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EFFECTS OF NANOSCALE INCLUSIONS ON THE
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EFFECTS OF NAN OSCALE INCLUSIONS ON THE DYNAMICS
AND PROPERTIES OF POLYMER MELTS

By

Anish Tuteja

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

2006

ABSTRACT

EFFECTS OF NANOSCALE INCLUSIONS ON THE DYNAMICS AND
PROPOERTIES OF POLYMER MELTS

By

Anish Tuteja

In recent times, nanofillers have attracted the interest of a variety of research
groups as these materials can cause unusual mechanical, electrical, optical and thermal
enhancements. These enhancements are induced by the presence of the nanoparticles,
their interaction with the host matrix, and also quite critically, by their state of dispersion.
In this work we find that nanoparticles can be dispersed in linear polymers, despite
chemical dissimilarity, when the nanoparticle is smaller than the linear polymer, as
demonstrated by the miscibility of polyethylene (PE) nanoparticles in linear polystyrene
(PS) or PS nanoparticles in poly (methyl methacrylate) (PMMA) (PS-PE and PS-PMMA
are classical phase separating systems). If the particles become larger than the polymer,
phase separation occurs with even polystyrene nanoparticles phase separating from linear
polystyrene. In addition, small angle neutron scattering shows the linear polymer
becomes distorted on the addition of nanoparticles in the stable systems and is far from
its equilibrium conformation. This aspect demonstrates the uniqueness of nanoscale
thermodynamics as phase separation is expected (i.e. depletion flocculation) and we
believe that the nanoparticles are stabilized by enthalpic gain. When properly dispersed,
the addition of nanoparticles causes a large reduction (up to 90%) in the melt viscosity of
the system, a result at odds with Einstein’s century old prediction and experimental

observations of the viscosity increase particles provide to liquids (i.e. slurries and

suspensions) and melts. Also, the addition of specific nanoparticles, apart from improving
the polymer processing by reducing the viscosity, can simultaneously lead to enhanced
electrical conductivity (greater than Maxwell’s prediction), enhanced mechanical
damping (up to 5 fold increase), enhanced thermal stability / fire retardancy, and can even
make the polymers magnetic. The above and other unusual nanoscale phenomena are

discussed in this work.

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. vi
LIST OF FIGURES .......................................................................................................... vii
CHAPTER 1: INTRODUCTION ....................................................................................... 1

Research Objectives ................................................................................................ 7

CHAPTER 2: THE MOLECULAR ARCHITECTURE AND RHEOLOGICAL

CHARACTERIZATION OF NOVEL INTRAMOLECULARLY CROSSLINKED

POLYSTYRENE NANOPARTICLES .............................................................................. 9
Introduction ............................................................................................................. 9
Experimental ......................................................................................................... l 3
Results and Discussion ......................................................................................... 20
Conclusion ............................................................................................................ 38
Appendix Chapter 2. ............................................................................................. 40

CHAPTER 3 : GENERAL STRATEGIES FOR NANOPARTICLE DISPERSION ...... 45
Introduction ........................................................................................................... 45
Experimental ......................................................................................................... 46
Results and Discussion ......................................................................................... 47
Conclusion ............................................................................................................ 59

CHAPTER 4: NANOSCALE EFFECTS LEADING TO NON-EINSTEIN—LIKE

REDUCTION IN VISCOSITY ........................................................................................ 60
Introduction ........................................................................................................... 60
Experimental. ........................................................................................................ 6 I
Results and Discussion ......................................................................................... 62
Conclusion ............................................................................................................ 76

CHAPTER 5 : EFFECT OF IDEAL, ORGANIC NANOPARTICLES ON THE FLOW

PROPERTIES OF LINEAR POLYMERS: NON-EINSTEIN—LIKE BEHAVIOR ........ 77
Introduction ........................................................................................................... 77
Experimental ......................................................................................................... 84
Results and Discussion ......................................................................................... 89
Conclusion .......................................................................................................... 106

Appendix for Chapter 5 ...................................................................................... 107

CHAPTER 6: BREAKDOWN OF THE CONTINUUM STOKES-EINSTEIN

RELATION FOR NANOSCALE INCLUSIONS IN POLYMER MELTS .................. 109
Introduction ......................................................................................................... l 09
Results and Discussion ....................................................................................... l 10
Conclusion .......................................................................................................... 122

CHAPTER 7 : DESIGNING MULTIFUNCTIONAL NANOCOMPOSITES .............. 123
Introduction ......................................................................................................... 123
Experimental ....................................................................................................... 124
Results and Discussion ....................................................................................... 125
Conclusion .......................................................................................................... 143

CHAPTER 8: CONCLUSION ....................................................................................... 144

LIST OF PUBLICATIONS ............................................................................................ 148

REFERENCES ............................................................................................................... 149

LIST OF TABLES

Table 2.1. Number average molecular masses (Mn) and polydispersity index (PDI) of the
linear precursors for the lightly (2.5 mol% crosslinker) and tightly (20 mol% crosslinker)
crosslinked nanoparticles together with their abbreviations. ............................................ 14

Table 2.2. Radius of gyration determined from a Guinier regression, Debye flexible
polymer fit and hard sphere fit as well as the hydrodynamic radius for the various
nanoparticles and their linear precursors in d-THF (SANS data) and THF (DLS data);
concentration is 5 mg/ml and temperature is 35°C. Corresponding values with d-
cyclohexane and cyclohexane as the solvents are provided in the Appendix (Table 2.4).25

Table 2.3: The variation of Huggins and Kraemer coefficients with molecular weight for
the 2.5% and 20% crosslinked nanoparticles in THF and cyclohexane, at 35°C. ............ 40

Table 2.4. Radius of gyration determined from a Guinier regression, Debye flexible
polymer fit, as well as the hydrodynamic radius for the various nanoparticles and their
linear precursors in d-cyclohexane (SANS data) and cyclohexane (DLS data);
concentration is 5 mg/ml and temperature is 35°C ........................................................... 42

Table 2.5. The shift factors as a function of temperature for linear polystyrene, lightly
and tightly crosslinked nanoparticles ................................................................................ 44

Table 5.1. Polystyrene materials used in this study. ........................................................ 85

Table 5.2. The plateau modulus for pure PS 393 kDa and its blends with various
nanoparticles at 170°C ...................................................................................................... 97

Table 5.3. The viscosity ratio, under terminal conditions, glass transition temperature and
degree of confinement for the pure nanoparticles, linear polystyrenes and their blends.104

Table 7.1. Design parameters for nanoparticle dispersion and producing multifunctional
nanocomposites. .............................................................................................................. 141

vi

LIST OF FIGURES

Figure 2.1. Schematic representation of the intramolecular crosslinking process. .......... 15

Figure 2.2. Intrinsic viscosity normalized with the maximum value plotted against
solubility parameter at 35°C. The data for the linear precursor (52.0kDa-20%-L,
triangles) and the lightly crosslinked nanoparticles (60.1kDa-2.5%—X, squares) have been
shifted by 2 and 1, respectively, from the tightly crosslinked nanoparticles’ (52.0kDa-
20%-X, circles) data .......................................................................................................... 22

Figure 2.3. Scaling of the viscosimetric radius (Rh) and the extrapolated hydrodynamic
radius (RhO) with molecular mass. The data for the linear precursor (downward triangles)
agrees well with that for polystyrene standards (upward triangles) while the lightly
crosslinked (2.5% crosslinker, squares) and tightly crosslinked (20% crosslinker, circles)
nanoparticles deviate significantly from the linear polymer scaling. However, neither
approaches the scaling predicted for a sphere of density equal to that for bulk
polystyrene. Example error bars are shown for the tightly crosslinked system ................ 24

Figure 2.4. Burchard’s p-ratio (ratio of radius of gyration to hydrodynamic radius)
variation for the lightly (2.5% crosslinked, circles) and tightly crosslinked (20%
crosslinked, squares) nanoparticles with molecular mass in THF at 35°C. A non-draining
hard sphere should have a value of 0.775 while a Gaussian coil has a range of values
depending upon solvent conditions. The lightly crosslinked nanoparticles behave similar
to coil while the tightly crosslinked nanoparticles approach the hard sphere limit,
particularly at higher molecular weight. ........................................................................... 28

Figure 2.5. Kratky plots for the lightly crosslinked (a) and the tightly crosslinked
nanoparticles (b). A peak in the Kratky plot is indicative of particle-like behavior, while a
plateau is expected for a Gaussian coil. ............................................................................ 29

Figure 2.6. The glass transition temperatures for the lightly (a) and the tightly (b)
crosslinked nanoparticles. The error bars represent the spread of the transition, indicating
its beginning and end. ....................................................................................................... 32

Figure 2.7. The complex viscosity as a function of frequency at 170°C, for the 3 arm
polystyrene star and linear polystyrene (a), lightly crosslinked (b) and tightly crosslinked
(c) nanoparticles. Increasing molecular mass and crosslink density causes an increase in
the zero shear viscosity. A gel like behavior is evident for the high molecular mass,
tightly crosslinked nanoparticles. (d) The zero shear viscosity as a function of molecular
mass (Ag/Q for polystyrene melts at 170°C. Data from Fox and Flory,“ 65 Mackay and
Henson and Tuteja et al.96 are used. The zero shear viscosities for the pure lightly and
tightly crosslinked nanoparticles are also shown (a zero shear viscosity is not observed
for the 52 kDa-20%-X and 135 kDa-20%-X NP’s). ......................................................... 34

Figure 2.8. The storage (0’) and loss (6”) modulus as a function of frequency for the 3

arm polystyrene star and linear polystyrene (a), lightly crosslinked (b) and tightly
crosslinked (c) nanoparticles, at 170°C. A terminal zone behavior similar to linear

vii

polymers is evident for all of the lightly crosslinked nanoparticles, while a transition zone
behavior similar to linear polymers is evident for both the lightly and tightly crosslinked
nanoparticles. .................................................................................................................... 36

Figure 2.9. Typical I (cm'l) versus q (A!) graphs obtained after normalization of the
SANS data in d-cyclohexane and d-THF. The data was obtained at 35°C, and the
concentration was 5 mg/ml. The fits to the Debye function for the obtained data are also
shown. ............................................................................................................................... 43

Figure 3.1. (a) Rapid precipitation of fullerene/polystyrene blends, followed by drying
and melt processing allows manufacture of fibers. The fibers contains 1 wt% C60
fullerenes that were melt spun into long fibers with a diameter of ca. 1 mm. (b) F ullerene
(1 wt%)lpolystyrene blends developed through regular solvent evaporation produce large,
phase separated domains which are not apparent in the fiber ........................................... 49

Figure 3.2. (a) Cartoon showing branched, dendritic polyethylene. (b) TEM of a 4 wt%
blend of dendritic polyethylene with 393 kDa linear polystyrene shows the individual
polyethylene macromolecules with a size of order 20-30 nm. The Rg for the linear
polystyrene is 17.4 nm and so is larger than the dendritic polyethylene. The inset shows a
higher magnification. (c) Mixing with a smaller molecular mass polystyrene (75 kDa, R8
= 7.5 nm) produces phase separation. Power law scattering of intensity (1) versus wave
vector (q) is present at small wave vector for the lower mass polystyrene, whereas the
higher mass system demonstrates miscibility without a power law region. The intensity
profile can be fitted with a polydisperse sphere model yielding a mean radius (11.0 nm)
for the dendritic polyethylene that agrees well with the TEM images. ............................ 51

Figure 3.3. (a) The polymer radius of gyration (Rg), relative to that without nanoparticles
(R30), for three different molecular mass linear polystyrenes: 21, 63, 155 kDa, as a
function of volume fraction ((6) of 52.0 kDa tightly crosslinked polystyrene nanoparticles.
The nanoparticles clearly stretch the polymer chains. The solid line represents the radius
of gyration variation if the polymer density does not change upon mixing, and the
behavior [14111]”3 is expected. Instead, the data obeys l+c¢, with c about one. (b) A
polymer radius of gyration - nanoparticle radius phase diagram, with the filled circles
representing data where phase separation was detected and the open circles where
miscibility occurs. Open circles with an x represent conditions where some
agglomeration was detected by SANS, yet large scale phase separation was not observed.
Squares are the Cal/polystyrene system; circles, the polystyrene nanoparticle/polystyrene
system; and triangles, the dendritic polyethylene/polystyrene system. The dashed line
represents the reptation tube radius suggesting phase stability does not depend on the
entanglement structure. The nanoparticle fraction used to generate each data point was 2
wt%. (c) Cartoon illustrating that the attraction between pure nanoparticles is effective
only over a fraction (AC) of the available surface area (A) due to the limited range (6)
over which dispersion forces operate ................................................................................ 55

