness of 0.26 nm and a C60
bulk modulus of 6.8 GPa are shown in Figure IV-2b and match well with the observed
values of K0 for loadings greater than 0.5v%. These estimates are all less than the
previously discussed lK, even approaching the size of a styrene monomer, lending

credence to this as a realistic length scale based on the limited flexibility of the polymer

63

chain. Moreover, this weak interaction is consistent with a previously suggested") slightly
repulsive chi-parameter for the PS—Cm interaction.

In addition to the value of bulk modulus at zero pressure, it is instructive to
measure the slope of the bulk modulus as a function of pressure close to zero pressure, K,
(Figure IV-3). For the blends of C60 in PS, K. reaches a maximum at a particle volume

fraction of 0.5v% to 1v%.

 

 

 

 

 

12.6 5 , . , . . . 320
2.4:— ~ 2.3..
12.2 3: *_ 280

4) 12.0— :73

A E" l- 260 g

g 11.8 ;— 9"”

g -24o .

xv- 11.6 E """""""" ('5
11.4 — . ' 220
11.2 ;— ?-- 200
11.0E 1 . l . 1 . l 180

0.00 0.02 0.04 0.06

Volume Fraction of Particle
Figure IV-3. The free volume asymmetry number, and internal pressure as function of C60
volume fraction in PS 393 kD. The free volume asymmetry number goes through a
maximum before decreasing with increasing particle loading. The internal pressure is
decreased by particle addition, consistent with a decrease in the strength of intermolecular
interactions.

The quantity, K1, is related to the shape of the free energy minimum and is

referred to as the free energy anhar'monicity.53 A K value of five is equivalent to a

64

harmonic potential, for which compression and dilation are equally favorable processes.
However, intuition and experience suggest that K1 is generally greater than five,
consistent with a material for which dilation is favored relative to compression. Typical
K, values for polymeric materials are 11.0 i 1.5.53

It has been shown through changes to K0 that the addition of C60 introduces a
driving force towards free-volume expansion within the nanocomposite. This driving
force is also manifested in an increase in the free-volume anharmonicty, K, as the system
becomes increasingly biased towards dilation over compression. This is specifically
apparent for (p=0.5% where a maximum value of K1 is observed, in concert with the
maximum free volume increase calculated according to K0 values. At a higher volume
fraction (5v%) K1 decreases relative to the unfilled PS. High K1 values are characteristic
of repulsive intermolecular forces, but as material becomes more porous, there is less
driving force toward dilation — the system is already in a high volume state — and the free
energy well becomes more neutral.

In addition to the shape of the free energy well, the sensitivity of internal energy
to volumetric changes can be calculated from PVT data. This sensitivity is defined as the
internal pressure, P,.54 The internal pressure is not a direct measure of the magnitude of
intermolecular interaction energy, but rather a measure of the response of this energy to a
change in volume.52 The direct measure of the interaction energy between molecules is
the Cohesive Energy Density (CED) which is defined55 as

Eq. 18 CED = U/V
In the past, the difference between CED and P, has sometimes been wrongly neglected

and values of P,- have been used for CED. While not strictly correct, it was shown by

65

Hildebrand et al.56 that the ratio, n, of P,- to CED is approximately one for low molecular
weight liquids. In further analysis Sauer and Dec55 showed for a number of polymeric
materials that n is between 0.88 and 1.35.

The internal pressure is strictly defined as the response of the internal energy to a
change in volume:

Eq. 19 P.- E (6U/6V)1~
Eq. 20 P,- = T «38/th - P
The internal pressure can also be written as the difference between the thermal pressure
(TorK) and the system pressure (P).
Eq. 21 P,- = TaK - P

As free volume is increased in a system, additional regions are introduced for
stress relief in the event of a change in volume. This diminishes the system’s energetic
response to changes in volume, and therefore reduces Pi. This effect is clearly observed
with the addition of C60 to PS. The additional free volume introduced to the system leads
to a ca. 25% reduction of the internal pressure. There is, however, an apparent limit to the
P,- reduction that can be caused by particle introduction and the accompanying free
volume layer, as P.- increases for C60 loadings greater than 1v%. This may highlight the
effect of particle crowding; particle addition enhances mobility at low volume fractions,
but at higher loadings the particles begin to impinge on another, eventually decreasing
mobility by acting as obstacles themselves. This increases the volumetric dependence of
free energy as the particles become close enough to interact with one another rather than

only interacting with the polymer matrix.

66

IV.C.2. Non-Equilibrium Tensile Behavior

In addition to equilibrium techniques for understanding the C60-PS interaction, an
understanding of the solid state tensile properties is needed to evaluate the potential for
application of C60 as a route to structural reinforcement. Of particular interest is the
tensile behavior of samples that have been subjected to a uni-axial hot drawing process
which introduces alignment to the polymer matrix.

Similar to the previously discussed quantities, a material’s strain-to-failure, 8f,
may be indicative of free volume introduced near a filler particle surface. The hot draw
ratio, 1, dependence of 8f is shown for two C60 loadings in Figure IV 4b. The ductility for
both studied C60 loadings is increased compared to unfilled PS at low to moderate (1.75
to 2.5) values of it. At higher values of A the blend with a lower concentration of C60
shows a 8f value that is similar to the behavior of the unfilled polymer. The blend with a
higher C60 loading, on the other hand, shows a stark drop-off at higher draw ratios, a

behavior that will be discussed later.

67

 

 

    

   
    

   

 

 

 

 

 

 

 

 

 

5..
10
Tu‘ 5“
CL 2
Q, 2
a 4- Li
3 D
U 4—l
O E
2 91
um _ H
m 3 (n_
g or
,0.
P5393kDa neat
—e—P3393k0a,neet “9‘ - -
— 460.1% I 5' ciao-1%“
2x100- +Cw,2.5%vol ~ .2 I
I III] 10 c
s 2 3 4 5 5 7 as 1
1
7.=L/L0
J. I I
t: - d
o
2- 10 E
-1
2 10 .

+PS 333103,“ +PS$3¢DLMJ

Tensile Energy to Break (X108J/m3)

 

Ours- Ultimate Tensile Strength (M Pa)
8
l

I IIIIII

 

 

 

 

 

 

 

 

-Ia-C‘°,1%vol -E-Cm.1%vol
4. cw, 25% vol "' Caz“ "°'
‘2 l I l l I I I I I l l J r I I I I I l
E 2 3 4 5 5 7 3 9 E 2 3 4 5 8 7 8 Q
l 10 1 10
7“ : ULCI l. = LILO

Figure IV-4. The Young's Modulus (a), strain to failure (b), ultimate tensile strength (c),
and energy to failure (d) of hot drawn PS 393 kD with buckminsterfullerenes as a function
of hot draw ratio. The modulus (a) and ultimate tensile strength (c) are unchanged for the
undrawn case and increased by C60 inclusion at low draw ratios for both loadings. At
higher loading (2.5v%) the modulus and ultimate tensile strength are reduced at draw
ratios greater than 2.5. The ductility (a) is increased for both loadings at moderate (1.75 to
2.5) draw ratios. At higher draw ratios the samples with low loading (lv%) are similar to
unfilled PS while the higher loading (2.5v%) is much less ductile than the neat polymer.

Weak interfacial contact between the matrix and filler can enhance ductility by
introducing a region of increased polymer mobility which increases the plasticity of the
polymer.” 57‘ 58 In the absence of avenues for uniform stress relief or distribution, stress
becomes concentrated at flaws or cross-sectional area minima, which gives rise to

catastrophic failure at these points. Added free volume is not, however, the only avenue

68

for ductility increase for hot drawn films. Previous work with unfilled PS has shown that
chain orientation also increases the value of 8f.36' 37’ 62’ 100’ ’01 This is attributed to an
enhanced capacity to distribute stress through the sample along the oriented chain. In
addition to stress transfer, the chain orientation may decrease the stress to flow initiation,
an important quantity in determining whether or not a sample will break. When the stress
to flow initiation is less than the stress to failure, a sample under load will deform, and
vice versa. Chains oriented in the direction of flow and chains in a higher free volume
environment have fewer entanglements in the stress direction, making them more likely
to flow than an equivalent unoriented or tightly packed chain.

The increase in the ductility for the blend with a lower C60 loading suggests again
that C60 is introducing free volume to the blended sample. The inability of the additive to
induce ductility at higher draw ratios is indicative of a maximum in the polymer
alignment. Beyond a sufficient alignment, the tensile stress on the material is being
applied more directly along the polymer chain backbone. In this case it is the chain bonds
themselves that are experiencing stress which cannot be redistributed or relieved.

A study of the Young’s Modulus as a function of the hot draw ratio (Figure IV—4a)
lends insight to the effects of buckminsterfullerene inclusion on PS alignment. The first
thing to note is that despite the remarkably high bulk modulus of buckrninsterfullerene,
the Young’s Moduli of the unstretched samples (7:1) are essentially unchanged by the
addition of C60. As the draw ratio increases to 2.5, however, Young’s Modulus shows
immediate improvement for both low (lv%) and moderate (2.5v%) C60 loading. While
both these modifications show similar behavior at low draw ratio — E increases from an

unstretched value of ca. 2.5 GPa to ca. 3.0 GPa — the Young’s modulus of unfilled PS

69

increases much less, from ca. 2.4 GPa to ca. 2.5 GPa. Much higher draw ratios show a
volume-fraction dependent behavior. At a draw ratio of 4.5 unfilled PS surpasses PS-Cw-
2.5v% while PS-C6o-lv% continues to show improvement greater than that of the unfilled
system. In fact, while PS-C60-2.5 vol.% demonstrates a plateau in Young’s Modulus with
draw ratio near 4 GPa, unfilled PS continues to increase up to 5.5 GPa at X=lS while PS-
C60-1 vol.% reaches 6.0 GPa at the same draw ratio.

Trends seen for Young’s Modulus become even more obvious for the ultimate
tensile strength (Figure IV-4c). At draw ratios of 5 and higher, PS-C60-2.5v% shows
marked deterioration of the strain and especially stress to failure. While PS-Coo-lv%
shows some improvement in ultimate tensile strength, the strain-to-failure is essentially
unchanged, leading to little change in the energy required to fracture the specimen.

Larger draw ratios show a deviation from universal enforcement by C60. At draw
ratios greater than 2.5, the polystyrene film bearing 2.5v% C60 shows a decrease in
Young’s modulus, strain-to-failure, and ultimate tensile strength. A reduction in the
tensile modulus is often indicative of phase separation, leading to stress concentration at
the phase interface. In the case of C60, even strong interfacial contact with the matrix
would be insufficient to provide a significant tensile modulus increase, as the extremely
small fullerene particles lack the high aspect ratio that is the norm for traditional fillers,
making an aggregate of C60 incapable of withstanding even a moderate tensile stress. The
notion of strain-induced phase separation is reinforced when one examines the
interparticle gap in the blend. The average interparticle gap for a volume fraction of 2.5%
is 1.36 nm. If the particles in the composite move relative to one another in an affine

fashion during orientation, then two particles oriented perpendicular to the stretch

70

direction would decrease their interparticle gap during hot drawing. In fact, at a draw
ratio of 4, close to the drop-off in tensile properties, the calculated interparticle gap is less
than the particle radius. This suggests that forced particle motion during processing may

promote phase separation, leading to erosion of mechanical performance.