Figure 4.1. Cartoon of the intramolecularly crosslinked nanoparticles produced

from linear chain precursors having pendent crosslinking groups. Varying the
amount of crosslinker allows fabrication of lightly (2.5 mol% crosslinker) or tightly

viii

crosslinked (20 mol% crosslinker) nanoparticles. Nanoparticles were produced by
dripping a solution into hot solvent to activate the crosslinking process. Typical
conditions of volume (V), concentration (c), flow rate and temperature are given. ......... 63

Figure 4.2. SANS spectrum for lightly and tightly crosslinked nanoparticles
demonstrating the particle-like nature of the nanoparticles when sufficient
crosslinking is present. a, Kratky plot of SANS intensity (I) multiplied by wave vector
(q) squared as a function of q for solutions of linear precursor polymer or lightly
crosslinked nanoparticle containing 2.5 mol% crosslinker. The lower concentration data
of 2.5 wt% are for the 158 kDa linear chain precursor polymer and nanoparticle while the
higher concentration curves, 5wt%, are for the precursor polymer and nanoparticle with
24.5kDa and 158 kDa nominal molecular masses. These data demonstrate the scattering
from the lightly crosslinked nanoparticles is equivalent to a linear polymer. All data are
in d-THF solvent and at 35°C. The plateau near 0.2 A" does not scale linearly with
concentration due to concentration effects. b, Kratky plot for the tightly crosslinked
nanoparticles containing 20 mol% crosslinker of various molecular masses (25.3kDa,
52kDa, 135kDa) compared to the linear chain precursors (curves labeled Linear). These
nanoparticles demonstrate considerably different scattering behavior to the linear
precursors with the curve maxima revealing particle-like behavior. Same solvent and
temperature as in a were used, concentration is 5 wt%. The maximum does not
significantly depend on the nanoparticle concentration .................................................... 64

Figure 4.3. SANS spectrum for 52.0 kDa tightly crosslinked nanoparticles blended
with 63 kDa linear d-polystyrene at 50 wt% with the incoherent background
subtracted from the intensity. The solid line represents a hard sphere fit, including
polydispersity, and a Lorentzian (I(0)/[1+§2q2], g = 29.5 i 0.2 nm and [(0) = 623 i 7 cm'
) to account for the deuterated polystyrene chains’ conformation. The mean nanoparticle
phase’s radius from the hard sphere fit is 2.66 nm i 0.01 nm, polydispersity (standard
deviation divided by mean) is 0.942 i 0.001 and the volume fraction is 0.45. Power laws
of 3 and 4 are shown, neither is satisfactory, suggesting that a fractal network is not
present. The inset is a Kratky plot of the same data (solid line) compared to data for the
same nanoparticles in dilute solution (0.05 wt% in THF at 35°C) demonstrating increased
scatterer size. The intensity is in arbitrary units and the curves were shifted to overlap at
high q. ............................................................................................................................... 67

Figure 4.4. Viscosity and glass transition temperature for 52 kDa tightly crosslinked
nanoparticles, 75 kDa linear polystyrene and their blends. a, Viscosity versus
frequency (measured with a Rheometrics ARES rheometer) for the neat nanoparticles
(NP 52k), neat linear polystyrene (PS 75k) and selected blends containing 10 wt%, 50
wt% and 80 wt% nanoparticles. Note the pure nanoparticle system shows no terminal
viscosity. Various temperatures were used and time-temperature superposition was
followed, the reference temperature was 170°C. b, Terminal viscosity of the blends
divided by neat 75 kDa linear polystyrene viscosity versus 52 kDa tightly crosslinked
nanoparticle mass fraction. c, Glass transition temperature (T g) measured with
differential scanning calorimetry (TA Instruments Q1000) for the blends showing a
general decrease with nanoparticle addition up to moderate volume fi'actions. Note the Tg
for the two pure components are equal. ............................................................................ 70

ix

Figure 4.5 Graphs showing how the viscosity changes with temperature and
nanoparticle concentration. a, Viscosity of 75 kDa neat polystyrene and nanoparticle
blends as a fimction of T -T g. Open circles are the viscosity for the neat polystyrene while
the other symbols represent data for tightly crosslinked 52 kDa nanoparticles dispersed in
the same polystyrene at various mass concentrations (5 — 80%). The measurement
temperature range for all systems was 140 — 190°C with some extending down to 130°C.
There is no clear trend with concentration and it is hypothesized that the viscosity is a
unique function of distance from the glass transition temperature. b, Comparison of the
lower concentration blends containing the tightly crosslinked 52 kDa nanoparticles in 75
kDa linear polystyrene (blue squares) and 393 kDa linear polystyrene (blue circles) at
170°C to the Einstein prediction. It is clear that a hydrodynamic contribution to the
viscosity, in the contemporary sense, is not provided by the nanoparticles. To the
contrary, addition of 1.6 pm diameter crosslinked polystyrene microspheres shows the
conventional viscosity increase with particle addition to 75 kDa linear polystyrene (white
squares). ............................................................................................................................ 74

Figure 5.1. Viscosity as a function of molecular mass (M) for polystyrene melts at
170°C. Data from Fox and Flory”, Mackay and Henson5 and this work are used to show
how, below the critical molecular mass for entanglement coupling (MC) the Rouse model
is followed, except from deviations caused by a free volume change. Above Me the
entangled regime results with a much larger power law exponent of viscosity with M.
Changes in the entanglement structure or dynamics could reduce the viscosity to the
Rouse limit. ....................................................................................................................... 79

Figure 5.2. (a) Neutron scattering intensity (I) multiplied by the wave vector (q) squared
as a function of wave vector (Kratky plot) for 2 wt% 52 kDa NP blended with d-PS 155
kDa. The peak is associated with globular objects and the associated Schulz polydisperse
hard sphere fit reasonably represents the data (mean radius of 2.3 :1: 0.02 nm with a radius
spread of 0.8 :t 0.03 nm). The other curve is the result of a simulation assuming a
monodisperse system of spheres with a radius given by the Guinier result (4.0 nm = \/
(5/3) X 3.1 nm). (b) Log-log graph of intensity versus wave vector for the same system
and the associated polydisperse hard sphere fit. ............................................................... 90

Figure 5.3. Viscosity ratio of the nanoparticle blends with respect to pure polystyrene,
with polystyrene below (19.3 kDa) (a) and near (31.6 kDa) (b) the critical entanglement
molecular mass at 170°C. The curves labeled theory are the values predicted by
Batchelor’s relation for this system, ending at the limit of the relation’s applicability (4) ~
0.1). It can be seen that the blend viscosity is much greater than the predicted value for
the blend below MC, however, when the polymer is near Me, the viscosity hardly varies
with addition of nanoparticles, again contradicting the Einstein and Batchelor predictions.
........................................................................................................................................... 92

Figure 5.4. Viscosity ratio of the nanoparticle blends with respect to pure polystyrene for
two different entangled systems, PS 75 kDa (a) and PS 393 kDa (b) at 170°C. The curves
labeled theory are the values predicted by Batchelor’s relation and these end at the limit
of the relation’s applicability (4) ~ 0.1). The viscosity falls precipitously when the radius
of gyration is greater than the inter-particle half-gap for the entangled systems .............. 94

Figure 5.5. (a) Complex viscosity as a function of frequency for PS 393 kDa, 52 kDa NP
and their blends at 170°C. It can be seen that the pure nanoparticles display a gel like
behavior with an infinite terminal viscosity. All the blends however have a distinct
terminal viscosity which is lower than the pure component. (b) Storage modulus variation
with frequency for the same systems at 170°C. Blends with a nanoparticle concentration
below 10% have a plateau modulus equivalent to the virgin polymer while the 10% blend
has a reduced modulus and complex viscosity at all frequencies. .................................... 95

Figure 5.6. (a). Complex viscosity as a function of frequency for pure PS 393 kDa and its
blends with 25 kDa NP at 170°C. In this case, the viscosity is decreased at all
frequencies. A large viscosity reduction is apparent with just 1% addition of the
nanoparticles. (b) Complex viscosity as a function of frequency for the blends of 135 kDa
NP with PS 393 kDa also at 170°C. Here, only the terminal viscosity is reduced with
nanoparticle addition until the concentration reaches 20%. ............................................. 98

Figure 5.7. Complex viscosity (a) and storage modulus (b) data for pure PS 19.3 kDa and
its blends with 52 kDa NP at 170°C. Both these properties increase at all frequencies
upon nanoparticle addition. Same symbols used in each graph ........................................ 99

Figure 5.8. Bulk density variation as a function of nanoparticle concentration for PS 19.3
kDa blends (a) and PS 393 kDa blends (b) at 25°C. For polymer molecular below Me, the
density increases, and when it is above Me, the density decreases or remains constant, on
nanoparticle addition ....................................................................................................... 101

Figure 5.9. Relaxation spectra for pure PS 393 kDa and its blends with 52 kDa NP up to
concentrations of up to 8% (a) and for a concentration of 10% (b). The Rouse, Plateau
and Terminal regimes are also shown. It can be seen that the nanoparticles only affect the
terminal regime, by reducing the longest relaxation time, at lower concentrations while at
higher concentrations, a reduction occurs at all relaxation times. .................................. 102

Figure 5.10. Viscosity ratio of the nanoparticle blends with respect to pure polystyrene as
a function of nanoparticle volume fraction, with different molecular weight linear
polystyrenes’ at 170°C: (3) 19.3 kDa, (b) 31.6 kDa, (c) 75 kDa, (d) 393 kDa. The curves
labeled theory are the values predicted by Batchelor’s relation for this system, ending at
the limit of the relation’s applicability (4) ~ 0.1). ............................................................ 108

Figure 6.1. Inorganic nanoparticles can be dispersed in polymer matrices by the
process of rapid precipitation and cause a large reduction in the polymer melt
viscosity. a. TEM micrograph of a 38wt.% blend of oleic acid capped quantum dots
dispersed in polystyrene (molecular mass 393kDa). The dispersion of inorganic
nanoparticles is possible in polymers as long as the Rg of polymer > radius of
nanoparticles. b. An optical picture of the QD-PS blend, showing the pink color of the
blend. c. The complex viscosity as a function of frequency for pure PS and the PS-QD
blend. The melt viscosity reduces by ~ 60% on the addition of quantum dots even at this
high weight loading, contradicting Einstein’s prediction for a viscosity increase. (1. A
TEM micrograph of the 5 wt% blend of the magnetite nanoparticles in PS (molecular
mass 393kDa). e. The complex viscosity as a function of frequency for pure PS and the

xi

PS-magnetite nanoparticle blend. The addition of just 5 wt% of the magnetite
nanoparticles causes ~ 90% reduction in the melt viscosity of pure polystyrene. .......... 112

Figure 6.2. The diffusion coefficients of quantum dots and magnetite nanoparticles
in PS (molecular mass 393 kDa). a. A single fi'ame (CCD image) obtained from the X-
ray diffraction of the 5 wt% magnetite nanoparticles in PS. For each sample, 400-500
such frames were taken at each temperature, at intervals of 0.1 secs. b. Each frame was
divided into equally spaced q regimes, based on their angular distance from the upper
right hand comer of the frame (the centre of the X-ray beam). The scattering fi'om these
regimes was used to calculate the intensity-intensity autocorrelation function (g2 (q,t))
using the mean q value from each regime. The data from 6 of those q values can be seen
here (a is the radius of the nanoparticle = 5 nm; the sample is at 160°C). Each data set has
been offset with respect to the previous data set by 0.2, starting from q X a = 0.370, to
allow for easier visibility (so the data set for q X a = 0.370 has been offset by 0.2, while
the data set for q X a = 0.998 has been offset by l). The data is then fitted to a single
exponential (the solid blue line), to obtain 1, as a function of q c. The ratio of the
measured diffusion coefficient to the diffusion coefficient calculated from the SE relation
for the quantum dots in PS. (1. The same ratio for the magnetite nanoparticles in PS.... 117

Figure 6.3. Addition of magnetite nanoparticles to 3-arm PS stars. a. A TEM
micrograph showing the dispersion of magnetite nanoparticles (2 wt%) in a 3 arm PS star
(molecular mass of each arm ~ 108 kDa). b. The complex viscosity as a function of
frequency for the pure 3 arm star as well as its blend with the magnetite nanoparticles. It
can be seen that the addition of the nanoparticles causes a large increase in the viscosity
of the star, in contrast to the viscosity decrease seen on the addition of the same
nanoparticles to linear PS. c. The ratio of the measured diffusion coefficient (from XPCS
data) to the diffusion coefficient from the SE relation. Even though the addition of the
magnetite nanoparticles causes an increase in the melt viscosity, their diffusion
coefficient is almost an order of magnitude higher than the prediction from the SE
relation. ........................................................................................................................... 121

Figure 7.1. It is possible to disperse fullerenes in polystyrene by rapid precipitation.
Fullerene-polystyrene nanocomposites developed through solvent evaporation produce
large phase separated domains a, while rapid precipitation yields homogeneous blends
that allow melt spinning of fibers b. The nanocomposites can also be compression
molded to prepare free standing thin films as shown in the optical micrographs c, and d.
Markings on the films are from the platens. ................................................................... 127

Figure 7.2. Dispersion of 1 wt% fullerenes is possible, however, higher
concentration mixtures tend to have slight phase separation with small crystallite
formation. a, Dispersion of 10 wt% fullerenes in 393 kDa polystyrene via rapid
precipitation leads to a single (glass) transition of the nanocomposite (PS — 10 wt% C60
RP) with a glass transition that is slightly greater than that for pure polystyrene (Pure 393
kDa PS). Pure fullerenes have a crystal structure transition around -15°C (Pure C60)
which is absent in the nanocomposite produced by rapid precipitation, but is present in
the phase separated film produced by solvent evaporation (PS — 10 wt% C60 SE), as can
be seen more clearly in the inset. b, The change in the polystyrene WAXS intensity

xii

profile (Pure 393 kDa PS) with the addition of fullerenes for mixtures produced with
rapid precipitation can be significant. At 5 and 10 wt% fullerenes (5 wt% RP and 10 wt%
RP) evidence of a crystalline structure becomes clear while the amorphous halo for
polystyrene is only slightly changed through addition of 1 wt% fullerenes (1 wt% RP).
The lines at an intensity of 2000 are positions of the structure peaks seen for a filllerene
single crystal plotted as a function of d-spacing. c, The WAXS intensity profiles, as a
function of q-vector, for 10 wt% fullerene - polystyrene mixtures produced via rapid
precipitation (PS — 10 wt% C60 RP) and solvent evaporation (PS — 10 wt% C60 SE) are
vastly different with the latter showing low q scattering indicative of large scale phase
separation. The data for the sample prepared by rapid precipitation agrees well with that
for pure polystyrene (Pure 393 kDa PS) at low q-vector. d, A TEM micrograph for the 10
wt% fullerene mixture produced by rapid precipitation shows some phase separated
crystallites. e, An electron diffraction pattern from a crystallite (present in a blend
prepared by solvent evaporation) at room temperature demonstrating six-fold symmetry.
f, Electron diffraction pattern from another crystallite, from the same sample, at -50°C.
......................................................................................................................................... 132

Figure 7.3. Addition of fullerenes to linear polystyrene has multifunctional effects on
the properties including a viscosity reduction, increase in dissipation, increase in
degradation time and increase in conductivity. a, The addition of fullerenes to
polystyrene leads to a sharp decrease in the melt viscosity as long as the samples are
prepared by rapid precipitation. This behavior directly contradicts Einstein’s prediction
(theory) of a viscosity increase in such a system. The inset shows the effect of fiJllerene
addition on the viscosity of unentangled polystyrene (Mw= 19.3 kDa). The blend was
prepared by rapid precipitation. b, Minimal changes are seen in the storage (E’) modulus
on the addition of fullerenes while a five fold increase is observed in the loss (E”)
modulus, indicating a significant improvement in the damping properties of the
composite. The samples are pure 393 kDa polystyrene (Pure 393 kDa PS) and the same
polystyrene containing 50 wt% fullerenes produced by rapid precipitation (PS- 50 wt%
C60 RP). c, The addition of filllerenes, when well dispersed, greatly reduce the rate of
thermal decomposition of the nanocomposite as shown by weight loss curves obtained by
heating the samples to 330°C, under a nitrogen atmosphere. The samples containing 1
and 10 wt% C60 samples were produced by rapid precipitation (labeled RP) and when
compared to pure 393 kDa polystyrene (Pure 393 kDa PS) have a much greater time to
degrade. For comparison, phase separated fullerenes perform much worse and a 10 wt%
blend prepared by solvent evaporation (PS - 10 wt% C60 SE) only slightly increases the
degradation time. d, Conductivity of C60 - 393 kDa polystyrene nanocomposites, relative
to pure polystyrene. When fullerenes are well dispersed in polystyrene, prepared by rapid
precipitation the conductivity rises above the Maxwell model prediction for an infinitely
conducting particle. In comparison a sample containing phase separated structures
produced by solvent evaporation has a relative conductivity that is ~ 90% lower than pure
polystyrene. Conductivity was measured at a variety of frequencies and only the 10", 102
and 105 Hz data are shown. ............................................................................................. 139

Figure 7.4. It is possible to disperse ferromagnetic nanoparticles in linear

polystyrene (393 kDa) to make a ferromagnetic polymeric material. a, Polystyrene is
slightly colored by the dispersed magnetite nanoparticles which cause the sample to be

xiii

attracted to a permanent magnet. b, A TEM micrograph showing the nanoparticle
dispersion with gross phase separation. c, Nanoparticle - polystyrene blends developed
through solvent evaporation produce large phase separated domains. Also, as shown for
the fullerene nanoparticles, the magnetite nanoparticles at 5 wt% reduce the amount of
degradation (d) and the melt viscosity at all frequencies (e). The degradation experiment
was performed at 330 °C under a nitrogen atmosphere and the viscosity was measured at
multiple temperatures and shified to a reference temperature of 170 °C. ...................... 142

xiv

CHAPTER 1

INTRODUCTION

 

Polymer composites are an important class of functional materials formed by the
incorporation of useful organic/inorganic materials (filler) into the matrix of the host
polymer. The composite produced aims to successfully combine the attractive electronic,
optical or magnetic properties of the filler with the elasticity, film formation ability and
processability of conventional polymers.

Recently, polymer—nanoparticle composite materials have attracted the interest
from a variety of research groups. These materials offer the unique opportunity to
synergistically combine the properties of the various components on a nanoscale, and
have been used to provide enhanced mechanical,I electrical,l opticalz’ 3 and thermal
properties"4 both in solution and in bulk. These enhancements are induced by the
physical presence of the nanoparticle, its degree of dispersion and by the interaction of
the polymer with the particle.” 6 The biggest advantage of nanoparticles, as polymer
additives, is their extremely large surface area per unit mass, as compared to traditional
additives, which usually leads to low loading requirements. Efficient nanoparticle
dispersion combined with good polymer—particle interfacial adhesion presents the
exciting possibility of developing multifunctional7 coatings and membranes.

In this project we attempt to provide a deeper understanding of first the various
methods of creating nanocomposites and then detail the advantages of using nanoparticle

filled polymeric systems over traditional composites. It was recently seen that the

addition of nanoscale fillers to materials can change various properties which cannot be
accounted for using traditional models!"10 With the increased trend towards
miniaturization in recent years, the need to understand the differences in the properties
between micron sized or colloid filled bulk polymer systems and nanoparticle filled
polymeric systems has greatly enhanced. To provide a better understanding of
nanoparticle — polymer systems, we start out by studying the ideal system of polystyrene
nanoparticlesll blended with linear polystyrene.

In Chapter 2 of this thesis, we present the complete solution and rheological
characterization of the above mentioned polystyrene nanoparticles. They were
synthesized by the controlled intramolecular crosslinking of linear polymer chains to
produce well defined single-molecule nanoparticles of varying molecular mass,
corresponding directly to the original linear precursor chain.ll These nanoparticles were
also ideal to study the relaxation dynamics/processes of high molecular mass polymer
melts,12 as the high degree of intramolecular crosslinking potentially inhibits
entanglements.”"'6 Both the nanoparticles and their linear analogs were first
characterized by measuring their intrinsic viscosity, hydrodynamic radius (Rh) and radius
of gyration (R3).'7’ '8 The ratio Rg/Rh19 was computed to characterize the molecular
architecture of the nanoparticles in solution, revealing a shift towards the constant density
sphere limit with increasing crosslink density and molecular mass.20 Further, confirming
particulate behavior, Kratky plots obtained from neutron scattering data show a shift
towards particle-like nature.‘8 The rheological behavior of the particles was found to be
strongly dependent on both the extent of intramolecular crosslinking and molecular mass,

with a minimal viscosity change at low crosslinking levels and a gel-like behavior

evident for a large degree of crosslinking. These and other results suggest the presence of
a secondary mode of polymer relaxation/movement besides reptation in these molecules,
which in this case is influenced by the total number of crosslinked loops present in the
nanoparticle?" 22

In Chapter 3 of this thesis, we address the issue of miscibility between nanoparticles
and polymers, with the objective of understanding the key parameters that enable
nanoparticle dispersion.23 Traditionally, the dispersion of particles in polymeric materials
has proven difficult and frequently results in phase separation and agglomeration.24
Contrary to the observation in colloid — polymer blends, recent simulations have shown
that nanoparticles can slow down the phase separation of two incompatible polymers,
suggesting the use of nanoparticles as compatibilizers in polymer blends.25 There have
also been some experimental studies on the dispersion / distribution of nanoparticles in
polymer blends, suggesting enhanced miscibility of nanoparticles in polymers. For
example, in our previous work we showed that 2.7 nm radius polystyrene nanoparticles8
could be blended with linear polystyrene to large volume fraction ((p 2 0.5) without the
expected phase separation.

We show in this chapter that thermodynamically stable dispersion of
nanoparticles into a polymeric liquid is enhanced for systems where the radius of
gyration of the linear polymer is greater than the radius of the nanoparticle. Dispersed
nanoparticles swell the linear polymer chains, resulting in a polymer radius of gyration
which grows with the nanoparticle volume fraction. It is proposed that this entropically
unfavorable process is offset by an enthalpy gain due to an increase in molecular contacts

at dispersed nanoparticle surfaces, as compared to the surfaces of phase-separated

nanoparticles. It was also found that even when the dispersed state is thermodynamically

7

stable,26 it may be inaccessible unless the correct processing strategys’ 2 is adopted,

which is particularly important for the case of fullerene dispersion into linear polymers.”
29

With this understanding of nanoparticle dispersion in polymers, we move towards
the potential applications of the produced nanocomposites and extend our work by first
looking at their rheological properties. To minimize extraneous enthalpic or other
effects,8 the polystyrene nanoparticlesH (characterized in Chapter 2), were blended with
linear polystyrene macromolecules. Nanoparticles have been demonstrated to influence
mechanical properties of polymers?“32 however, transport properties such as viscosity
have not been adequately studied. This may be due to the common observation that
particle addition to liquids produces a viscosity increase, even in polymeric liquids, as
predicted by Einstein nearly a century ago.33 Yet, confinement and surface effects
provided by nanoparticles have been shown to produce conformational changes to
polymer molecules and so it is expected that nanoparticles will affect the macroscopic
viscosity. Remarkably, the addition of polystyrene nanoparticles to linear polystyrene
was found to decrease the blend viscosity and scale with the free volume change
introduced by the nanoparticles and not with entanglement reduction. Indeed, the
entanglements did not appear to be affected at all, suggesting unusual polymer dynamics.
These and other rheological results have been discussed in detail in Chapter 4.