IV.D. Conclusion
Buckminsterfullerene demonstrates a complex behavior when used as an additive

for linear polystyrene. Like some other nanoparticulate fillers, C60 introduces a layer of
free volume around the particle surface that increases polymer chain mobility, decreasing
Tg and increasing er in many cases. However, the high modulus of C60 leads to an
increase in the bulk and tensile moduli of the composite material. Additionally, the very
small radius leads to small interparticle gaps that have consequences for particle-particle

interaction.

71

Chapter V: Dispersion of hyperbranched polyethylene in
polystyrene leading to improvements in stiffness and ductility

V.A. Introduction
A route to the controlled branching of polyethylene was described by Guan et

al102 in 1999. By controlling the monomer pressure during polymerization, the rate of

occurrence of chain-growth steps is controlled.103

In the intervening time between chain
additions, the active radical is free to isomerize, moving randomly along the chain by a
process referred to as chain-walking. According to this mechanism, a chain grown under
low monomer pressure (PELP) has been found to have greater branching, and a dendritic-
type structure. In the present work, the addition of PELP to linear polystyrene (PS) is
studied to understand how the polymer-particle interaction gives rise to changes in the
equilibrium thermal, as well as non—equilibrium mechanical properties of the composite.
Polyethylene is generally considered to be immiscible in polystyrene, but Mackay et al.'0
demonstrated that these hyperbranched PE macromolecules can be stably dispersed,
provided a sufficiently high molecular weight of polystyrene is used.

Studies of particle addition to polymers for reinforcement in the literatures' 14’ 29'

104406 and in the present work have tended to focus on higher modulus, rigid fillers added
to a weaker polymer matrix. In this case, however, the particle additive is quite soft,
while still having a defined, branched structure and a radius, a, of 11 nm which is less
than the polymer radius of gyration. While this larger size is still within the general limit
for particle dispersion defined by Mackay et al.10 (a < Rg) it does have consequences for

other key characteristics of the nanocomposite. Notably, the interparticle gap, h, of a

3.2v% blend of PELP in PS is greater than the R8 of the polymer. This means that the

72

polymer is not confined between the particles and is more free to assume its equilibrium,

unfilled conformation than a polymer in a confined state would be.

V.B. Experimental

Polystyrene standards were purchased from Scientific Polymer Products (Ontario,
NY) with MW: 393,400 Da and Mw/Mn=1.16. Branched polyethylene chains were
generously provided by Zhibin Guan and synthesized according to a previously reported
method.102 Linear polymer/nanoparticle blends were made by dissolving both the linear
polymer and nanoparticle in a mutual solvent, THF. The solution was then dripped into a
mutual non-solvent, methanol, where the polymer and nanoparticles rapidly precipitated,
forming an intimately mixed, homogeneous dispersion of nanoparticles in the linear
polymer.43 After removing the majority of the liquid from the sample by decanting and
vacuum filtration with copious methanol rinsing, the blend was dried for a week in an
oven at 50 °C and under rough vacuum. Sample processing and characterization

techniques were identical to those described in section II.B.

V.C. Results & Discussion
V.C.1.Equilibrium Thermal Analysis

The glass transition temperature (T8) is an indicator of polymer chain mobility in
amorphous polymers. More mobile chains require less thermal energy to initiate the
Brownian motion of 20 to 50 carbon atoms that is characteristic of a material above its
Tg.24 This transition is sensitive to the polymer’s chemical structure and molecular
weight, as well as the environment in which it is located. Studies have shown that placing
a polymer in a thin film, pore, or other confined geometry alters its conformation

sufficiently to change the Tg.”27 One possible route to increase chain mobility is an

73

increase of free volume. As obstacles to motion are reduced, especially by the
introduction of unoccupied area (free volume), the thermal energy needed to initiate free
motion of the amorphous chains is decreased, leading to a reduction in the glass transition
temperature.

The glass transition temperature as measured by DSC of PS-PELP blends is found
to be lower than that of the unfilled matrix polymer. For measured blends with volume
fractions between 1.3v% and 6.4v%, the Tg is reduced relative to PS by 1.72 i 0.61 0C.
The trends in glass transition temperature with PELP addition to PS confirm a number of
expectations. First, the glass transition temperature of the PELP is well below 0 °C,
although the thermal behavior of the hyperbranched PE macromolecule and its Tg is
somewhat difficult to ascertain with certainty. The low Tg of this filler material is
expected to, and does, decrease the Tg of the blend. In addition to the low Tg of the filler,
PS and PE are known to have a weak, or even repulsive interaction. This negative
interaction generates a weak interface, permitting chain mobility.

In addition to the change in Tg, other features of the DSC trace (Figure V-l) reveal
information about the particle/polymer blend. Hyperbranched PE shows a large
endothermic peak at ca. -33 °C. This transition is not clearly apparent for the l.3v%
blend, but a small peak is noticeable for the 6.4v% blend. This suggests, but does not
guarantee46 that 1.3v% blend is well-dispersed, while the 6.4v% blend seems to indicate

the possibility of phase separation in the blend.

74

 

. y ; -—'PELP ' 1
, 2 s 2 ---PS,PELP1°/oj

-0.4 X ~ ‘ , , — PS,PELP5%-

Reversible Heat Flow (mW)

IIIIIIIIIIIIIrrlrrrrlIrIIlIIII

 

 

III!"

-50 0 50 ‘l 00 1 50

Temperature (°C)
Figure V-l. DSC traces of pure PELP and blends of PELP with linear PS. Phase separation
becomes apparent in the DSC trace for the 5% blend.

The overall compressibility of the system and its volumetric response to changes
in temperature and pressure are sensitive to internal structure and the presence of void
space. Engineering properties of interest that can be derived from PVT data are the bulk
modulus, K = -V(6P/6V)T, and the coefficient of thermal expansion,47 or = V'1(6V/6T)p.
Analysis of the volumetric response of PS-PELP blends to temperature and pressure is
consistent with expectations based on intuition about the component particles. The
hyperbranched polyethylene shares the low Tg of other ethylene based polymers.
However, likely due to the steric effects of branching, PELP appears to be hindered in its

ability to crystallize at room temperature. Consequently, at ambient conditions and above

75

the sample is a liquid and is expected to have a very low modulus. This expectation is
confirmed by measurements of the bulk modulus of PS-PELP blends as a function of
increasing PELP content (Figure V-2). The modulus decreases quickly, falling by 18% at
a 3.2v% loading of PELP. At higher loadings, the modulus increases, consistent with the
observation made by DSC that phase segregation becomes prevalent at the higher
concentration. The decrease in K0 is quite significant in magnitude. While PELP is
expected to have a very low bulk modulus, the reduction observed is greater than that

expected for a material with bulk modulus of zero.

 

 

3.5 - I I I I I I I I 6.6
3.0 :- -- 6.4
4) 2.5 L --6.2 i
: 1‘.
A : 0.
w 2.0 -~ -— 6.0 0..
to, 5 0.
24" 1.5 :- -— 5.8 T
- A
"' l
1.0 :- — 5.6
: l l l I l J l 1

 

 

 

0.00 0.02 0.04 0.06

Volume Fraction of Particle
Figure V-2. Bulk modulus and thermal expansivity of a polystyrene/hyperbranched
polyethylene nanoparticle blend. The PELP decreases the modulus and increases the
thermal expansivity as expected for a system with little chemical interaction. Similar trends
are seen in the bulk modulus both above and below the glass transition temperature.

76

In lieu of the seemingly unphysical conclusion that the bulk modulus of PELP is
negative, the system can be viewed as having a layer of free volume surrounding the
approximately spherical PELP macromolecules. The void space may be considered to
have an infinite compressibility (Ko'l) and for lack of a better estimate of the
compressibility of PELP, we also assume infinite compressibility for the dendritic PE.
Based on these estimates and the known K0 of unfilled PS, the bulk modulus of the
composite can be used to estimate a lower limit of the free volume in the sample based on
a volumetric average of the bulk moduli of the PS, PELP, and free volume, following the
method described in section II.C.l. For the stable PELP loadings of 1.3v% and 3.2v%,
the calculated size of the excluded volume layer is 3.2 nm and 12.6 nm thick,
respectively. It is more likely, however, that the free volume is more evenly distributed
throughout the material rather than being located exclusively at the particle surface. In
fact, calculations of free volume may be interpreted as diffuse regions of low density,
rather than a full region of absolute void space. In either case, the estimate of the free
volume is 2v% and 15v% at PELP loadings of 1.3v% and 3.2v%, respectively.

The view of the system as one having a high amount of void space is supported by
the trend in thermal expansivity. Systems with high free volume and mobility have been
identified as having increased values of 01.4952 For the PELP/PS blend, the thermal
expansivity shows a maximum at 3.2v%, concurrent with the minimum in KO at the same
volume fraction.

The decrease in the bulk modulus suggests a porous, free volume laden structure
of the nanocomposite. Additionally, the material also becomes more favored towards

dilation with the addition of PELP. This is reflected by the increase in the free energy

77

anharrnonicity, K1 with PELP content (Figure V-3). This trend emphasizes the
unfavorable interaction between the PS matrix and the PE filler, with the blend showing
an energetic preference toward dilation — increasing the PS to PELP separation — rather
than compression. The internal pressure, P,-, is the sensitivity of the internal energy to
changes in volume and is sensitive to porosity, or free volume in the material. An
increase in free volume is expected to decrease the volumetric dependence of internal
energy as the mean nearest-neighbor spacing increases. This behavior is observed for the

PS-PELP blend, with internal pressure decreasing by as much as 30%.

 

 

12.8 , . . . . . . . . 320
12.6;— ~-—3oo
12.4:— ~— 280
12.2:- ~260’g‘

is? a ‘0

n. 5 8

g 12.0 ;— ~24o .

.. a A

X E I
11.8 g.— —220
11.6 .— «~200
11.45 i I l I L I l I 180

 

 

 

0.00 0.02 0.04 0.06

Volume Fraction of Particle
Figure V-3. The free volume asymmetry number, and internal pressure as function of PELP
volume fraction in PS 393 kD. The free volume asymmetry number is increased with
nanoparticle addition, suggesting an increased energetic penalty to compression as
compared to dilation. The internal pressure is decreased by particle addition, consistent
with a decrease in the strength of intermolecular interactions.

78

 

V.C.2. N on-Equilibrium Tensile Behavior
While dilatometric measures of bulk modulus reflect a volumetric average of the

overall sample composition and the interaction between components, the solid state
tensile behavior is largely dominated by the state of the continuous matrix. Therefore, a
soft filler that weakens the composite when tested in compression may lead to a reduction
in bulk modulus but an increase in the tensile modulus. This may occur if the expulsion
of the matrix polymer from the vicinity of the filler causes the polymer to be more rigid
due to its tendency to shrink away from the unfavorable filler environment. Efforts by the
polymer to avoid the unfavorable particle interface may lead to the chains being strained
beyond their normal equilibrium state. While this chain stretch would not be in any
particular orientation, the strained state could lead to some increase in Young’s Modulus,
E. Additionally, the already strained polymer should be susceptible to orientation by a hot
drawing process, increasing the modulus relative to the undrawn case or an equivalently
drawn, but neutral environment chain. A study of the Young’s Modulus as a function of
the hot draw ratio, it, for PS samples with and without PELP addition reveals this type of
behavior.

The Young’s Modulus of the undrawn sample increases from 2.37 to 2.85 GPa
(20%) by the addition of 3.2v% PELP (Figure V-4a). The PELP laden sample is highly
sensitive to orientation in the low draw ratio regime, increasing in E by 35% at a hot draw
ratio of 1.5. By comparison, the unfilled polymer does not increase in E by that much
until a draw ratio of more than 2.5. While the strained nature of the chains seems to make

them easier to align, it does not appear to improve the maximum alignment, or a least the

79

maximum Young’s Modulus that can be achieved by the hot drawing process. In fact, at
the higher draw ratios the modulus of the PELP filled PS is similar to, or slightly less
than, the unfilled polymer. The stiffening effect seen for Young’s Modulus is also

observed for the ultimate tensile strength (Figure V-4b), albeit to a lesser degree.

 

 

   

 

 

 

 

 

 

 

2.
Sr 10” ‘
7; “5
11 S 5'
g 2 4:
In 4 ‘6 _
3 LL
3 9 2'
0 E
m .1
E :10 .
b 3, (n 3:
g ‘ a!" 6:
o "
>—
2_ .
—6— PS 393kDa, ned :Sggg‘g213m
0 l —~,~7PELP3%}vol 10.2 I , , . . . .11
A l L J A I ll
2xlOg 2 3 4567890 E1 2 3 45678910
1 1
AzH'lo
7t=LlL0

 

 

   

OUTS, Ultimate Tensile Strength (M Pa)
Tensile Energy to Break (X1 OaJ/ma)
ES

+PS 393an,ned“ _ +95 39301063 3
+PELP 3%vol . AiPELP 3%vol
“<1 i iiééie‘é s i Siééiéél

1 10 1 10

7t = LIL,J 7t : ULO

Figure V-4. The Young's Modulus (a), strain to failure (b), ultimate tensile strength (c), and
tensile energy to break (d) of hot-drawn PS 393 kD with 3v% PELP as a function of hot
draw ratio. All four key tensile properties are increased at draw ratios less than five. At
higher draw ratios, the behavior of the matrix dominates and the composite follows the
tensile properties of unfilled polystyrene.

 

 

 

 

 

 

80

In addition to changes in Young’s Modulus, changes in the strain—to-failure (8f)
and mode of failure in simple tension are observed. The alignment induced by the hot
drawing process is known to increase 8f for unfilled PS. At low hot draw ratios, PS fails
by an abrupt, brittle fracture mechanism at a very low strain value, which increases
slightly across the low draw ratio regime. Beyond a critical processing threshold, the
failure occurs by a ductile mechanism, characterized by neck formation and failure at
much higher strain values. For the test and processing conditions of the present study,
that transition occurs for unfilled PS at A _>_ 2. The PS-PELP blend undergoes a similar
shift in tensile failure mechanism, but at a hot draw ratio of 1.5. The stress-strain curves
of unfilled PS and PS-PELP 3.2v%, each processed to a hot draw ratio of 1.5 are shown
in Figure V-5. The two samples show the classic stress-strain curves for their respective
failure modes. The unfilled polymer fails abruptly and completely at a low strain value
after a monotonic increase in stress. The ductile PS-PELP blend shows a maximum stress
at a strain similar to [if of the unfilled polymer. This stress maximum occurs at the yield
point and is indicative of the onset of necking. After the constant stress necking process
has propagated across the length of the specimen, a strain hardening process occurs

before final rupture.

81

 

:I l I I I l I I

(D
O

O)
O

N
O

   

 

Engineering Stress, 6 (MPa)
.5
C

-e- PS 393kDa, neat
—e— PELP, 3% vol

 

 

 

 

 

 

l I l l l
0.8 1.2

Strain, 8

Figure V-S. Stress-strain curves for polystyrene with (green diamonds) and without (black
circles) PELP, each processed to a hot-draw ratio of 1.5. The PELP induces ductile failure
under conditions for which the unfilled polymer fails by a brittle mechanism at low strains.

In addition to shifting the critical hot draw ratio needed to induce ductility, the
addition of PELP increases 8f at all draw ratios up to 2.5 by as much as 825% relative to
the unfilled polymer (Figure V-4b). Both of these effects reflect the low modulus of PELP
and weak interaction at the interface between PS and PELP. This weak interface, which
has been previously evaluated by trends in KO, permits an avenue for stress relief in the
PS matrix. The even special distribution of these sites for stress relief throughout the
sample allows the material to distribute stress evenly throughout the sample, permitting
larger deformations. In the absence of these stress relief sites, internal stresses become

concentrated at a single sample flaw or cross-sectional area minimum. Eventually, the

82

 

accumulation of stress at this location gives rise to failure at lower deformations than
would be expected if stress were more evenly distributed.

At the higher draw ratios PELP is less effective at improving sample ductility.
With the continuous matrix more oriented by the hot drawing process, tensile stress is
propagated more directly along the polymer chain backbone. In this case, the matrix is
less capable of distributing stress to the matrix-filler interface and the 8f of the blend is

dominated by the continuous phase.

V.D. Conclusion
Hyperbranched polyethylene macromolecules (PELP) can be well-dispersed in

linear PS. Like other nanoparticle fillers, the addition of PELP at low volume fractions
has been shown by DSC and PVT to increase the free volume and mobility of the
material due to the poor interaction between PS and PELP. The increase in free volume is
reflected by a decrease of the bulk modulus of nearly 20%. Estimates of the free volume
fraction from the bulk modulus indicate that the free volume fraction is as much as five
times the particle volume fraction. This free volume appears to be well—dispersed and
leads to an increase in polymer mobility, and therefore, ductility rather than nucleating
stress concentrations.

The unfavorable polymer-particle interaction is also found to cause chain strain in
the polymer, which leads to an increase in the tensile modulus, an unexpected
observation based on the addition of a low modulus material to one of higher modulus
and the observed free volume increase. The increase in tensile modulus (E) and the

decrease in bulk modulus (K) suggest a change in the shear modulus (G) as well. Based

83

on the well known relation between the moduli for the three modes of strain, an estimate
can be attained for the shear modulus with and without PELP addition.

Eq. 22 E" = (3G)" + (910‘1
For a 3% loading of PELP in PS, the shear modulus at 50 °C is expected to increase by

ca. 20%.

84

Chapter VI: Rigid nanoparticle inclusion with polystyrene
VLA. Introduction

A class of nanoparticles that has garnered a great deal of attention for behavior
peculiar to their nanometer size is semiconductor nanocrystals, also know as quantum
dots. A particularly interesting and well-studied semi-conductor crystal type is II-VI
semiconductors, such as CdS and CdSe. These materials have shown variation in a
number of material properties based on the size of the crystal which includes a shift in
band gap,107 melting temperature,108 and pressure required to induce a transformation in
the crystalline structure.109 This peculiar behavior arises from the quantum-confined

nature of the semiconductor crystal. The potential functionality of these materials has

110-113 ll4-ll6

garnered interest for potential use as light-emitting diodes, photovoltaic cells,
and bio—sensors.117 In addition to these potential applications, these particles are attractive
for composite formulation due to their small, well-defined size, rigid composition, and

the ability to coat them with a variety of stabilizing layers.”8’ “9

VI.B. Experimental

Polystyrene standards were purchased from Scientific Polymer Products (Ontario,
NY) with MW: 393,400 Da and Mw/Mn=1.16. CdSe-pyr nanoparticles were generously
provided by Michael Wong at Rice University. Linear polymer/nanoparticle blends were
made by dissolving both the linear polymer and nanoparticle, which was originally in
solution with pyridine, in a mutual solvent, THF. This quaternary solution was then
dripped into a mutual non-solvent, water, where the polymer and nanoparticles rapidly
precipitated, forming an intimately mixed, homogeneous dispersion of nanoparticles in

the linear polymer.43 After removing the majority of the liquid from the sample by

85

decanting and vacuum filtration with copious water rinsing, the blend was dried for a
week in an oven at 50 °C and under rough vacuum. Sample processing and
characterization techniques were identical to those described in section H.B. Samples for
TEM were embedded in Polybed 812, which was prepared and cured according to the
manufacturer’s instructions. Thin section of the bulk samples were cut with an

ultramictome and samples were observed and photographed with a JEOL 100 CXII.

VLC. Results & Discussion

The glass transition temperature observed by DSC is an indicator of polymer
chain mobility and may reveal signs of phase separation in a particle-polymer blend. In
the case of PS blended with CdSe-pyr, the glass transition temperature is decrease by 1.0
to 1.5 °C with O.9v% to 1.0v% loading of particles. This indicates that the mobility of the
polymer is increased by the particle addition. This is likely due to weak adhesion between
the particle and polymer which leads to a region of low polymer density near the particle
surface.

The tensile behavior of a PS-CdSe-pyr blend is interesting due to the rigid
structure of the particle and its intermediate size. Previous studies of the tensile behavior
of nanoparticle filled polymers have been limited to particles that were of similar (PSNP,
Chapter 11:) or lower (PELP, Chapter V:) modulus than the matrix polymer, or had a size
that was much smaller than the Kuhn segment length (C60, Chapter IV:) of the matrix.
The comparison to the previously described particles is complicated, however, by the
presence of a chemical stabilizing layer attached to the particle. This layer permits the
particle to be dissolved in solution, allowing blending with the matrix, but provides an

obstacle at the polymer-particle interface. This interface has been shown to be weak in

86

other nanoparticle systems, often associated with a layer of free volume around the
particle. This has been attributed to both poor polymer-particle interaction and geometric
restrictions to efficient packing near the particle surface.