In Chapter 5, we extend our work on the study of the rheological properties of
polystyrene nanoparticles - linear polystyrene blends. First, homogeneous blends are

developed based on our understanding of the key parameters for nanoparticle dispersion34

(Chapter 3) and next the dispersion in the blends is confirmed through small angle
neutron scattering (SANS) experiments.‘8 In Chapter 4 we discussed that nanoparticles
can reduce the viscosity of high molecular mass linear PS. On extending our work to
lower nanoparticle concentrations, we find that the confinement of entangled polymers is
necessary for the viscosity reduction since lower concentrations provide a viscosity
increase. Further, the viscosity behavior is found to be dependent on the presence or
absence of entanglements, and confinement is seemingly not important for unentangled

POIymers. It is proposed that constraint release‘s' 3’

caused by the addition of
nanoparticles is responsible for some of the observed changes in viscosity although it is
suspected that the introduction of free volume by the nanoparticles is certain to play a key
role.

The possibility that constraint release might be an important factor causing the
reduction in viscosity is discussed further in Chapter 6. The knowledge of the

translational diffusion coefficient of nanoparticles is extremely useful for a variety of

fields. First, various research groups have investigated the kinetics for the directed and

23, 36-38 39, 40

self assembly of nanoparticles and bionanoparticles in polymer matrices of
natural and syntheric origin. Any study targeting the assembly of nanostructures requires
an understanding of the nanoparticle dynamics, spatial arrangement and ordering kinetics
in the polymer matrix, thus requiring the knowledge of the translational diffusion
coefficient of the nanoparticles. Further, with the development of new techniques like

microrheology, 4" 42

the direct measurement of the diffusion coefficient of nanoparticles
has become critical for experimental planning and data interpretation. Also, as stated

above, the surprising viscosity decrease in entangled polymers on the addition of

nanoparticles is expected to be related the diffusion of nanoparticles in the polymer
matrices. In this chapter we report the first successful, direct measurements of the
translational diffusion coefficients of different inorganic nanoparticles dispersed in
entangled polymer matrices, using X-ray photon correlation spectroscopy (XPCS).43’ 44
The diffusion coefficients of the nanoparticles were found to be as much as 100 times
faster than predictions from the continuum Stokes - Einstein relation based on the
measured viscosity of the polymer. We hypothesize that the extremely fast diffusion
coefficients contribute to the observed reduction in viscosity of nanoparticle-linear
polymer blends that we have found, by providing a faster mode for polymer relaxation.
The nanoparticle dynamics is sure to influence the usual kinetics of self assembly as well
as the transport properties, which we exemplify through the viscosity.

Finally, in Chapter 7, again with our understanding the important parameters for the
dispersion of nanoparticles (Chapter 3), we study different nanoparticle - polymer
systems with the final aim of producing multifiJnctional nanocomposites. As we Stated
before, nanomaterials hold the promise of providing new properties that exceed
traditional material performance. However, in many instances, significant improvements

in material properties of nanocomposites have not been achieved as yet,7’ 45' 4°

mainly
because the factors affecting nanoparticle dispersion are poorly understood.47 We study
first the dispersion of filllerenes (C60, diameter ~ 0.7 nm) into polystyrene and show that
their incorporation into the polymer matrix is possible by employing the rapid
precipitation technique.“ 48 The addition of fullerenes in this manner simultaneously

leads to better processability (reduction in viscosity of up to 80%, contrary to Einstein’s

prediction),48' 49 higher electrical conductivity (greater than Maxwell’s prediction),SO

improved mechanical damping and enhanced thermal stability, leading to a first truly
‘multifunctional’ nanocomposite.7 Our study is then extended by utilizing rapid
precipitation as a tool for dispersing an inorganic filler (magnetite nanoparticles) into the
polystyrene matrix. The addition of these nanoparticles, apart from making the
nanocomposite ferromagnetic, also reduces the viscosity by ~ 90% while simultaneously
enhancing the nanocomposite thermal stability. These observations suggest the exciting
possibility of manufacturing materials with desired electrical or magnetic properties,
coupled with enhanced thermal stability and a reduced viscosity enabling easier and

faster processing using existing industrial technologies.

Research Objectives

The two major objectives of this research are to understand the fundamental
factors affecting the miscibility / dispersion and flow properties of nanoparticle —

polymer systems. We start out by studying the idealSl

system of polystyrene
nanoparticles being added to polystyrene. After understanding the basic factors affecting
the miscibility in this system, we extend our work to study a wide variety of organic and
inorganic nanoparticles blended with various polymers. The final goal of the work is to

apply this acquired knowledge to create multifunctional nanocomposites, having

enhanced thermal, mechanical and rheological properties.

A summary of the specific objectives in this work is as follows:

Characterize the intramolecularly crosslinked polystyrene nanoparticles in
solution to determine the effect of crosslinking on their molecular
architecture and rigidity.

Examine in detail the various factors affecting the miscibility and phase
stability in nanoparticle-polymer systems.

Determine the effects of nanoparticle addition on the rheological
properties of various nanoparticle - polymer blends.

Test the hypothesis that the unusual viscosity decrease seen for various
nanoparticle — polymer blends is related to the diffusion of the
nanoparticles within the polymer matrix by measuring the diffusion
coefficients of various nanoparticles in an entangled polymer matrix and
comparing them with the predictions from the Stokes — Einstein relation.
Create multifunctional nanocomposites with the understanding of the
various factors affecting nanoparticle dispersion and flow properties.
These composites have the specific optical, electric or magnetic properties
required for an application, and are coupled with enhanced mechanical,

thermal and flow properties.

CHAPTER 2

THE MOLECULAR ARCHITECTURE AND RHEOLOGICAL
CHARACTERIZATION OF NOVEL INTRAMOLECULARLY
CROSSLINKED POLYSTYRENE NANOPARTICLES

 

Introduction

There has been a phenomenal growth of interest in the development and study of
nanomaterials due to the many unusual and unique effects that can only be seen in this
size range. Nanoparticles serve the role of being an important building block for the
production of nanomaterials with a broad range of future and present applications in
electronic, mechanical, and biomedical processes.52

Various polymer particles with size ranging from 50 nm to several microns are
now commercially available; however, the synthesis and study of smaller polymeric
nanoparticles still remains a challenge. In this work, we characterize unimolecular,
organic (polystyrene) nanoparticles produced by the intramolecular crosslinking of
functional polymers, having sizes ranging from 3-15 nm. These molecules are then used
to discern the various modes of relaxation in both low and high molecular mass polymers
as a function of crosslink density.

The synthesisll of the nanoparticles was accomplished by first incorporating the
crosslinking agent 4-vinylbenzocyclobutene (denoted as BCB in Fig. 2.1) into the linear
polystyrene chain as a comonomer, and subsequently collapsing the chain under ultra-
dilute conditions by intramolecular crosslinking. The extent of crosslinking within the

nanoparticles produced by this method can therefore be controlled by the amount of

crosslinker that is copolymerized within the linear polymer.

Considerable work has been done previously to initiate intramolecular
crosslinking within polymers and then to measure the effects of this crosslinking on the
polymer properties in solution. Kuhn and BalmerS3 carried out crosslinking in an aqueous
solution of poly(vinyl alcohol) by the addition of terephthaldehyde, and then studied the
intrinsic viscosity behavior of the crosslinked polymer as a fiJnction of increasing
solution concentration of the starting monomer. They found that when the monomer
concentration was low, the intrinsic viscosity of the solution decreased indicating a
decrease in polymer size because of intramolecular crosslinking; however, at higher
monomer concentrations the intrinsic viscosity increased, indicating intermolecular
crosslinking. Also, Longi et a1.54 synthesized intramolecularly crosslinked styrene -
methyl acrylate copolymers and found that the intrinsic viscosity decreased in proportion
to the number of crosslinks per polymer.

55, 56

Research in this area was furthered by Martin and Eichinger who conducted

the first complete theoretical and experimental analysis to determine the change in the
unperturbed radius of gyration (Ry/6)) of a linear coil caused by intramolecular
crosslinking. First, they developed a method to determine Rgo(6) by assuming that the
crosslinked polymer consists of a number of sub-polymer Gaussian chains. Eichinger57
had found earlier that Rgo(t9) for any Gaussian chain can be computed by finding its
Kirchoff matrix and its generalized inverse. Thus, the unperturbed dimensions of the
whole molecule could be computed, as the sum of its parts. Using this analysis, for an
intramolecularly crosslinked polymer chain, the Zimm-Stockmayer contraction factor (g)
is given as

g = 1 - 0.7/3.05 (2-1)

10

where g is the ratio of Rgo(6l)2 for the crosslinked molecule to that of the
equivalent linear chain and p, is the crosslink density defined as the moles of crosslinks
per mole of Gaussian statistical segments.

To confirm their theoretical analysis, they produced intramolecularly crosslinked
polystyrene using a Friedel-Crafts crosslinking reaction, with (dichloromethyl)benzene as
the crosslinking agent. The change in the molecules’ hydrodynamic radii (Rh), caused by
the crosslinking, was then experimentally measured by means of photon correlation
spectroscopy (dynamic light scattering). The results were related to the Zimm-
Stockmayer contraction factor by the relation

h = ‘lg (2.2)
where h is the ratio of Rho(6) for the crosslinked particle to that for the linear chain and
R1100? is the unperturbed hydrodynamic radius. Indeed they found close agreement
between the observed unperturbed dimensions of the crosslinked molecules and their
theoretical predictions.

Our systems differ from theirs primarily due to the extent of intramolecular
crosslinking induced in polystyrene. The most heavily crosslinked polystyrene used by
Martin and Eichinger had 100 crosslinks per molecule which amounts to l in every 48
monomer units on average being crosslinked (mention of a more tightly crosslinked
sample is given in a table, yet, no data are presented on this system). In contrast, even the
lightly crosslinked polystyrene synthesized in this study has 1 in 40 monomer units on
average crosslinked, whereas the more tightly crosslinked molecule has 1 in every 5

monomer units crosslinked.

ll

At this point it is important to mention the significant work done by Antonietti et
al. in the development and rheological characterization of intramolecularly crosslinked
polystyrene microgels. Apart from detailing the clever techniques employed by the

authors to synthesize and characterize the microgels,58'6'

their work also provides a
descriptive introduction to the rheological behavior of intramolecularly crosslinked
particles.”‘ 62 Comparison between these studies and the present work is however
reserved for the results and discussion section and next we provide a brief introduction to
the mechanism of chain motion in polymer melts.

The terminal viscosity of polymer melts is a strong function of the polymer
molecular mass (M). Below the so called critical mass for entanglement couplingl3 (MC)
the viscosity scales as M while above MC a much larger power law, approximately 3.4-

3.8 power,“’3'65

is present. This steep increase of viscosity above Mc is attributed to the
presence of entanglements, which are basically constraints on the motion of polymer
chains caused by the fact that the chains cannot pass through each other. Such a
geometrically constrained environment thus limits molecular motion/diffusion of the
chain to a snake like motion along its own contour,66 denoted as reptation.67

The reptation model has been very useful in providing a mechanistic
understanding of bulk polymer dynamics, as well as in providing a quantitative
explanation of the plateau modulus, diffusion coefficient and scaling of viscosity with
molecular mass (in its native form the theory predicts a power law as 3 instead of 3.4).
However, results from many computer simulations and experiments68 on widely differing

70,71

systems (for example ring polymers,69 star polymers, crosslinked microgels,12 block

73-75

copolymers72 and polymer blends ) do not match reptation predictions, clearly

12

demonstrating that the model doesn’t provide a complete understanding of all the
diffusion or molecular motions in high molecular mass polymer melts, at least in its
present form. The nanoparticles considered in this work are ideal for discerning the
presence of other mobility mechanism besides reptation as the high degree of
intramolecular crosslinking minimizes chain entanglements (the network chains/loops are
too short), even for the high molecular mass nanoparticles.

The nanoparticlesll considered here were found to produce anomalous flow
behavior when blended with linear polymer.76 Yet, this behavior depended strongly on
the degree of crosslinking with light crosslinking producing no unusual effect while tight
crosslinking yielded unusual rheological behavior. The purpose of the present work is
thus two fold; to characterize these unique nanoparticles in dilute solution to determine
their molecular architecture and to study the dynamics of polymer relaxation in this novel

and ideal system as a function of that architecture.