The Young’s modulus of PS and PS blended with 0.9v% CdSe-pyr is shown in
(Figure VI-la). The tensile modulus of the polymer particle blend is nearly 50% greater
than for the unfilled polymer. While a modulus increase in expected with the addition of
a rigid filler, the observed increase is not necessarily due to the rigidity of the filler. A
larger, softer particle filler (PELP) was shown to increase the modulus similarly, an effect
attributed to polymer chain strain at the polymer-particle interface due to a negative
interaction. Another filler of similar size to the present system but lower modulus was
observed to bring about a similar increase in E, attributed to the close proximity of the
particles to one another, complicating chain extension under stress by the additional
friction of the filler. In that case, the interparticle center-to-center distance was 22.4 nm,
less than twice the Rg of the matrix polymer. The interparticle center-to-center distance of

the present case is 23.0 nm, still less than twice the Rg of the matrix.

87

 

 

 

        
      

 

 

 

 

 

 

 

 

   
 

6 I I I I I I I I I I I I I II
‘ ‘ 0
.%~, 10 r b
-’ 8-
n 5- - 6~
E 4'
a, e
9, ‘5 _
(fl 4.. .. =
g If 2-
13 9
O
C
2 '510‘1 _— 1
.U’ is s- -
3' 3' ’0 6C ‘
3 HI: r-
). 4i- .
—9— PS 393kDe.neat 2_' —e— P8393kDa. near _
-v-CdSe—pyr1%vol -‘2—CdSe-pw1%vol
2XIDO IL I I I I I I I II I I I I I I I I II
5 2 3 456789 to 2 3 456789
10 10 FL] 10
7t:L/L0 ' Lo
3 I *Ii I f I I ll 2 If I I I I I
-- o d
I 10 ’

I IIIIIII

ha)

I IIIIIIII

N
M

UIO'lem

_.
DI

Tensile Energy to Break (X103 me3)
O

—e—PS 393kDa.ned:
_v . CdSepyrtiwol‘

a

—e—PS393kDa,neq
-v- CdSe-pyrfitvol -

g
f

 

 

 

 

s 2 iis'éiéél s '2 éis‘éiéél

1 10 1 10

x = mg i = LILO

Figure VI-l. The Young's Modulus (a), strain to failure (b), ultimate tensile strength (c),
and tensile energy to break (d) of hot-drawn PS 393 kD with lv% CdSe-pyr as a function of
hot draw ratio. The modulus and tensile strength are both increased at all draw ratios less
than five. The strain to failure and tensile energy are increased at moderate (2 to 2.5) draw
ratios but unchanged from the unfilled polymer under other processing conditions.

 

 

Like the unfilled polymer, the polymer-particle blend shown an increase in E
with increasing it. This is a natural consequence of the alignment process and reaches a
plateau at high it for the filled and unfilled polymer, which both show a similar high draw
ratio plateau in modulus. The modulus of the particle filled system, however, increases

much more quickly than the neat polymer. The CdSe-pyr particles improve the modulus

88

 

by as much as 100% over the unfilled polymer at an equivalent draw ratio. However, the
maximum achievable value of Young’s Modulus is not change significantly by CdSe-pyr
inclusion. This supports the idea that the observed enhancement is caused by a change in
the matrix polymer rather than the inherent rigidity of the additive. This is likely due to
poor adhesion between the matrix and filler, hindering stress transfer across the interface.
It is possible that this adhesion could be improved by the used of a different stabilizing
ligand.”8' 120. 121

Experience with a different nanoparticle system suggests that the use of a
compatible ligand may improve adhesion enough to bring about increases in modulus.
Cross-linked polystyrene nanoparticles (PSNP) are chemically similar to PS, suggesting
that adhesion between the two species would be favorable. The particle themselves are
intramolecularly cross-linked, having an aver coordination number of 2.2. This creates a
higher modulus filler with a favorable particle—polymer interaction, leading to an increase
in the maximum Young’s Modulus of 20% greater than the unfilled polymer.

The poor adhesion between the particle and matrix has consequences for the
strain—to-failure in tension (Figure VI-lb). This weak interaction causes a layer of low
density to form around the particle. While this region is ill-suited to transferring stress
from the matrix to the filler for reinforcement, it does act as a soft region for stress relief.
The effective range of ductility enhancement is limited, however, by the rigidity of the
particle, with 8f enhancement occurring primarily for hot draw ratios between 2 and 2.5
before conforming to the behavior of unfilled PS.

TEM rrricrographs indirectly support the conclusion of a weak particle-polymer

interaction. Samples of drawn and undrawn PS-CdSe-pyr films were prepared for

89

 

observation by TEM to observe the influence of hot drawing on particle dispersion.
However, the particles were so poorly adhered to the matrix that the ultramicrotomy
process generated aggregates of CdSe-pyr particles and aligned them normal to the
direction of cutting, or parallel to the knife edge. This orientation was observed
regardless of sample processing, and specifically for the undrawn film (Figure VI-2). This
suggests that the loose adhesion of the particle to the polymer permitted the
ultramicrotome knife to dislodge the particles, depositing them periodically as the knife
moved across the sample surface. While not informative about the dispersion or
orientation of the particles, this does confirm the poor state of adhesion of the particle to

the polymer matrix.

90

       

Figure VI-2. TEM micrograph of CdSe-pyr in PS. The wrinkles in the film are a familiar
artifact of ultramicrotomy, reflecting imperfections in the knife edge. The particles are
oriented perpendicular to these striations, suggesting that the particles are disturbed during
the microtomy process and deposited intermittently as the knife moves across the sample.

 

VI.D. Conclusion
Blends of CdSe nanocrystals stabilized with a pyridine ligand were blended with

linear polystyrene and characterized according to their thermal and mechanical behaviors.
Similar to other nanoparticle-polymer blends, the interface between the particle and
polymer is found to be quite weak, leading to a decrease in the glass transition
temperature and modest improvement of the strain-to—failure for solid samples tested in

tension. The Young’s Modulus of the blend is greater than the unfilled polymer processed

91

to the same conditions, but does not exceed the maximum value for the unfilled polymer.
The failure of the rigid particle to increase the modulus of the composite beyond the
maximum for the polymer is attributed to poor stress transfer across the particle-polymer

interface.

 

92

Chapter VII: Conclusions

Blends of polystyrene with four different classes of nanoparticles have been
investigated to better understand the particle-polymer interaction and its significance for
mechanical property enhancement. Cross-linked polystyrene nanoparticles (PSNP) are
used as an enthalpically simple system with moderate particle stiffness.
Buckminsterfullerenes (C60) are rigid, high modulus particles with a size scale much
smaller than PSNP. Hyperbranched polyethylene macromolecules (PELP) are a low
modulus filler with an unfavorable interaction with PS and a size on the order of the PS
chains’ Rg. Finally, pyridine stabilized cadmium selenide nanocrystals are rigid particles
with a size scale comparable to PSNP.

Generally, the particle inclusion increased polymer mobility and free volume.
This is observed through decreases in the glass transition temperature, bulk modulus, and
internal pressure, as well as increases in the free energy anharmonicity, and strain-to-
failure for a sample in tension. In fact, the particles behave in a manner similar to a good
solvent, increasing polymer chain mobility and ductility. Neutron scattering results
confirm this, showing the chains to swell the polymer matrix, increasing the Rg and
changing the chain conformation from that of a random coil with a Gaussian distribution
to a swollen coil. The free volume layer size is dependent on particle size, increasing with
increasing particle size (Figure VII—la). The ratio of free volume to particle volume is
less dependent on particle size (Figure VII-1b), having values of 1.5 to 3 for the studied
systems in the melt state. The exception to this trend is C60 in PS, which leads to a free

volume fraction approximately 13 times greater than the included particle fraction.

93

a b

 

 

 

  

 

  

 

 

 

 

 

 

 

 

I I I I 35 r l I I
' +“d‘jzoo'0 I I C +Men', 200 'c ' 3
- -o-0Iass,50'c . r 4-0.3350“; :
15 - _ 30 _3 1
L- —
" 1 25 3 _:
i- I!- _‘ m ’- .1
L 9 fl 3 20 : 3
H 10 _ , x _ 4 j
E - ,’ .1 6% C -
V '- " - K :
“I ' g 15 1
_ _ +5; _ ‘
l- .. : :
5 ‘ — 10 _ —,
- 1 : l :
_ A _ ‘
- 4 5 ,_ uuuuuuuuuuuuuuuuu —_:
I- d I. :1
0 0 '. 1 l 1

0 4 8 12 16 0 4 8 12 15

Particle Radius (nm) Particle Radius (nm)

Figure VII-1. The calculated free volume layer size (a) and free volume fraction relative to particle
volume fraction (b) for nanoparticles for four different sizes. The free volume thickness associated
with the particle addition increases with particle size. With the exception of the extreme case of C60
(a = 0.38 nm), the ratio of free volume to particle volume is independent of particle size.

The details of the size, loading, and type of particle introduce other nuances to the
polymer-particle behavior. Bulk modulus increases have been observed for many
systems, although this increase is rarely beyond the maximum value for the matrix. This
suggests a different mode for nanocomposite property enhancement that that of tradition,
macroscale composites. The nanoscale additive improves the behavior of the composite
by changing the conformation of the matrix polymer, rather than simply by transferring
stress to the particle. The increased ductility and, sometimes, stiffness leads to a general
observation of increase in the materials’ ability to dissipate energy, its toughness. This
supports the application of nanoparticles as additives for improving engineering

materials.

94

 

Appendix A. Notes on PVT Analysis

Specific Volume Measurements: A simple probe of free volume in a sample is
to measure its specific volume under ambient conditions. Deviations in the observed
specific volume (Vobs) from predictions based on relative composition (Vprcd) and specific
volume of each pure species may indicate a more or less tightly packed system. This can
be quantified by the Excess Volume Fraction, measure of the free volume fraction.

Eq. 23 (pexcess = (Vobs - Vpred)/V obs
The measured specific volume and the corresponding Excess Volume Fraction are shown
in Figure A-l. While trends can be readily observed in the specific volume, the changes

in Excess Volume Fraction are not beyond the error of measurement.

 

 

 

   

 

 

 

 

 

 

I a T : b

Q98 7 ‘ t O 01 ~ 1
me E : _s_ : ' 1 2
E T - 1 T5 .' I :
v _ " : E - ‘ :
'— 65.1.11-.. —‘ . ' . .lr ‘
E 0'm: ”5 : E 000: 1 ii I :
g : 1 : g : l :
u r F : > r ‘ j
u: I I a _ i I
u 0.94 _— -j 3 -o.n1 :— _j
A. Z ‘9‘ can _ Ifi Z I _Q_ can _
' , LP : l ‘ 1 PELP S
'_ PSNP "3 k0 ‘ : e-PSNP7BkD Z
PSNP 211 kD : I I. PSNP211 k0:

0'92 ' I . I 1 I , I ' -0112 I l . l 1 l

0.00 0.02 0.04 am 0.00 0.02 0.04 0.06
Particle Volume Fraction Pamela Volume Fractlon

Figure A-l. The measured specific volume (a) of polystyrene-nanoparticle blends. Blends of
polystyrene with nanoparticles follow close to a rule-of-mixtures type trend for specific
volume. The deviation from that trend is apparent in the Excess Free Volume (b) for which
a positive value represents the presence of free volume in the blend. It must be noted that
the measurement technique is very subject to environmental variations and small changes
in free volume may not be apparent in specific volume measurements.

95

 

Free Volume Calculation From Bulk Modulus: The bulk modulus of a
nanoparticle linear polymer blend provides information about the presence of free
volume in the composite. If a value of the bulk modulus for the nanoparticles is assumed,
a relative amount of free volume present in the sample can be computed based on a
volumetric average of the moduli of the three components: the continuous PS (c),
particulate filler (p), and free volume (f).

59-24 1=<Pc+(Pp+(Pf
Eq. 25 Ko=<ppKo.p+<pcKo..
The known bulk modulus of the composite, K0, and the nominal volume fraction of filler,
(p1,, p, can be used to calculate the free volume fraction.
ECl- 26 (Pa. pzvp/(Vp + Vc)
Eq- 27 (pr = 1 — Ko[(l-<pn,p)Ko. c + <1)... 1. K0, 1.1"
If one assumes that the free volume is concentrated in an even layer around the particle,
with a radius a, the free volume layer thickness, If, can also be calculated.
Eq. 28 11 = a map. + <1») cppz >"3 / 1)..) — 11
The free volume sizes of certain blends have been discussed previously. Values

for each particle type and concentration are presented below.

96

 

Table A-1: Values of free volume layer sizes based on the bulk moduli of composites
at 200 °C

 

Nanoparticle Blends with PS 393 kDa
Particle ¢ Hm“)

PSNP 78kD 1.0% 1.98 :I: 0.31
PSNP 78kD 2.5% 0.95 :I: 0.45
PSNP 78kD 5.0% 1.16 :I: 0.42

PSNP 211kD 1.0% 2.63 :I: 0.40
PSNP 211kD 2.0% 1.65 :I: 0.52

050 0.50/0 0.90 :t 0.11
C60 1 0% 0.42 :t: 0.23
C50 2.5% 0.39 :I: 0.24
C60 5.0% 0.43 :t 0.22
PELP 1.3% 4.69 :I: 1.43
PELP 3.2% 13.45 :I: 0.80
PELP 6.4% 3.37 :I: 1 .76

The Tait Equation: The empirical Tait equation has been used to model the PVT
behavior of polymer in both the melt and glass statessz’ 122425
Eq. 29 1-VN0=Cln (1+P/B)
The parameter C is a constant with a value of 0.0894, V0 is the initial volume at ambient
pressure, and B is a function of temperature given by Eq. 30.
Eq. 30 B(T) = Bo exp (B, T)
While some effort has been made to associate theoretical importance to the empirical

parameters,126 the values are reported primarily for completeness of comparison to other

such characterized polymer systems.

97

 

Table A-2: Tait EOS parameters in the melt state of polymer/nanoparticle blends

Nanoparticle Blends with PS 393 kD

 

Bo
Particle 6 (MPa) 31 x103 (°C")
Unfilled PS 0.0% 214.9 3.235
PSNP 78kD 1.0% 219.5 3.451
PSNP 78kD 2.5% 216.4 3.369
PSNP 78kD 5.0% 211.2 3.172
PSNP 211kD 1.0% 225.3 3.529
PSNP 211kD 2.0% 220.1 3.410
060 0.5% 21 1 .3 3.704
060 1.0% 210.2 3.035
060 2.5% 212.4 2.971
060 5.0% 353.0 5.799
PELP 1.3% 206.7 3.194
PELP 3.2% 200.6 3.756
PELP 6.4% 202.7 3.308

 

The Coefficient of Thermal Expansivity: The coefficient of thermal expansion
has been used as an indicator of the system’s free volume. Simha and Boyer"9 suggested
that thermal expansivity in the glassy state was due entirely to occupied volume (01g 2
010cm). The increase in the coefficient of thermal expansion in the melt state was
attributed to thermal expansivity due to free volume:

Eq. 31

This allowed the difference between coefficients of thermal expansion in the melt or

glass states to provide a relative measure of system free volume. In later work Dlubek,5 I
and later Kilburn,127 used the Simha-Somcynski equation of state (S-S eos) hole fraction
to separately determine the specific free (Vf = h V) and occupied (VOCC = (l-h)V) volumes

where h is the statistical hole fraction in the melt state. From these quantities, the

98

coefficients of thermal expansion of the free volume in the glass and melt states were
determined by

Eq. 32 afig = vg"(6V./ 6r) (T<Tg)

Eq. 33 a... = Vg“(av./ 6T) (T>Tg)

It is shown in these studies that 01g is significantly greater than aoccm and am— 01g <
01m, contrary to the earlier work of Simha and Boyer. Each of these studies are
confounded by the difficulty in measuring 01 in the glassy state. The restricted mobility of
materials in their glassy state means that external conditions, especially pressure, are not
necessarily transferred uniformly throughout the sample. This stress transfer is a time
dependent process and often exceeds the time-scale of measurement. While some
empirical relations, specifically the Tait equation, have been successful in modeling the
PVT surface in the glassy state, true thermodynamic conclusions should generally not be
drawn from PVT behavior of the glassy state.

The Simha-Somcynsky (S-S) equation of state: Several equations of state have
been proposed to model the behavior of polymer melts,125‘ 12“” but one of the most
successful and widely used131 has been the Simha-Somcynsky (S-S) equation of state.38
The melt is described in this model as an amorphous assembly of chain segments that
occupy a lattice with a certain fraction (h) of unoccupied sites, representative of free
volume within the melt. The thermodynamic properties of the melt are characterized by
three key parameters: the maximum interaction energy between two chain segments (8*),
the segmental repulsion volume (v*), and the number of volume-dependent external
degrees of freedom (3c). In turn, the characteristic pressure, volume, and temperature are

defined as

99

 

Eq. 34 P“ = zqe*/(sv*); 7* = zqe*/(Rc); v“ = WM,
where R is the universal gas constant, 3 is the number of chain segments, M,- is the molar
segmental mass, z is the lattice coordination number (2 =12), and zq = s(z—2)+2. These
characteristic parameters, P‘, V*, and T’ scale their respective physical parameters, P, V,
and T to produce a universal, reduced 13- V-T surface.

Table A-3: Simha-Somcynsky EOS parameters in the melt state of

polymer/nanoparticle blends
Nanoparticle Blends with PS 393 kD

 

 

 

4; P* (MPa) v* (cm3/g) T* (K)
Unfilled PS 0.0% 826.6 0.9486 11946.7
PSNP 78kD 1.0% 830.5 0.9505 11805.9
PSNP 78kD 2.5% 847.1 0.9489 11644.8
PSNP 78kD 5.0% 837.3 0.9459 11817.6
PSNP 211kD 1.0% 861.7 0.9506 11638.1
PSNP 211kD 2.0% 840.9 0.9501 11797.6
C60 0.5% 831.8 0.9448 1 1255.9
060 1.0% 825.2 0.9456 12051.8
060 2.5% 830.2 0.9404 12168.7
C60 5.0% 824.3 0.9261 12149.8
PELP 1.3% 819.4 0.9471 11795.1
PELP 3.2% 819.8 0.9472 10993.8
PELP 6.4% 799.1 0.9656 11700.1

 

The S-S eos is based on the free energy function, F, defined as
Eq. 35 F: 1311271710273]
The free volume fraction, 11, is a function of the reduced temperature and volume, which
arises from the minimization of the free energy at a given temperature and pressure:
Eq. 36 (6F/6h)v,1 = 0

and the reduced pressure is described as:

100

Eq. 37 15 = 4613761717
The solution to the reduced pressure term yields the first of two equations that constitute
the equation of state:
Eq. 38 PV/T": (1-77)'l+2 yQ2(1.011 Q2 — 1.2045)/T~
where y is the occupied site fraction (l—y = h), Q = (1217)", and r7 = 2‘1’6yQ1/3. The free
energy minimization yields the second equation:
Eq. 39 3c[(77 — 1/3)/(1 — 77) — yQ2(3.033 Q2 - 2.409)/6T‘]+(1 — s) — (s/y)ln(l — y) = 0
The statistical hole fraction, h, is computed from the S-S eos and presented as a
function of particle volume fraction (Figure A-2) for samples at 200 °C and 0 MPa. It is
interesting to note that all the samples show an increase in the hole fraction with
nanoparticle addition, regardless of the change in bulk modulus or coefficient of thermal
expansivity. It is counterintuitive that the statistical hole fraction, h, increases, regardless
of the relative change in bulk modulus or thermal expansivity. This may indicate that free
volume is introduced around the exterior of all nanoparticles. However, changes in
physical properties may be due to the way in which the occupied volume is filled.
Different nanoparticles may differently affect the packing of the polymer chains outside

the excluded volume region.

101

 

 

0.15 I I I I I I I

 

      

 

 

:- 014 ‘5'- ............................................................................................... .2
.9 = :
IO-I‘ : 1
o ; :
g 0.13 :— -:
0 E E
f 0.12 _:_" "E
(U : :
.2 = =
*5 E E
z 0.11 :-— ~-._.
59 E —e— PSNP 78kD 3
"’ E .. 1 4::— PSNP 211kD 5
CI.) 0.10 E— ........ , ... ,_.. .. .5. 060 .--..E
(D E. ' «'9— PELP E

 

0.09 i r i L I l I
0.00 0.02 0.04 ‘ 0.06

Volume Fraction of Particle
Figure A-2. The Simha-Somcynsky statistical hole fraction for blends of PS 393 kD with
four different nanoparticle types.

102

Appendix B. Additional Tensile Data

In addition to the low loadings (lv%) presented in Chapter II:, the tensile

 

behavior of 5v% blends of PSNP has also been measured (Figure B-l). The behavior

tends to be similar to the 1v% loading described previously.

 

 

 

    

  

 

 

 

 

 

 

 

 

 

 

 

   

     

 

 

 

 

 

 

 

E
9 E.
m '5
2 u.
13 a
C
2 $1 .
V)
.m 0 -
g2x10 —9—PS393kD.neat u,— -e—P5393k0,neut .
o -a-PSNP41k01v% .
-e.psup 41mm:
>. -e.PSNP78kD‘lv% _
'° ' PSNP 7811011196 ... PSNP 78 k0 5v%.
+PSNP 78kD 5v%. psmp211k01v% .
» PSNP 211kD1v% PSNP211k05v%
93149 2111105171. I
I J I r r i r 111 10’ I ' I I I I‘
1s 2 3 456789 3 “5578910
1 10
1=UL0
A 3 l ' ' |
m ' n
CL C ME
é a
2.
E ”C,
D) '— l
C x
a v i
03' %
2 1029* 9
.fi . m
C 8- 0
153 7' ' Ex”
6. 1
u.) k.
"‘ 0)
E 5&1, —e—PS393KD.mat ‘ c +Psasako.neat __
4.: 4. .134P5NP41k01vxi L“ -13-PSNP41kD,1v%E
5 —o-PSNP78kD1v% g --2.PSNP78|ID1V% _
i1 3. +PSNP7ekDSv%. g +PSNP78k05vr. :
I- ‘ PSNP211|tD1v% a) PSNP211kD1I/i6_
6" 1 PSNP211kD5v% '— PSNP211kD5v%
9 L I I I I I r l I I _ I I I I I J 1]
s 2 3 456739 10: 2 3456789
1 10 1 10
1:”‘0 KZLILO

Figure B-l. The Young's Modulus (a), strain to failure (b), ultimate tensile strength (c), and
tensile energy to break (d) of hot-drawn PS 393 kD with PSNP as a function of hot draw
ratio. Blends of l % PSNP are represented by open symbols while blends of 5% PSNP are
represented by closed symbols. Larger PSNP species have very little effect on Young's
Modulus or ultimate tensile strength, while smaller (41 kD) particles increase these
properties for the unprocessed and slightly processed case. The ductility (b) is increased for
all cases at low draw ratios and at all draw ratios for PSNP 78 kD, which gives rise to an
increase in the material toughness (d).