Experimental

Materials. The synthesis of the nanoparticles and their linear analogs has been
discussed previously.ll Table 2.1 shows the molecular masses and polydispersity indexes
(PDI = weight to number average molecular mass ratio) of the linear precursors for the
lightly (2.5 mol% crosslinker) and tightly (20 mol% crosslinker) crosslinked
nanoparticles used in this study together with abbreviations. The molecular weights were
determined using Gel permeation chromatography relative to linear polystyrene

standards. All polymers were dissolved in tetrahydrofuran (THF) and passed through a

13

Waters chromatograph equipped with four S-pm Waters columns (300 mm X 7.7 mm)

connected in series with increasing pore size (100, 1000, 100,000, 1,000,000 A).

Table 2.1. Number average molecular masses (Mn) and polydispersity index (PDI) of the
linear precursors for the lightly (2.5 mol% crosslinker) and tightly (20 mol% crosslinker)
crosslinked nanoparticles together with their abbreviations.

 

 

 

 

 

 

 

 

 

 

Mn (kDa) % crosslinker (mol%) PDI Abbreviation if linear (crosslinked)
24.5 2.5 1.14 24.5kDa-2.5%-L (-X)
60.1 2.5 1.16 60.1kDa-2.5%-L (-X)
158 2.5 1.40 158kDa-2.5%-L (-X)
25.3 20 1.08 25.3kDa-20%-L (-X)
52.0 20 1.18 52.0kDa-20%-L (-X)
135 20 1.20 135kDa-20%-L (-X)

 

 

 

Figure 2.1 illustrates the crosslinking

process. The linear precursors are first

dissolved in an excess of benzyl ether (BCB concentration ~ 0.2 M) and then this solution

is added drop wise to a reservoir of hot benzyl ether. The high temperature (T = 250°C)

initiates the crosslinking process and the ultra-dilute conditions (final BCB concentration

~ 0.05 M) ensure that intermolecular crosslinking is minimized. Thus, the crosslinked

nanoparticles potentially have the same molecular mass as the linear precursors. All the

solvents were purchased from Sigma-Aldrich and used as received.

14

O O O O 0 Linear Chain Precursor

f x / BCB

T = 250°C fl/ \:k§ F 9‘ F n I H

 

 

 

BCB Ultradilute Conditions
/ r = 250°C
3’ j
Nanoparticle

Images in this dissertation are presented in color.
Figure 2.1. Schematic representation of the intramolecular crosslinking process.
Intrinsic viscosity. The solutions for the measurement of intrinsic viscosity were
prepared at least 1 day before the measurement by dissolving the polymer in pure solvent.
Before usage, the solution was filtered with a 1pm filter to remove any undissolved
impurities. The intrinsic viscosity was calculated by measuring the density of the
solution, the flow time in a Cannon—Manning Semi-Micro viscometer (size 75) of the
pure solvent and the solution, and the concentration of the solution. The measurements
were made at low shear rates (typical flow times were close to 200 seconds), with four
different concentrations, at a constant temperature of 35°C. The data obtained was then

analyzed using the two leading terms in the Huggins77 and Kraemer78 relations

asp/F ['7] +1... [0126+ (Ma)

and

15

I"(’7rel)/C = ['7] - kk ['1]2 c + (2-3-b)
where 115,, is the specific viscosity ([qsoluuon - nsolvem] / nsolvcm), nrel, the relative viscosity
(2750mm / 7750mm), [77], the intrinsic viscosity, c, the polymer concentration (g-polymer /
mL-solution) and k}, and k1,, the Huggins and Kraemer coefficients (the values for these
constants in THF and cyclohexane are given in appendix, Table 2.3), respectively. The
[n] values obtained from both these relations agreed within :1: 2%, therefore, only the [n]
values obtained from the Huggins relation are reported in this paper.

For each of the different polymer nanoparticles and their linear analogs, the
intrinsic viscosity was measured in 5 different solvents. Each solvent had a different

solubility parameter (8 in (cal/cm3)“2

at 25°C) shown in parentheses: cyclohexane (8.2),
toluene (8.9), tetrahydrofuran (THF, 9.1), benzene (9.2) and chloroform (9.3).79

Light scattering. The hydrodynamic radius (Rh) was measured using a Protein-
Solutions Dynapro dynamic light scattering (DLS) instrument. In the instrument,
fluctuations in the intensity of the scattered light are related to the diffusion coefficient of
the molecules (De). Then, Rh is calculated from the diffusion coefficient using the Stokes-
Einstein relation33

_ kBT

6 — 6377mm: Rh

 

D (2.4)

where k3 is the Boltzman constant and T, temperature. Thus, the Rh obtained from
DLS data is the size of a spherical particle that would have a diffusion coefficient
equivalent to that of the molecule tested.80

Again, all the solutions used for dynamic light scattering were prepared at least

one day before the measurement and filtered with a 0.1um filter to remove any

16

undissolved impurities. To compare with the intrinsic viscosity measurements, all

experiments were performed at 35°C. Further, as Rh is a function of concentrations"83

the
extrapolated value to zero concentration (RhO) was used and determined as described in
the Appendix.

Neutron scattering. The small angle neutron scattering (SANS) measurements
were carried out using the 30m NG3 and NG7 SANS instruments at the National Institute
of Standards and Technology (NIST), Centre for Neutron Research (NCNR) in
Gaithersburg, MD. Two instrument configurations were used. The first had five guides, a
sample to detector distance of 600 cm with a 250m detector offset, giving a scattering
vector (q) range of 0.0084-0.l 136 A]. The second configuration also had five guides, a
sample to detector distance of 135 cm with a 25 cm detector offset, giving a q range of
0.018-0.47 A". Both configurations had a neutron wavelength of 6 A with a 15% spread.
All the measurements were performed at 35°C, in deuterated solvents. The use of
deuterated solvents greatly reduces the scattering time required for each solution by
significantly enhancing the scattering contrast, even though this might slightly affect the
polymer-solvent interactions. Several concentrations were used to examine the effect of
concentration on Rg to determine the extrapolated value (R30). The modified Zimm
analysis we used to account for this effect is provided in the Appendix for this chapter.

Kratky and Guinier plots. Further quantification of the molecular characteristics
can be gleaned through careful consideration of neutron scattering data. The Debye
function'7 is used to characterize polymer chains in the theta condition (second virial
coefficient, A2 = 0) and can describe scattering from polymer molecules in a good

solvent. The scattering intensity (or differential cross-section)1(q) is given as'g’l2

l7

I(q) = ¢ x V<Ap>2 {2(exp<-<qR, )2 ) + <ng )2 —1>/<qR,)“} (2.5)
Here, (13 is the volume fraction of scattering centers, V, the volume of a single
scattering center, (21p)? the difference in the scattering length densities between solvent
and scatterer (or the contrast) and q, the scattering vector (47r/2 X sin(6l’2); 6 is the

scattering angle and 21, the neutron wavelength.) The term in the curly brackets is the

form factor (P(q)) that describes how I(q) is modulated by neutron interference effects

from the different parts of the same scattering center. In the high q limit, eq 2.5 reduces to
1(4) X 612 = 29" X V(Ap)2 /(Rg2) (2.6)

For a given sample, ¢, V, Ap, Rg are constant, thus, from eqs 2.5 and 2.6, a plot of
I(q)><q2 versus q should asymptotically approach a plateau value at high q values for a
Gaussian coil and is known as a Kratky plot. Deviations from the asymptotic behavior in
the Kratky plot can be used as an indicator of the segment distribution within the system.
Both ring and star polymers have a peak (maximum) prior to the asymptote revealing
different distributions than linear polymers.84 Indeed a gel-like crosslinked polymer
nanoparticle has a large peak.85 However, the high q limit is still a constant asymptote as
Gaussian chains are present between the robust crosslinks. Finally a constant density
sphere has no plateau and a series of ever decreasing peaks is seen. Thus, the Kratky plot
shape is a good indicator of the molecular architecture and is used by us to infer particle-
like nature.

In the low q scattering range, one can use the Guinier approximation, when q X R3

is small (<< 1), and the scattering firnction can be written as

18

log 1(4) = log 1(0) - (ng)

where 1(0) is given by ¢V(Ap)2. The Guinier plot,86 log(I(q)) versus qz, allows

 

(2.7)

determination of Rg and, further, can be used as a concentration check through the
neutron intensity at zero wave vector.

Burchard’s p—ratio. An extremely useful, quantitative indicator of the molecular
conformation and the segment density within a polymer molecule is Burchard’s p-ratio'9
which requires SANS (or other scattering) as well as hydrodynamic data. This ratio can
be computed from the molecular architecture of the molecule without the knowledge of
chemical details and is given by

p = R80 / Rho (2.8)

The radius of gyration of a molecule is intimately related to the segment density

variation p(r) within the molecule (where r is the radial distance from the centre of mass).

For a spherical architecture one finds,

Rg2 = £ Ir4p(r)er/[ Ir2p(r)dr] (2.9)

where R is the radius of the sphere. Since a hard sphere is non-draining, one has R
= Rho and finds p = \/(3/5) 2 0.775 while Gaussian coils have p = 1.2 — 1.6 depending on
solvent conditions.20

Differential scanning calorimetry (DSC) measurements. A TA instruments Q-
1000 DSC was used to perform all glass transition (T g) measurements. All of the samples
were subjected to at least three heating - cooling cycles, where each cycle consisted of
heating the sample from 0°C - 200°C, at a rate of 5°C / min, followed by cooling back to

0°C, also at 5°C / min. The inflection point for the heat flow as a function of temperature

19

was taken as the glass transition temperature for a particular cycle. The glass transition
temperatures reported in this work are the mean of the glass transition temperatures
obtained from the second and the third run cycle.

Rheology measurements. The nanoparticles were molded by compression, under
vacuum, in a pellet press (8 mm diameter) to ensure that no trapped air remained in the
sample. The samples were then aged at 130—170°C, under vacuum, for several hours. The
8-mm diameter discs obtained from the pellet press were placed on the 8-mm parallel
plates fixture of a Rheometrics ARES rheometer set at a gap of approximately 0.4 mm.
Measurements were done in the dynamic (oscillatory) mode. Frequency sweeps in the
range 0.1-100 rad/sec were performed at various temperatures (130°C-230°C). These
were then combined using time-temperature superposition87 to yield a master curve at

170°C (all quoted temperatures refer to the surface temperature of the lower plate).

Results and Discussion

Hydrodynamic Properties. The utility of dilute solution viscosity measurements
is well known,88 more recently, Burchard19 illustrates the importance of studying dilute
solutions with a variety of techniques to fully understand a given system. Further, the
polymer volume change with solvent under dilute conditions is a good indicator of the
polymer — solvent thermodynamic interaction26 which may be dependent on molecular
architecture. The solvent in which the polymer has the greatest intrinsic viscosity (highest

volume) is assumed to have the same solubility parameter as the polymer.89 This method

20

allows determination of the best solvent for the polymer as well as the change in the
molecular volume with solvent type.

Fig. 2.2 shows the intrinsic viscosity variation as a function of the solvent
solubility parameter for the 52.0 kDa tightly crosslinked nanoparticle and linear analog as
well as the 60.1 kDa lightly crosslinked nanoparticle. The intrinsic viscosity is made into
a dimensionless ratio by the maximum intrinsic viscosity to compare the relative change

in volume for each polymer.

 

3.0 -

 
    
   
 

52kDa Linear Analog
2.5 — —

 
 
 

 

 

 

 

E 2.0 — 1
E 60.1kDa Lightly crosslinked N.P.
E 1.5 —
1.0 - a
52kDa Tightly crosslinked NP.
1%
0.5 *- -
1 l l l 1 l
8.2 8.4 8.6 8.8 9.0 9.2

SO'Ubl'itY Parameter (cal cm-3)1/ 2

Figure 2.2. Intrinsic viscosity normalized with the maximum value plotted against
solubility parameter at 35°C. The data for the linear precursor (52.0kDa-20%-L,
triangles) and the lightly crosslinked nanoparticles (60.1kDa-2.5%-X, squares) have been

21

shifted by 2 and 1, respectively, from the tightly crosslinked nanoparticles’ (52.0kDa-
20%-X, circles) data.

It can be seen that the relative intrinsic viscosity for the tightly crosslinked
nanoparticles varies between 0.64 (cyclohexane) and 1 (THF) while for the lightly
crosslinked nanoparticles, it varies between 0.44 (cyclohexane) and 1 (benzene). On the
other hand, for the linear precursors of the tightly crosslinked nanoparticles, it varies
between 0.38 (cyclohexane) and 1 (benzene) revealing that the tightly crosslinked
nanoparticles do not expand or contract as much as the lightly crosslinked particles or its
linear analog.