103

REFERENCES

l. Seydel, T.; Kolln, K.; Krasnov, I.; Diddens, I.; Hauptmann, N.; Helms, G.;
Ogurreck, M.; Kang, S. G.; Koza, M. M.; Muller, M., Silkworm Silk under Tensile Strain
Investigated by Synchrotron X-ray Diffraction and Neutron Spectroscopy.
Macromolecules 2007, 40, (4), 1035-1042.

2. Vollrath, E; Knight, D. P., Liquid crystalline spinning of spider silk. Nature 2001,
410, (6828), 541-548. 1

3. Liu, Y.; Shao, Z. Z.; Vollrath, F., Relationships between supercontraction and l‘ 1‘
mechanical properties of spider silk. Nature Materials 2005, 4, (12), 901-905.

 

4. Liu, Y.; Shao, Z. Z.; Vollrath, F., Extended wet-spinning can modify spider silk :1
properties. Chemical Communications 2005, (19), 2489-2491. ..

5. Gersappe, D., Molecular mechanisms of failure in polymer nanocomposites.
Physical Review Letters 2002, 89, (5), -.

6. Tang, Z. Y.; Kotov, N. A.; Magonov, S.; Ozturk, B., Nanostructured artificial
nacre. Nature Materials 2003, 2, (6), 413-U8.

7. Tanner, D.; Fitzgerald, J. A.; Phillips, B. R., The Kevlar Story - an Advanced
Materials Case Study. Angewandte Chemie International Edition in English 1989, 28,
(5), 649-654.

8. Mackay, M. E.; Dao, T. T.; Tuteja, A.; Ho, D. L.; Van Horn, B.; Kim, H. C.;
Hawker, C. J ., N anoscale effects leading to non-Einstein-like decrease in viscosity.
Nature Materials 2003, 2, (1 1), 762-766.

9. Tuteja, A.; Mackay, M. E.; Hawker, C. J.; Van Horn, B., Effect of ideal, organic
nanoparticles on the flow properties of linear polymers: Non-Einstein-like behavior.
Macromolecules 2005, 38, (19), 8000-8011.

10. Mackay, M. E.; Tuteja, A.; Duxbury, P. M.; Hawker, C. J.; Van Horn, B.; Guan,
Z.; Chen, G.; Krishnan, R. 8., General Strategies for Nanoparticle Dispersion. Science
2006, 311, (5768), 1740-1743.

104

ll. Simha, R.; Utracki, L. A.; Garcia-Rejon, A., Pressure-volume-temperature
relations of a poly-epsilon-caprolactam and its nanocomposite. Composite Interfaces
2001, 8, (5), 345-353.

12. Utracki, L. A.; Simha, R.; Garcia—Rejon, A., Pressure-volume-temperature
dependence of poly-epsilon-caprolactam/clay nanocomposites. Macromolecules 2003,
36, (6), 2114-2121.

13. Utracki, L. A.; Simha, R., Pressure-volume-temperature dependence of
polypropylene/organoclay nanocomposites. Macromolecules 2004, 37, (26), 10123-
10133.

14. Winberg, P.; Eldrup, M.; Pedersen, N. J .; van Es, M. A.; Maurer, F. H. J ., Free
volume sizes in intercalated polyamide 6/clay nanocomposites. Polymer 2005, 46, (19),
8239-8249.

15. Dionne, P. J .; Ozisik, R.; Picu, C. R., Structure and dynamics of polyethylene
nanocomposites. Macromolecules 2005, 38, (22), 9351—9358.

16. Cerda, J. J .; Sintes, T.; Chakrabarti, A., Excluded volume effects on polymer
chains confined to spherical surfaces. Macromolecules 2005, 38, (4), 1469-1477.

17. Vacatello, M., Phantom chain simulations of realistically sized polymer-based
nanocomposites. Macromolecular Theory and Simulations 2006, 15, (4), 303-310.

18. Papakonstantopoulos, G. J .; Yoshimoto, K.; Doxastakis, M.; Nealey, P. F.; de

Pablo, J. J ., Local mechanical properties of polymeric nanocomposites. Physical Review
E 2005, 72, (3).

19. Desai, T.; Keblinski, P.; Kumar, S. K., Molecular dynamics simulations of
polymer transport in nanocomposites. Journal of Chemical Physics 2005, 122, (13).

20. Brown, D.; Mele, P.; Marceau, S.; Alberola, N. D., A molecular dynamics study
of a model nanoparticle embedded in a polymer matrix. Macromolecules 2003, 36, (4),
1395-1406.

21. Brown, D.; Clarke, J. H. R.; Okuda, M.; Yamazaki, T., The Preparation of
Polymer Melt Samples for Computer-Simulation Studies. Journal of Chemical Physics
1994, 100, (8), 6011-6018.

105

 

 

22. Neyertz, S.; Brown, D., Preparation of bulk melt chain configurations of
polycyclic polymers. Journal of Chemical Physics 2001, 115, (2), 708-717.

23. Merkel, T. C.; Freeman, B. D.; Spontak, R. J .; He, 2.; Pinnau, I.; Meakin, P.; Hill,
A. J ., Ultrapermeable, reverse-selective nanocomposite membranes. Science 2002, 296,
(5567), 519-522.

24. Boyer, R. F., Dynamics and Thermodynamics of the Liquid-State (T Greater-
Than Tg) of Amorphous Polymers. Journal of Macromolecular Science-Physics 1980,
B18, (3), 461-553.

25. Priestley, R. D.; Ellison, C. J.; Broadbelt, L. J.; Torkelson, J. M., Structural
relaxation of polymer glasses at surfaces, interfaces and in between. Science 2005, 309,
(5733), 456-459.

26. McCoy, J. D.; Curro, J. G., Conjectures on the glass transition of polymers in
confined geometries. Journal of Chemical Physics 2002, 116, (21), 9154-9157.

27. Alcoutlabi, M.; McKenna, G. B., Effects of confinement on material behaviour at
the nanometre size scale. Journal of Physics-Condensed Matter 2005, 17, (15), R461-
R524.

28. Xiao, P.; Xiao, M.; Gong, K. C., Preparation of exfoliated graphite/polystyrene
composite by polymerization-filling technique. Polymer 2001, 42, (l 1), 4813-4816.

29. Fragiadakis, D.; Pissis, P.; Bokobza, L., Glass transition and molecular dynamics
in poly (dimethylsiloxane)/silica nanocomposites. Polymer 2005, 46, (16), 6001-6008.

30. Bansal, A.; Yang, H.; Li, C.; Benicewicz, B. C.; Kumar, S. K.; Schadler, L. S.,
Controlling the thermomechanical properties of polymer nanocomposites by tailoring the
polymer-particle interface. Journal of Polymer Science Part B: Polymer Physics 2006,

44, (20), 2944-2950.

31. Bansal, A.; Yang, H. C.; Li, C. 2.; Cho, K. W.; Benicewicz, B. C.; Kumar, S. K.;
Schadler, L. 8., Quantitative equivalence between polymer nanocomposites and thin
polymer films. Nature Materials 2005, 4, (9), 693-698.

32. Rittigstein, P.; Torkelson, J. M., Polymer-nanoparticle interfacial interactions in
polymer nanocomposites: Confinement effects on glass transition temperature and

106

 

 

suppression of physical aging. Journal of Polymer Science Part B: Polymer Physics
2006, 44, (20), 2935-2943.

33. Xu, H. Y.; Yang, B. H.; Wang, J. F.; Guang, S. Y.; Li, C., Preparation, thermal
properties, and T-g increase mechanism of poly(acetoxystyrene-co-octavinyl-polyhedral

oligomeric silsesquioxane) hybrid nanocomposites. Macromolecules 2005, 38, (25),
10455-10460.

34. Cheatham, R. G.; Dietz, A. G. H., Effect of Orientation on the Mechanical
Properties of Polystyrene. Modern Plastics 1951, September, 113-192. H

35. Cleereman, K. J.; Karam, H. J.; Williams, J. L., Polystyrene Monofilarnents and
Bristles. Modern Plastics 1953, May, 119.

 

36. Stendahl, J. C.; Li, L. M.; Zubarev, R.; Chen, Y. R.; Stupp, S. I., Toughening of
polymers by self-assembling molecules. Advanced Materials 2002, 14, (21), 1540-+.

 

37. Stendahl, J. C.; Zubarev, E. R.; Arnold, M. S.; Hersam, M. C.; Sue, H. J .; Stupp,
S. 1., Structural modifications to polystyrene via self-assembling molecules. Advanced
Functional Materials 2005, 15, (3), 487-493.

38. Harth, E.; Van Horn, B.; Lee, V. Y.; Germack, D. S.; Gonzales, C. P.; Miller, R.
D.; Hawker, C. J ., A facile approach to architecturally defined nanoparticles via
intramolecular chain collapse. Journal of the American Chemical Society 2002, 124, (29),
8653-8660.

39. Potschke, P.; Bruni g, H.; Janke, A.; Fischer, D.; Jehnichen, D., Orientation of
multiwalled carbon nanotubes in composites with polycarbonate by melt spinning.
Polymer 2005, 46, (23), 10355-10363.

40. Miaudet, P.; Badaire, S.; Maugey, M.; Derre, A.; Pichot, V.; Launois, P.; Poulin,
P.; Zakri, C., Hot-drawing of single and multiwall carbon nanotube fibers for high
toughness and alignment. Nano Letters 2005, 5, (11), 2212-2215.

41. Dror, Y.; Salalha, W.; Khalfin, R. L.; Cohen, Y.; Yarin, A. L.; Zussman, E.,
Carbon nanotubes embedded in oriented polymer nanofibers by electrospinning.
langmuir 2003, 19, (17), 7012-7020.

107

 

42. Ruan, 8.; Yu, T. X.; Gao, P., Ultra-strong gel-spun UHMWPE fibers reinforced
using multiwalled carbon nanotubes. Polymer 2006, 47, (5), 1604-1611.

43. Zoller, P.; Bolli, P.; Pahud, V.; Ackermann, H., Apparatus for Measuring
Pressure-Volume-Temperature Relationships of Polymers to 350Degreesc and 2200
Kg/Cm2. Review of Scientific Instruments 1976, 47, (8), 948-952.

44. Jain, R. K.; Simha, R., On the Equation of State of Argon and Organic Liquids.
Journal of Chemical Physics 1980, 72, (9), 4909-4912.

 

4S. Tuteja, A.; Mackay, M. E.; Narayanan, S.; Asokan, S.; Wong, M. S., Breakdown
of the Continuum Stokes-Einstein Relation for Nanoparticle Diffusion. Nano Lett. 2007,
7, (5). 1276-1281.

 

46. Lodge, T. R; Wood, E. R.; Haley, J. C., Two calorimetric glass transitions do not EJ
necessarily indicate immiscibility: The case of PEO/PMMA. Journal of Polymer Science ‘
Part B: Polymer Physics 2006, 44, (4), 756-763.

47. Yu, S. 2.; Hing, P.; Hu, X., Thermal expansion behaviour of polystyrene-
aluminium nitride composites. Journal of Physics D-Applied Physics 2000, 33, (13),
1606-1610.

48. Tuteja, A.; Mackay, M. E.; Hawker, C. J .; Van Horn, B.; Ho, D. L., Molecular
architecture and rheological characterization of novel intramolecularly crosslinkedl
polystyrene nanoparticles. Journal of Polymer Science Part B-Polymer Physics 2006, 44,
(14), 1930-1947.

49. Simha, R.; Boyer, R. E, On a General Relation Involving the Glass Temperature
and Coefficients of Expansion of Polymers. The Journal of Chemical Physics 1962, 37,
(5), 1003-1007.

50. Dlubek, G.; Sen Gupta, A.; Pionteck, J .; Krause-Rehberg, R.; Kaspar, H.;
Lochhaas, K. H., Temperature dependence of the free volume in fluoroelastomers from
positron lifetime and PVT experiments. Macromolecules 2004, 37, (17), 6606-6618.

51. Dlubek, G.; Bondarenko, V.; Pionteck, J .; Supej, M.; Wutzler, A.; Krause-
Rehberg, R., Free volume in two differently plasticized poly(vinyl chloride)s: a positron
lifetime and PVT study. Polymer 2003, 44, (6), 1921-1926.

108

 

52. Schmidt, M.; Maurer, F. H. J ., Pressure-volume-temperature properties and free
volume parameters of PEO/PMMA blends. Journal of Polymer Science Part B-Polymer
Physics 1998, 36, (6), 1061-1080.

53. Sanchez, 1. C.; Cho, J .; Chen, W. J ., Universal Response of Polymers, Solvents,
and Solutions to Pressure. Macromolecules 1993, 26, (16), 4234-4241.

54. Cho, J .; Sanchez, 1. C., An analytical free energy and the temperature-pressure
superposition principle for pure polymeric liquids. Macromolecules 1998, 31, (19), 6650-
6661.

 

55. Sauer, B. B.; Dee, G. T., Surface tension and melt cohesive energy density of
polymer melts including high melting and high glass transition polymers.
Macromolecules 2002, 35, (18), 7024-7030.

 

56. Hildebrand, J .; Prausnitz, J. M.; Scott, R. L., Regular and Related Solutions: The
Solubility of Gases, Liquids, and Solids. Van Nostrand Reinhold: New York, 1970.

57. Anderson, S. L.; Grulke, E. A.; Delassus, P. T.; Smith, P. B.; Kocher, C. W.;
Landes, B. G., A Model for Antiplasticization in Polystyrene. Macromolecules 1995, 28,
(8), 2944-2954.

58. Forsyth, M.; Meakin, P.; MacFarlane, D. R., C-13 NlVIR spin-lattice relaxation
times as a probe of local polymer dynamics in plasticized polyethers. Journal of
Materials Chemistry 1997, 7, (2), 193-201.

59. Rehner, J ., Theory of filler reinforcement in natural and synthetic rubber. The
stresses in and about the particles. Journal of Applied Physics 1943, 14, (12), 638-645.

60. Nielsen, L. E.; Landel, R. F., Mechanical Properties of Polymers and Composites.
Marcel Dekker, Inc.: New York, 1994.

61. Choi, K. J .; Spruiell, J. E.; White, J. L., Structure Development in Biaxially

Stretched Polystyrene Film .1. Property-Orientation Correlation. Polymer Engineering
and Science 1989, 29, (21), 1516-1523.

62. White, J. L.; Spruiell, J. E., The Specification of Orientation and Its Development
in Polymer Processing. Polymer Engineering and Science 1983, 23, (5), 247-256.

109

63. Choi, K. J .; Spruiell, J. E.; White, J. L., Structure Development in Biaxially
Stretched Polystyrene Film .2. Theoretical-Analysis of Orientation Development.
Polymer Engineering and Science 1989, 29, (21), 1524-1527.

64. Picot, C.; Duplessix, R.; Decker, D.; Benoit, H.; Boue, F.; Cotton, J. P.; Daoud,
M.; Famoux, B.; Jannink, G.; Nierlich, M.; de Vries, A. J .; Pincus, P., Neutron-Scattering
by Uniaxially Hot Stretched Polystyrene Samples. Macromolecules 1977, 10, (2), 436-
442.

65. Ramzi, A.; Hakiki, A.; Bastide, J .; Boue, F., Uniaxial extension of end-linked
polystyrene networks containing deuterated free chains studied by small-angle neutron

scattering: Effect of the network chains and the size of the free chains. Macromolecules
1997, 30, (10), 2963-2977.

66. Embery, J .; Graham, R. S.; Duckett, R. A.; Groves, D.; Collis, M.; Mackley, M.
R.; McLeish, T. C. B., Tearing energy study of "oriented and relaxed" polystyrene in the
glassy state. Journal of Polymer Science Part B: Polymer Physics 2007, 45, (4), 377-394.

67. Ender, D. H.; Andrews, R. D., Cold Drawing of Glassy Polystyrene under Dead
Load. Journal of Applied Physics 1965, 36, (10), 3057-&.

68. Tanabe, Y.; Kanetsuna, H., Structure of Oriented Polystyrene Monofilaments and
Its Relationship to Brittle-to-Ductile Transition. Journal of Applied Polymer Science
1978, 22, (6), 1619-1630.

69. Boue, F.; Nierlich, M.; Jannink, G.; Ball, R., Polymer Coil Relaxation in
Uniaxially Strained Polystyrene Observed by Small-Angle Neutron-Scattering. Journal
De Physique 1982, 43, (1), 137-148.

70. Pellerin, C.; Prud'homme, R. E.; Pezolet, M.; Weinstock, B. A.; Griffiths, P. R.,
Deformation and Relaxation of Polymers Studied by Ultrarapid Scanning FT-IR
Spectrometry. Macromolecules 2003, 36, (13), 4838-4843.

71. Bent, J .; Hutchings, L. R.; Richards, R. W.; Gough, T.; Spares, R.; Coates, P. D.;
Grillo, I.; Harlen, O. G.; Read, D. J .; Graham, R. S.; Likhtman, A. E.; Groves, D. J .;
Nicholson, T. M.; McLeish, T. C. B., Neutron-mapping polymer flow: Scattering, flow
visualization, and molecular theory. Science 2003, 301, (5640), 1691-1695.

72. De Francesco, A.; Duckett, R. A., Effects of orientation on mechanical properties
of uniaxially oriented polystyrene films. Polymer 2004, 45, (23), 8005-8011.

110

 

73. Theodorou, M.; J asse, B.; Monnerie, L., Fourier-Transform Infrared Investigation
of Conformational-Changes Occurring at the Yield-Point in Uniaxially Drawn Atactic
Polystyrene. Journal of Polymer Science Part B-Polymer Physics 1985, 23, (3), 445-450.

74. Yokouchi, M.; Yokota, A.; Kobayashi, Y., Tensile and Impact Behavior of Drawn
Polystyrene and Hi gh-Impact Polystyrene. Journal of Applied Polymer Science 1982, 27,
(8), 3007-3018.

75. Dvoranek, L.; Machova, L.; Sorm, M.; Pelzbauer, Z.; Svantner, J .; Kubanek, V.,
Effects of Drawing Conditions on the Properties of Optical Fibers Made from Fe

Polystyrene and Poly(Methyl Methacrylate). Angewandte Makromolekulare Chemie
1990, 174, 25-39.

76. Han, H. Z. Y.; Duckett, R. A.; McLeish, T. C. B.; Ward, N. J .; Johnson, A. F.,
Drawing and orientation-relaxation behaviour of monodisperse linear and 3-arm star _‘ J
polystyrenes. Polymer 1997, 38, (7), 1545-1555. it

 

77. King, S. M., Small-angle Neutron Scattering. In Modern Techniques for Polymer
Characterisation, Pethrick, R. A.; Dawkins, J. V., Eds. John Wiley & Sons Ltd: 1999; pp
171-228.

78. Higgins, J. S.; Benoit, H. C., Polymers and Neutron Scattering. Clarendon Press:
Oxford, 1994.

79. Forster, S.; Burger, C., Scattering Functions of Polymeric Core-Shell Structures
and Excluded Volume Chains. Macromolecules 1998, 31, (3), 879-891.

80. Li, Y. Q.; Ishida, H., A study of morphology and intercalation kinetics of
polystyrene-organoclay nanocomposites. Macromolecules 2005, 38, (15), 6513-6519.

81. Tung, J .; Gupta, R. K.; Simon, G. P.; Edward, G. H.; Bhattacharya, S. N .,
Rheological and mechanical comparative study of in situ polymerized and melt-blended
nylon 6 nanocomposites. Polymer 2005, 46, (23), 10405-10418.

82. Plummet, C. J. G.; Rodlert, M.; Bucaille, J. L.; Grunbauer, H. J. M.; Manson, J.
A. E., Correlating the rheological and mechanical response of polyurethane
nanocomposites containing hyperbranched polymers. Polymer 2005, 46, (17), 6543-6553.

111

83. Weon, J. 1.; Sue, H. J., Effects of clay orientation and aspect ratio on mechanical
behavior of nylon-6 nanocomposite. Polymer 2005, 46, (17), 6325-6334.

84. Tanoue, S.; Utracki, L. A.; Garcia-Rejon, A.; Tatibouet, J .; Cole, K. C.; Kama],
M. R., Melt compounding of differenet grades of polystyrene with organoclay. Part 1:
Compounding and characterization. Polymer Engineering and Science 2004, 44, (6),
1046-1060.