Also, the linear analog and the lightly crosslinked 60.1 kDa nanoparticle have a
maximum at a solubility parameter of 9.2 (cal/cc)”2 (benzene), while the tightly
crosslinked particle has a maximum at 9.1 (cal/cc)”2 (THF). So the degree of crosslinking
has a slight effect on the polymer solubility parameter and hence the thermodynamic
interactions between the nanoparticles and the solvents. However, these results clearly
indicate that the solubility parameter for all the systems is quite close to that frequently
quoted for linear polystyrene (9.1 - 9.2 (cal/cm3)"2).79

When the viscosimetric radius was determined from the intrinsic viscosity (R,,)26
and compared to the hydrodynamic radius, we found little difference. In Fig. 2.3, the
variation of the hydrodynamic radius with molecular mass in THF is shown for the
lightly crosslinked nanoparticles, tightly crosslinked nanoparticles and their linear
analogs. The viscosimetric radius for polystyrene standards (Scientific Polymer Products)
in THF is also shown. It can be seen that the linear analog has radius values within

experimental error to pure polystyrene indicating that the linear analog does indeed

22

behave similarly to linear polystyrene. It can also be seen that the nanoparticles radius
decreases with increasing crosslink density, with the linear analog being the largest and
the tightly crosslinked nanoparticles the smallest in size. This suggests that, as may be
expected, intramolecular crosslinking causes a collapse of the linear polymer chain. Also
shown is the scaling for a constant density sphere, of equal density to bulk polystyrene,
showing that the tightly crosslinked nanoparticles are not exactly equivalent to hard

spheres when in solution.

 

I I I I I I I I I f

Pure Pol s ene
10 Y M

— 0.72 ‘1
R,1 ~ Mw

   
  
   
 
    
  

 

8 - Linear Analog Lightly X-linked

(20% crosslinker)

  

 

A _ 0.75
g 7 Rho ~ Mw .1
F? 6 - ' Ti htly X-Linked -
1r
:— / /
0 5 _ I -
3 /
/
CE I
4 - / 4
/
/
’ Constant density sphere limit
113
3 (RhO~Mw ) .1

 

 

l l l I l J l I

3 4 5 6 7 a 9
100
Molecular Mass (kDa)

 

Figure 2.3. Scaling of the viscosimetric radius (Rh) and the extrapolated hydrodynamic
radius (Rho) with molecular mass. The data for the linear precursor (downward triangles)
agrees well with that for polystyrene standards (upward triangles) while the lightly
crosslinked (2.5% crosslinker, squares) and tightly crosslinked (20% crosslinker, circles)
nanoparticles deviate significantly from the linear polymer scaling. However, neither

23

approaches the scaling predicted for a sphere of density equal to that for bulk
polystyrene. Example error bars are shown for the tightly crosslinked system.

Neutron scattering. Small angle neutron scattering (SANS) was used to measure
the radius of gyration of the particles in solution (due to a paucity of scattering time,
measurements were carried out in d-THF (deuterated THF) and d-cyclohexane only). The
raw SANS data was reduced to an absolute scale (1 (cm") versus q (A")) using the
standard NIST procedure (Typical 1 (cm") versus q (A") graphs obtained after
normalization have been shown in the appendix, Fig. 2.9). To determine the molecular
size (radius of gyration), each absolute data set was then analyzed by fitting to both the
Debye equation (Gaussian coil fit) as well as the hard sphere form factor. The fits
obtained from both these equations were compared with the Rg values obtained from the
Guinier plots. The fitting results for the Gaussian coil model (typical fits of the data with
the Debye model have been shown in the appendix, Fig. 2.9), hard sphere model as well
as the Guinier radii for the samples in d-THF, are given in Table 2.2.

It can be seen that the Guinier fits for the lightly crosslinked nanoparticles and the
linear analogs compare well with the fits obtained from the Debye equation for flexible
polymers, showing that the lightly crosslinked particles as well as the linear precursors
indeed behave similar to a Gaussian coil in solution. However, the data for the tightly
crosslinked particles could not be accurately fitted with the Debye equation. Instead, their
Guinier radii were found to be close to the radii obtained by fitting the data to a hard
sphere model.

Defining the contraction as the ratio of hydrodynamic radii of the NPs’, with

respect to the linear precursor, at zero concentration (11, Table 2.2), one can see that the

24

size of the nanoparticles is greatly reduced on crosslinking. For Antonietti et al.’s
microgels,58 which had 1 in every 10 monomer units (on average) crosslinked, the h value
varied between 0.96-0.98. In comparison, the lightly X-linked NP’s have h values similar
to those reported in their work, whereas the tightly X-linked NP have an h value between
0.65-0.86. Thus, the use of a larger amount of BCB as the crosslinking agentll does
provide greater reduction in nanoparticle volume as compared to p-bis(chloromethyl)

benzene.58

25

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26

Burchard’s p-ratio (Rgo/Rho) is shown in Fig. 2.4 as a function of the molecular
mass for both the tightly and lightly crosslinked nanoparticles. The Gaussian coil and the
hard sphere (constant density) limits are also shown. It is seen that the lightly crosslinked
nanoparticles always have a value close to or within the range determined for a Gaussian
coil. The tightly crosslinked nanoparticles, however, always have a value between the
hard sphere and the Gaussian coil limits. Also, the ratio decreases with increasing
molecular mass showing a shift towards the hard sphere limit. Thus, particle-like
behavior for the tightly crosslinked nanoparticles is suggested, which becomes more

apparent as the molecular mass is increased.

 

1_4_ l I l ' I T- l _

1,3 — Gaussian Coil Regime _

1.2 ------ - --
. Lightly X-Iinked NP

    

Tightly X-linked NPfi

0.8 - Hard Sphere Limit —
--I--r-r-.--|--.--r-
40 80 120 160
Molecular Mass (kDa)

 

 

 

Figure 2.4. Burchard’s p-ratio (ratio of radius of gyration to hydrodynamic radius)
variation for the lightly (2.5% crosslinked, circles) and tightly crosslinked (20%
crosslinked, squares) nanoparticles with molecular mass in THF at 35°C. A non-draining
hard sphere should have a value of 0.775 while a Gaussian coil has a range of values
depending upon solvent conditions. The lightly crosslinked nanoparticles behave similar

27

to coil while the tightly crosslinked nanoparticles approach the hard sphere limit,
particularly at higher molecular weight.

The neutron scattering data were also used to construct Kratky plots for both the
lightly and tightly crosslinked nanoparticles. The Kratky plot for the lightly crosslinked
nanoparticles (Fig. 2.5.a) demonstrates the behavior expected for a Gaussian coil. The
data for the tightly crosslinked nanoparticles (Fig. 2.5.b), on the other hand, shows a peak
in the Kratky plots, indicative of particle-like behavior. It is also seen that the peak
becomes more pronounced with increasing molecular mass of the tightly crosslinked
nanoparticles. This trend further supports the shift towards particle-like behavior with

increasing molecular mass as seen with the p-ratio values (Fig. 2.4).

28

800x10
*E 600
NO
:55 400
g3: 200
O'
0

10x10‘3

'7" 3

E

NO’ 6

E5

,, 4

g

NU 2
o
0.

Note though that there is a plateau at large wave vector, q, seen in Fig. 2.5.b.

 

 

T
.4

 

m
.. {h

 

158k-2.5%X
60.1 k-2.5%X

 
 

    

_
IIIII

/ 24.5k-2.5%X

l l i l l l l l I l l l l I l l l l

III'IIIITIIIIII

 

0.00 0.05 0.10 0.15 0.20

q <A")

 

 

I I I l I I I I l T I I I I I I I I

b 135 kDa -20%X

52 kDa -20%X

\_

25.3 kDa -20%X

l l l l l l l l l l I l l I l l l I

oo 0.05 0.10 0.15 0.20

q <A")

Figure 2.5. Kratky plots for the lightly crosslinked (a) and the tightly crosslinked
nanoparticles (b). A peak in the Kratky plot is indicative of particle-like behavior, while a
plateau is expected for a Gaussian coil.

Hence, the overall segment distribution is apparently Gaussian, however, organized in
such a manner as to give a maximum due to constraints contributed by the crosslinked
monomer units. Modeling of the segment distribution more than this is beyond the scope
of this work. Clearly, assumptions would have to be made regarding the segment

distribution and possibly larger wave vector data would be needed to determine the pair

29

distribution function and to perform detailed analysis. However, the peak in the Kratky
plot together with the suppressed p-ratio and smaller variation of intrinsic viscosity with
solvent change clearly indicate particle-like behavior.

Certainly the degree of crosslinking has an effect on the ultimate molecular
morphology developed, as expounded above. However, the results in Figs. 2.4 and 2.5.b
suggest molecular mass affects the segment density distribution and hence morphology.

3 and Kuhn and Majer,90 we note that the

Recalling the work of Kuhn and Balmer5
average number of statistical segments in a cycle, <k>, at small degree of intramolecular
crosslinking, is related to the number of statistical segments in a molecule, N, by
<k> =2\/2/3 x N/N : VN

One may expect that the initial cycles formed in the intramolecularly crosslinked
nanoparticles will have 35 monomer units for the 25.3 kDa tightly crosslinked
nanoparticle and increase to ~ 80 for the highest molecular mass, 135 kDa (there are 5
monomer units in a statistical segment”). This phenomenon could affect the ultimate
molecular morphology afier crosslinking is completed and could account for the decrease
in the p-ratio with molecular mass shown in Fig. 2.4. We also note the ring
polydispersity,90 <k2>m/<k>, is ~O.46N”4 and so higher mass molecules could
potentially have a greater difference in initial ring size. These effects are noted here as
they could affect the ultimate molecular morphology and final molecular properties
surely deserving more attention in future studies since our system is simpler to study in
terms of molecular “folding” than polypeptides.”

Bulk properties. The thermal analysis performed on both the lightly and tightly

crosslinked nanoparticle systems also reinforces the observations above. It can be seen

30

from Fig. 2.6 that the glass transition for both the lightly and tightly crosslinked particles
increases with increasing molecular mass (the error bars represent the beginning and the
end of the glass transition). Also, the T g for the tightly crosslinked nanoparticles is always
greater than the T g of the lightly crosslinked nanoparticles of similar molecular mass. It
should be noted that the increase in Tg, caused by the intramolecular crosslinking of
polystyrene, although significant, is still less than the elevation caused in polystyrene

92, 93 as has

networks formed by the copolymerization of polystyrene and divinylbenzene;
been seen before.58 For example, Nielsen94 developed a simple relation to find the glass
transition temperature rise due to crosslinking: 39 kDa-°C/Mx, where Mx is the molecular
mass between crosslinks. One would expect a 9°C (lightly crosslinked) and 75°C (tightly
crosslinked) increase above T g for the equivalent linear polymer, which is clearly not the
case. In fact, a slight T g decrease may be apparent for the lightly and tightly crosslinked

nanoparticles at low molecular Weight. Thus, the discrete crosslinked nature of the bulk

nanoparticles clearly affects the glass transition temperature in unusual ways.

31

 

  
    

130 _ +Pure PS
+2.5%-X
+20%-X

 

120 a

.0

I-°’ 110 l
100 —

 

 

 

90 l I l I J I l _
4O 80 120
Molecular mass (kDa)

 

Figure 2.6. The glass transition temperatures for both the lightly and the tightly
crosslinked nanoparticles compared to pure linear polystyrene. The error bars represent
the spread of the transition, indicating its beginning and end.