85. Chae, H. G.; Sreekumar, T. V.; Uchida, T.; Kumar, S., A comparison of
reinforcement efficiency of various types of carbon nanotubes in poly acrylonitrile fiber. _
Polymer 2005, 46, (24), 10925-10935. _

86. Minus, M. L.; Chae, H. G.; Kumar, S., Single wall carbon nanotube templated
oriented crystallization of poly(vinyl alcohol). Polymer 2006, 47, (11), 3705-3710.

 

87. Kroto, H. W.; Heath, J. R.; Obrien, S. C.; Curl, R. F.; Smalley, R. E., C-60 -
Buckminsterfullerene. Nature 1985, 318, (6042), 162-163.

88. Iijima, S., Helical Microtubules of Graphitic Carbon. Nature 1991, 354, (6348),
56-58.

89. Affholter, K. A.; Henderson, S. J .; Wignall, G. D.; Bunick, G. J .; Haufler, R. E.;
Compton, R. N., Structural Characterization of C-60 and C-70 Fullerenes by Small-Angle
Neutron-Scattering. Journal of Chemical Physics 1993, 99, (l 1), 9224-9229.

90. Ruoff, R. S.; Ruoff, A. L., The Bulk Modulus of C60 Molecules and Crystals - a
Molecular Mechanics Approach. Applied Physics Letters 1991, 59, (13), 1553-1555.

91. Ruoff, R. S.; Ruoff, A. L., Is C60 Stiffer Than Diamond. Nature 1991, 350,
(6320), 663-664.

92. Wang, Y.; Tomanek, D.; Bertsch, G. F., Stiffness of a Solid Composed of C60
Clusters. Physical Review B 1991, 44, (12), 6562-6565.

93. Soifer, Y. M.; Kobelev, N. P.; Nikolaev, R. K.; Levin, V. M., Integral and Local
Elastic Properties of C60 Single Crystals. physica status solidi (b) 1999, 214, (2), 303-
308.

112

94. Lundin, A.; Sundqvist, B.; Skoglund, P.; Fransson, A.; Pettersson, S.,
Compressibility, specific heat capacity, and Gruneisen parameter for C60/C70. Solid
State Communications 1992, 84, (9), 879-883.

95. Schirber, J. E.; Kwei, G. H.; Jorgensen, J. D.; Hitterman, R. L.; Morosin, B.,
Room-temperature compressibility of C_{60}: Intercalation effects with He, Ne, and Ar.
Physical Review B 1995, 51, (17), 12014.

96. Sundqvist, B.; Andersson, O.; Lundin, A.; Soldatov, A., Phase diagram, structure,
and disorder in C60 below 300 K and 1 GPa. Solid State Communications 1995, 93, (2), r]
109-1 12.

 

97. Lundin, A.; Sundqvist, B., Compressibility of C-60 in the temperature range 150-
335 K up to a pressure of 1 GPa. Physical Review B 1996, 53, (13), 8329-8336.

 

98. Brazhkin, V. V.; Lyapin, A. G.; Hemley, R. J ., Harder than diamond: dreams and '3
reality. Philosophical Magazine a-Physics of Condensed Matter Structure Defects and
Mechanical Properties 2002, 82, (2), 231-253.

99. Ding, Y. F.; Kisliuk, A.; Sokolov, A. P., When does a molecule become a
polymer? Macromolecules 2004, 37, (1), 161-166.

100. Choi, K. J .; Spruiell, J. E.; White, J. L., Orientation and Morphology of High-
Density Polyethylene Film Produced by the Tubular Blowing Method and Its
Relationship to Process Conditions. Journal of Polymer Science Part B-Polymer Physics
1982, 20, (1), 27-47.

101. White, J. L., Structure Development in Polymer Processing. Pure and Applied
Chemistry 1983, 55, (5), 765-776.

102. Guan, Z. B.; Cotts, P. M.; McCord, E. F.; McLain, S. J ., Chain walking: A new
strategy to control polymer topology. Science 1999, 283, (5410), 2059-2062.

103. Guan, Z. B., Control of polymer topology through late-transition-metal catalysis.
Journal of Polymer Science Part a-Polymer Chemistry 2003, 41, (22), 3680-3692.

104. Suhr, J .; Koratkar, N.; Keblinski, P.; Ajayan, P., Viscoelasticity in carbon
nanotube composites. Nature Materials 2005, 4, (2), 134-137.

113

 

105. Chae, D. W.; Lee, K. H.; Kim, Y. C., Rheological properties of ferrite
nanocomposites based on nylon-66. Journal of Polymer Science Part B-Polymer Physics
2006, 44, (2), 371-377.

106. Lee, J. Y.; Zhang, Q.; Wang, J. Y.; Emrick, T.; Crosby, A. J ., Failure Mechanism
of Glassy Polymer-Nanoparticle Composites. Macromolecules 2007.

107. Vossmeyer, T.; Katsikas, L.; Giersig, M.; Popovic, I. G.; Diesner, K.;
Chemseddine, A.; Eychmuller, A.; Weller, H., Cds Nanoclusters - Synthesis,
Characterization, Size-Dependent Oscillator Strength, Temperature Shift of the W
Excitonic-Transition Energy, and Reversible Absorbency Shift. Journal of Physical '
Chemistry 1994, 98, (31), 7665-7673.

108. Goldstein, A. N.; Echer, C. M.; Alivisatos, A. P., Melting in Semiconductor .
Nanocrystals. Science 1992, 256, (5062), 1425-1427. 1

 

109. Tolbert, S. H.; Alivisatos, A. P., High-Pressure Structural Transformations in
Semiconductor Nanocrystals. Annual Review of Physical Chemistry 1995, 46, 595-625.

110. Alivisatos, A. P., Semiconductor Clusters, N anocrystals, and Quantum Dots.
Science 1996, 271, (5251), 933-937.

111. Lee, J .; Sundar, V. C.; Heine, J. R.; Bawendi, M. G.; Jensen, K. F., Full Color
Emission from H-VI Semiconductor Quantum Dot-Polymer Composites. Advanced
Materials 2000, 12, (15), 1102-1105. '

112. Schlamp, M. C.; Peng, X. G.; Alivisatos, A. P., Improved efficiencies in light
emitting diodes made with CdSe(CdS) core/shell type nanocrystals and a semiconducting
polymer. Journal of Applied Physics 1997, 82, (11), 5837-5842.

113. Gao, M. Y.; Richter, B.; Kirstein, S., White-light electroluminescence from a self-
assembled Q-CdSe/PPV multilayer structures. Advanced Materials 1997, 9, (10), 802-&.

114. Huynh, W. U.; Dittrner, J. J.; Alivisatos, A. P., Hybrid nanorod-polymer solar
cells. Science 2002, 295, (5564), 2425-2427.

115. Leatherdale, C. A.; Kagan, C. R.; Morgan, N. Y.; Empedocles, S. A.; Kastner, M.
A.; Bawendi, M. G., Photoconductivity in CdSe quantum dot solids. Physical Review B
2000, 62, (4), 2669-2680.

114

116. Wang, P.; Abrusci, A.; Wong, H. M. P.; Svensson, M.; Andersson, M. R.;
Greenham, N. C., Photoinduced charge transfer and efficient solar energy conversion in a
blend of a red polyfluorene copolymer with CdSe nanoparticles. Nano Letters 2006, 6,
(8), 1789-1793.

117. Kloepfer, J. A.; Mielke, R. E.; Wong, M. S.; Nealson, K. H.; Stucky, G.; Nadeau,
J. L., Quantum dots as strain- and metabolism-specific microbiological labels. Applied
and Environmental Microbiology 2003, 69, (7), 4205-4213.

118. Skaff, H.; Sill, K.; Emrick, T., Quantum dots tailored with poly(para-phenylene _
vinylene). Journal of the American Chemical Society 2004, 126, (36), 11322-11325. '

119. Asokan, S.; Krueger, K. M.; Alkhawaldeh, A.; Carreon, A. R.; Mu, Z. Z.; Colvin,
V. L.; Mantzaris, N. V.; Wong, M. S., The use of heat transfer fluids in the synthesis of
hi gh-quality CdSe quantum dots, core/shell quantum dots, and quantum rods. '
Nanotechnology 2005, 16, (10), 2000-2011. ; -

 

120. Lee, J. Y.; Zhang, Q.; Emrick, T.; Crosby, A. J ., Nanoparticle Alignment and
Repulsion during Failure of Glassy Polymer Nanocomposites. Macromolecules 2006, 39,
(21), 7392-7396.

121. Zhang, Q.; Russell, T. P.; Emrick, T., Synthesis and Characterization of CdSe
N anorods Functionalized with Regioregular Poly(3-hexylthiophene). Chem. Mater. 2007,
19, (15), 3712-3716.

122. Hay, G.; Mackay, M. E.; Hawker, C. J ., Thermodynamic properties of dendrimers
compared with linear polymers: General observations. Journal of Polymer Science Part
B-Polymer Physics 2001, 39, (15), 1766-1777.

123. Schmidt, M.; Maurer, F. H. J ., Isotropic pressure-densified atactic poly(methyl
methacrylate) glasses: Free-volume properties from equation-of-state data and positron
annihilation lifetime spectroscopy. Macromolecules 2000, 33, (10), 3879-3891.

124. Schmidt, M.; Olsson, M.; Maurer, F. H. J ., Macroscopic pressure-volume-
temperature properties versus free-volume characteristics of isotropic pressure-densified
amorphous polymer glasses. Journal of Chemical Physics 2000, 112, (24), 11095-11106.

125. Rodgers, P. A., Pressure Volume Temperature Relationships for Polymeric
Liquids - a Review of Equations of State and Their Characteristic Parameters for 56
Polymers. Journal of Applied Polymer Science 1993, 48, (6), 1061-1080.

115

126. Nanda, V. S.; Simha, R., Theoretical Interpretation of Tait Equation Parameters.
Journal of Chemical Physics 1964, 41, (6), 1884-&.

127. Kilbum, D.; Dlubek, G.; Pionteck, J .; Bamford, D.; Alam, M. A., Microstructure
of free volume in SMA copolymers 1. Free volume from Simha-Somcynsky analysis of
PVT experiments. Polymer 2005, 46, (3), 859-868.

128. Sanchez, 1. C.; Cho, J ., A Universal Equation of State for Polymer Liquids.
Polymer 1995, 36, (15), 2929-2939.

129. Dec, G. T.; Walsh, D. J ., Equations of State for Polymer Liquids. Macromolecules
1988, 21, (3), 811-815.

130. Flory, P. J .; Orwoll, R. A.; Vrij, A., Statistical Thermodynamics of Chain __.
Molecule Liquids .1. Equation of State for Normal Paraffin Hydrocarbons. Journal of the J
American Chemical Society 1964, 86, (17), 3507-&. '

 

131. Simha, R.; Somcynsky, T., On the Statistical Thermodynamics of Spherical and
Chain Molecule Fluids. Macromolecules 1969, 2, (4), 342-350.

 

116

llll I’ll