Furthermore, it was seen before that addition of the tightly crosslinked
nanoparticles caused a decrease in the glass transition temperature of linear polystyrene.76
This observation is quite interesting and contrary to the general mixing rule considering
that high molecular mass linear PS has a T g of ~ 106°C, while the 135 kDa-20%-X NP’s
have a T g of ~132°C and a 1% blend of the nanoparticles in linear polymer was found to
have a Tg of 103.5°C.95

The complex viscosity as a function of frequency is shown for a 3 arm
polystyrene star (molecular mass for each branch ~ 108 kDa) and linear polystyrene

(molecular mass 19.3 kDa, 75 kDa, 115 kDa), (Fig. 2.7.a), and the lightly (Fig. 2.7.b) and

tightly (Fig. 2.7.c) crosslinked nanoparticles (the data has been shifted to 170°C using

32

time-temperature superposition;l3 the shift factors have been tabulated in the appendix,
Table 2.5). Clearly, the rheological behavior of the crosslinked nanoparticles does not
match the behavior observed for the linear or star shaped polystyrene. Also, from Fig.
2.7.c it is apparent that only the lowest molecular mass (25.3 kDa) tightly crosslinked
nanoparticle shows a terminal viscosity. All of the higher molecular mass tightly
crosslinked nanoparticles in fact show a gel-like behavior, which is to be expected for a
crosslinked network.60 Note that we tried to measure the melt surface tension96' 97 of the
25.3k-20%—X-NP sample. At 220°C we found the surface tension was extremely large
and of order 150 mN/m, while linear polystyrene should have a surface tension of order
20 mN/m at this temperature. We conclude that this sample must have a terminal
modulus or yield stress that is small and probably less than 10 Pa. So this sample may be
similar to the higher mass 20%-X-NP samples, with a gel-like behavior, that is disrupted
in the rheological testing.

The observation of gel-like behavior for relatively low molecular mass tightly
crosslinked nanoparticles is in contrast to the behavior seen by Antonietti et al.12 In their
work, a zero shear viscosity was observed even for very high molecular mass
(Mw=l.03><106, R = 7.3 nm) microgels.12 However, the microgels only had 1 in every 10
monomer units crosslinked and the higher degree of crosslinking present in this work can
cause a significant impediment to the motion of the small chains between the crosslinks.
Antonietti et al. postulated that the viscosity behavior was linked to the cooperative
nature of the crosslinked loops’ motion. Thus, the gel-like behavior we observe may be
expected, and it is certainly affected by the intramolecular crosslink density and

nanoparticle size (or molecular mass).

33

 

 

  
    
      
      
 

     
   

 

 

 

 

 

  
  
   

 

   

 

 

 

 

 

 

l
10 a a
1
1
A10‘ 3
3 E
“1" I
9.“: 10: PS 19k kDa linea d
1. PS 75k kDa linear g
‘-’ PS115k kDalinear : 2
2 PS 324 kDa star ‘ 1° = o 24.5 kDa-2.5%-X
10 a: : I 60.1 kDa-2.5%-X
: 1 A 158kDa-2.5%-X
10 71 1 1 1 1
10’2 10° 02 10‘ 10‘2 10° 102 10‘
Frequency (rad / sec) Frequency (rad / sec)
108 l l I F f r l r 4.1 I 1— ' I l T l I I I I I Q
7 c 6 O Fox&Flory dO'l
1O . 25.3 kDa-20%-Xfi 10 ” O Mackay&Henson Q,
106 __ I 52.0 kDa-20%-X _ z gustgaxe‘ a'- a
A 1 k - ° - " 5 - ‘ °‘ —
G 5 35 Da20/oX 3 1o 0 20%-x 9A
3 1O " E,
I >
g 10‘ - '5
v O
U
. 2
r: 103 _ >
102 _ K _‘
101- 11 1111114 1 .1 L1.
- - 2 3 4 5 67 2 3 4
1o3 10‘ 10‘ 1o3 105 101 102
Frequency (rad I see) Molecular mass (kDa)

Figure 2.7. The complex viscosity as a function of frequency at 170°C, for the 3 arm
polystyrene star and linear polystyrene (a), lightly crosslinked (b) and tightly crosslinked
(c) nanoparticles. Increasing molecular mass and crosslink density causes an increase in
the zero shear viscosity. A gel like behavior is evident for the high molecular mass,
tightly crosslinked nanoparticles. (d) The zero shear viscosity as a fiJnction of molecular
mass (A? for polystyrene melts at 170°C. Data from Fox and Flory,” 64 Mackay and
Henson9 and Tuteja et al.95 are used. The zero shear viscosities for the pure lightly and
tightly crosslinked nanoparticles are also shown (a zero shear viscosity is not observed
for the 52 kDa-20%-X and 135 kDa-20%-X NP’s).

34

The zero shear viscosity as a function of molecular mass for linear polystyrene at
170°C is shown in Fig. 2.7.d together with the values for the lightly and tightly
crosslinked nanoparticles. The lightly crosslinked nanoparticles may have a lower zero
shear viscosity as compared to linear polystyrene of similar molecular weight,12
suggesting easier mobility of the crosslinked molecule as compared to the linear chains,
however, this is a tentative conclusion.

The modes for polymer relaxation and the effects of the relative motion of
crosslinked loops become clearer by viewing the storage modulus data. The storage and
loss modulus as a function of frequency for the 3 arm polystyrene star and linear
polystyrene of comparable molecular mass to the lightly and tightly crosslinked
nanoparticles is shown in Fig. 2.8, together with the nanoparticles’ data. All of the lightly
crosslinked nanoparticles as well as the 25 kDa-20%-X-NP show typical terminal zone
behavior with G’~a)2 and G"~a)1 at low frequencies ((0), with the caveat that the 20%

crosslinked system may have a delicate gel-like behavior.

35

 

 
  
 
 

 

   

    

   
 
   
 
 
    

 

 

 

 

 

”1 e G'PS153kDa1line;l I I Y I T 1 I 1
10° F I 6' PS Mekoa linear » o G'-24.5 kDa Lightly crosslinked
A 6' PS 324 kDa star ’ I G2-60-1 kDa
- o G" P819.3kDalinear 105 E“ (3:153 kDa
s ' D G" PS 115kDa linear 58 gig-‘15 :3:
10 A G PS 324 kDa star ’6 :A G'-158 kDa
11? a -
a :" 4
5 . 0 1° F
’ ' 10 E5 :
0 h A
103 103E' :‘
BL
10“ 10‘1 1o1 103 1o 10'2 10° 102 10‘
Frequency (rad lsec) Frequency (rad lsec)

 

 

 

 

I I I I I I I I I
107 ._ O G'-25.3 kDa
I G'-52.0 kDa
A G'-135 kDa
6 o G"-25.3 kDa
10 _ D G"-52.0 kDa -
A G'-135 kDa
is
:5 1o5 -
o
(D 104 _
1o3 -
10’ h
10‘5 10‘3 10'1 1o1 103 105
Frequency (rad lsec)

Figure 2.8. The storage (6’) and loss (G”) modulus as a function of frequency for the 3
arm polystyrene star and linear polystyrene (a), lightly crosslinked (b) and tightly
crosslinked (c) nanoparticles, at 170°C. A terminal zone behavior similar to linear
polymers is evident for all of the lightly crosslinked nanoparticles, while a transition zone
behavior similar to linear polymers is evident for both the lightly and tightly crosslinked
nanoparticles.

On increasing the molecular mass for the lightly crosslinked nanoparticles, the
development of a plateau zone (corresponding traditionally to the presence of

entanglements) can be seen and a ~ 10% increase in the plateau modulus is observed

36

(determined through the minima in tan 6 = G "/G'99). Traditionally the plateau modulus
corresponds to the entanglement density present in polymer melts. Clearly, reptation
motion, at least the way it is thought of traditionally, cannot account for the rheological
behavior observed in these crosslinked particles, even though the rheological spectra of
higher molecular mass lightly crosslinked nanoparticles is similar to the spectra obtained
for higher molecular mass entangled linear polymers.

This trend is reinforced as we look at the rheological behavior of the tightly
crosslinked nanoparticles. As the number of crosslinked loops present in the molecule
increase from ~ 25/ molecule (25.3 kDa-20%-X-NP) to ~ SO/molecule (52 kDa-20%-X-
NP), a distinct change in the terminal behavior of the molecules is observed. With the
increasing number of crosslinked loops, the storage modulus becomes essentially
constant with respect to frequency (for low frequencies), a behavior typical of gels.12 At
this point it can be imagined that the large number of intramolecularly crosslinked loops
present in the molecule, cannot move cooperatively, to allow for the molecules’
relaxation; and essentially a high stress (yield stress) is required to allow for the loops to
move together and hence for the molecule to relax. Further, the molecules become more
particle-like with increasing molecular mass, as discussed above, probably contributing to
the gel-like flow properties.

The observation of a constant storage modulus at low frequency as shown in Fig.
2.8.c, also provides some interesting insights about the nature of the crosslinked particles.
As can be seen, the modulus at low frequency increases with increasing nanoparticle
molecular weight (radius), with the caveat that the lowest molecular weight sample, 25.3

kDa-20%-X, has a very small terminal modulus as determined through our surface

37

. 9 . . .
tenS1on measurements. 6 However, predictions of flocculated suspensrons show that

modulus should scale inversely to the particle radius raised to a power;'°°’ 10'

indeed, even
jammed particle systems, at zero temperature, show a scaling inversely proportional to
the radius raised to the power of the system dimensionality.I02 The modulus increase seen
in our system may then be related to two factors. Firstly, our results above point to the
fact that the larger molecular weight system is more “particle-like” in nature which can
be expected to influence the flow properties (as demonstrated by the other "rheological
properties). Secondly, the glass temperature for the 135 kDa-20%-X system is
approximately 25°C higher than that for the 52.0 kDa-20%-X. For a given testing

temperature, 170°C in our case, this would tend to increase the flow properties by a factor

of approximately 30 — 40, accounting for the observed trend.

Conclusion

An innovative synthesis process was used to induce intramolecular crosslinks
within linear polystyrene. It was seen from intrinsic viscosity and dynamic light
scattering measurements that crosslinking causes a decrease in the size of the chain and
also that the tightly crosslinked nanoparticles have much limited changes in dimensions
between different solvents as compared to the lightly crosslinked and linear precursor
chains. This demonstrates that intramolecular crosslinking limits the expansion and
contraction of the molecule.

Small angle neutron scattering was used to show that the lightly crosslinked
nanoparticles and the linear precursors behave like Gaussian coils in solution. On the

other hand, the tightly crosslinked nanoparticles showed a peak in the Kratky plot

38

indicative of particle-like behavior. It was also seen that the peak in the Kratky plot
becomes more pronounced with increasing molecular mass of the nanoparticles. This

trend was reinforced by determining Burchard’s p-ratio for the various nanoparticles. It
was seen that the p-ratio values for lightly crosslinked particles are indeed close to the
Gaussian range while the values for tightly crosslinked nanoparticles were seen to move
towards the hard sphere limit with increasing molecular mass.

These molecules were ideal to study the rheological/relaxation behavior of high
molecular mass polymers in the absence of entanglements; as the high crosslink density
present in these molecules should influence entanglement coupling. It was seen that these
molecules show most of the rheological characteristics of both unentangled and entangled
polymeric systems. The terminal viscosity increased with increasing molecular mass and
increasing crosslink density (contrary to earlier observations for particles with lower
intramolecular crosslinking densities),l2 with the limiting case of high molecular mass
samples with high degree of intramolecular crosslinking showing gel like behavior, with
an infinite terminal viscosity. It was postulated that the mobility of these molecules is not
governed by the motion of individual chains, but rather by the c00perative and relative
motion of the crosslinked loops present in the system in accord with Antonietti et al.’s'2
hypothesis. This type of motion is indeed intuitive as the crosslinking present between the
molecules must cause many of the loops to move together.

It can then be said that the reptation model (or the presence of a tube for
relaxation) does not explain many of the important rheological features seen for our
systems. Clearly coupling or cooperative motion has to play a significant nature in the

relaxation processes of these molecules. Indeed, Schweizerz" 22 postulated a coupling

39

theory for polymers which predicts many of the polymer relaxation modes observed

experimentally.

Appendix Chapter 2.

Huggins and Kraemer Coefficients.

Equation 2.3 can be used to calculate the Huggins and Kraemer coefficients
through intrinsic viscosity measurements. Table 2.3 shows the variation of Huggins and
Kraemer coefficients with molecular weight for the 2.5% and 20% crosslinked
nanoparticles in THF and cyclohexane, at 35°C.

Table 2.3: The variation of Huggins and Kraemer coefficients with molecular weight for
the 2.5% and 20% crosslinked nanoparticles in THF and cyclohexane, at 35°C.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tightly Crosslinked THF Cyclohexane
Molecular Weight (Da) k... k.. k1. k1,
25300 1.24 -0.55 2.57 -l .8
52000 0.64 -0.13 2.97 -0.23
135000 0.23 0.26 NA81 NAa
Lightly Crosslinked THF Cyclohexane
Molecular Weight (Da) k1. k1. k1. R1,
24500 0.62 0.003 NA NA
60100 0.58 0.002 0.82 -0.55
158000 0.49 0.005 0.57 -0.33

 

 

 

' The 135 kDa tightly crosslinked nanoparticles had a very low solubility (< lmg/ml) in
cyclohexane.

Modified Zimm and Yamakawa approaches to size variation of macromolecules.
The Zimm equation is written”‘ '03
k1/1(q) = {1 + l/3 x {1211,02} /cM+ 2 x A2
where k, is [21,0]2 / NA pmz, with p,,. being the mass density of the scatterer. This

equation can be arranged to

40

log(I) =1n(Co)—log(1 + V. x qugoz/ {1 + 2 x Aszl)
2 ln(C0) - ‘/3 x qugoz/ {1 + 2 x Asz}

where Co is a grouping of variables that is constant for a given system and
concentration. Performing a Guinier analysis on the scattering data at low q will yield an
apparent radius of gyration, Rg, which is given by

Rg'2= 8.3 x {1+2 XAsz} (2.Al)

Thus, a plot of the inverse square of the apparent radius of gyration versus
concentration will yield the true radius of gyration, Rgo, at zero concentration. This
equation is useful when only a few concentrations are available for analysis thereby not
warranting a full Zimm analysis and explains the (apparent) radius of gyration variation
with concentration. This extrapolation procedure was used by us to determine Rgo and
yielded good linear regression.

Yamakawa8| applied non-equilibrium thermodynamics to determine the
translational diffusivity, and hence R1,, as a function of concentration via

R." = R..." x {1 + kg 6} (2.A2)

where the subscript “0” is again the zero concentration value and k0 is a constant.
This relation was used by us to determine the true hydrodynamic radius.
Radius of Gyration variation in cyclohexane.

The Radius of gyration determined from a Guinier regression, Debye flexible
polymer fit, as well as the hydrodynamic radius for the various nanoparticles and their

linear precursors in d-cyclohexane is provided in Table 2.4.

41

Table 2.4. Radius of gyration determined from a Guinier regression, Debye flexible
polymer fit, as well as the hydrodynamic radius for the various nanoparticles and their
linear precursors in d-cyclohexane (SANS data) and cyclohexane (DLS data);
concentration is 5 mg/ml and temperature is 35°C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Molecular % Guiner Flexible Polymer
Weight(kDa) crosslinker Nature Radius(nm) fit(nm)a Rhc (nm)
25.3 20 linear 4.6:t0.02 5.0:t0.02 3.0(42)
52 20 linear 7.0:h0.05 7.8i0.02 4.7(6.7)
135 20 linear 8.6:t0.l l 8.8i0.05 8.0(9.1)
25.3 20 X-linked NA“ NA“ NA“ (2.8)
52 20 X-linked NA“ NA“ NA“ (3.7)
135 20 X-linked NA“ NA“ NA“ (5.9)
24.5 2.5 linear 4.8:002 5.0i0.01 2.6(4.2)
60.1 2.5 linear 7.8i0.01 8.5i0.01 5.3(7.l)
158 2.5 linear 7.8i0.04 8.7:t0.02 7.8(8.Q
24.5 2.5 X-linked 5.3i0.01 5.0i0.02 2.5(4.1)
60.1 2.5 X-linked 6.1i0.03 6.6i0.02 5.2(6.4
158 2.5 X-linked 7.7i0.02 8.0i0.03 8.0(9.l)

 

 

 

 

 

 

 

° The tightly crosslinked nanoparticles were insoluble in cyclohexane at this high
concentrat1on.
SANS intensity data after normalization.

The scattering intensity as a function of the wave vector q for the 25.3 kDa and
52.0 kDa-20%X-linear precursors in d-cyclohexane and d-THF at 35°C, as reference to
typical data obtained after normalization, yet without background subtraction, is shown in
Fig. 2.9. As can be seen in the figure, the data is fitted well by Debye function. All of the
scattering data except for the data obtained for the tightly crosslinked nanoparticles could

be fitted quite well with the Debye function.

42

l LllLlJllllll l 1 lennnnl 1111111111111 ll

 

     

  
  
   
    
    

 

     
    
 
    
  
 

    

    
 

 

 

    

 

 

- .— "w 1. Flt to Debye function
~:.-.. Flt Greggbcignfiirflgn: 0an “‘5‘ '“- “ Fad“- 1-41 i 0-02
"i“ R, = 7.8 t 0.02 nm ~ 1 _3 b . 28 i 0-03 "m
., _ P 8: .
,r‘ 2 _ r ,r‘ 6-
'E . CydOhexane i 'E “ Fit to Debye function ’
9, " "__ 3 4-ScaleFactor:1.25:1:0.1
E Scale Factor. 6.8 :t 0.1 ‘-‘ : g . R9 = 26 i 0-04 "m
- 5 R0 = 5.0 1 0.02 nm I - 3
4 "73“. r J slo = -2
slope = -2 '- ~ 2; pe ‘ _
0 1 1: 52.0(Da-20%X-linear o_1 — D 52-0k08r20°/°X-"near
' 2 4 68 2 4 “7'2 ré'é'é'w'é "
0.01 0.1 0.01 -1 0.1

C1 (A4)

Figure 2.9. Typical I (cm'l) versus q (A") graphs obtained afier normalization of the
SANS data in d-cyclohexane and d-THF. The data was obtained at 35°C, and the
concentration was 5 mg/ml. The fits to the Debye function for the obtained data are also

shown.

Shift Factors for rheological data.

The shift factorsl3 (a1) at various temperatures used for the time-temperature
superposition of data shown in Fig. 2.7 and Fig. 2.8 are listed in Table 2.5. It can be seen
that the shift factors for both the lightly and tightly crosslinked nanoparticles are similar
to the shift factors for linear polystyrene. Note the glass transition temperature for the
crosslinked nanoparticles is different to that of linear polymer (Fig. 2.6), accounting for

some differences in the shift factors for a given temperature.

43

Table 2.5. The shift factors13 as a function of temperature for linear polystyrene, lightly
and tightly crosslinked nanoparticles.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Linear polystyrene
Linear PS 19k Linear PS 75k Linear PS 1 15k
Temp(°C) aT Temp(°C) aT Temp(°C) aT
130 284 130 881 130 966
140 45.8 140 85.2 140 92.0
150 10.3 150 14.8 150 15.1
160 4.12 160 3.44 160 3.48
170 1.00 170 1.00 170 1.00
180 0.26 180 0.35 180 0.35
190 0.14 190 0.14
200 0.07 200 0.06
_L_ightly crosslinked
24.5 kDa-2.5%-X 60.1 kDa-2.5%-X 158 kDa-2.5%—X
Temp(°C) aT Temp(°C) aT Temp(°C) a7
130 310 140 44.7 150 15.4
140 51.1 150 10.1 160 3.45
150 11.1 160 2.89 170 1.00
160 3.04 170 1.00 180 0.35
170 1.00 180 0.41 190 0.15
180 0.24 190 0.20 200 0.08
190 0.09 200 0.10 210 0.05
210 0.05 220 0.03
_'_l_‘ightly crosslinked
25.3 kDa-20%-X 52 kDa-20%-X 135 kDa-20%-X
Temp(°C) aT Temp(°C) a1 Temp(°C) a1
130 155 130 982 150 75.4
140 35.8 140 131 160 12.5
150 6.93 150 39.15 170 1.00
160 2.23 160 10.1 180 0.35
170 1.00 170 1.00 190 0.08
180 0.21 200 0.05
190 0.02 210 0.02

 

44

 

CHAPTER 3

GENERAL STRATEGIES FOR NANOPARTICLE DISPERSION

 

Introduction

Polymer phase stability in solution 26 or with another polymer ‘04 has been studied
for over 50 years and found to be a delicate balance of entropic and enthalpic
contributions to the total free energy. For example, it is possible to fractionate a polymer

by size with a small change in solvent quality,105

and to control miscibility of chemically
identical polymers whose only difference is architecture (branching).'°6 More recently the
phase stability of nanoparticle/polymer blends has attracted intense scrutiny '07 and is
challenging to predict due to computational difficulty in accessing the relevant length and
time scales. Flory theories, density functional theories and molecular dynamics methods
provide essential guidance, though accurate calculations are restricted to two or at most a
few nanoparticles in the relevant size regime'os' '09 Despite these difficulties a vast array
of applications are emerging that require nanoparticle dispersion such as the use of

110,111 and in

fullerenes to enhance the efficiency of polymer-based photovoltaic devices
the control of polymer viscosity using nanoparticles.8
We demonstrate here strategies for control of nanoparticle dispersion in linear

polymer melts. We start with discussion of processing procedures which enable stable

dispersion of fullerenes and then present an experimental characterization of the

45

parameters which control the phase boundary between the dispersed and phase
segregated states of carefully considered nanoparticle/polymer mixtures. Moreover it has
been proven possible to disperse polyethylene nanoparticles in polystyrene despite the
fact that linear polyethylene/linear polystyrene is a classic phase separating blend, which
implies that nanoparticle morphology may actually enhance dispersion. This hypothesis
is tested by using a system consisting of polystyrene nanoparticles dispersed in linear
polystyrene as the monomer-monomer contacts in this system are the same for all of its
constituents. An enthalpic mechanism that arises from nanoparticle packing effects
operates at the nanoscale and is necessary in order to understand dispersion in this size
regime. A Flory theory which includes this enthalpic contribution as well as chain
stretching caused by nanoparticle dispersion and the standard mixing entropy is used to
reconcile the experimental observations and emphasize the importance of the

nanoparticle to polymer size ratio in controlling nanoparticle dispersion.

Experimental

Polyethylene nanoparticles consisting of dendritic polyethylene, with a number-
averaged molecular weight of 225 kDa (polydispersity index of 1.6) as measured by a
Wyatt Technologies multi-angle light scattering detector, were synthesized at 0.1 atm

ethylene pressure using a chain walking palladium catalyst.”2

They were then blended
with 393 kDa linear polystyrene in a common solvent, rapidly precipitated in methanol
and dried to ensure complete solvent removal. A maximum polyethylene concentration of

5-10 wt%, relative to polystyrene, was used and the mixture heated to ca. 230°C for up to

46

24 hrs. to observe phase stability. Differential scanning calorimetry (TA Instruments)
reveals a broad transition at ~ 40°C for pure polyethylene which disappears in the blend.

The blend glass transition temperature (Tg) is slightly affected although not as much as

that seen for a phase separating blend containing 7 wt% tetracontane (n-C4OH82) prepared

in the same manner. Here the pure tetracontane melting point is observed at 81°C in the

blend with a ca. 10°C reduction in Tg for polystyrene (94°C) after the third heat cycle.
Conversely, the nanoparticle — polymer blend has a Tg reduction of 1 — 2 °C.8’ ”3 The fact

that dendritic polyethylene is soluble in linear polystyrene while tetracontane is not is

further confirmation of molecular architecture affecting phase stability.
Results and Discussion

First the dispersion of fullerenes into polystyrene is discussed motivated by earlier

work which suggested that fullerene dispersion in polymers ”4

is poor, limiting their
utility, for example, in solar cells.”°’ 1” For a polymer blend, the insertion energy of a
linear polymer chain with another controls dispersion and grows with the number of
monomers in the chain. So, the insertion enthalpy of a chain of N monomers is
proportional to N x, where z is the Flory mixing parameter and is the primary cause of
phase separation in incompatible blends. Nanoparticles have an insertion enthalpy which
grows in proportion to the surface area of the nanoparticle yielding an insertion enthalpy
of s ~ A x, where A=47r a2 for a nanoparticle of radius 0. Though this enhancement is not

as strong as for polymer blends, dispersion of nanoparticles still depends critically on 1.

Our experimental observation is that it is possible to disperse up to a concentration of 2

47

vol% of C60 in linear, monodisperse polystyrene. At small nanoparticle concentration,
Flory theory ”5 gives a binodal or phase stability volume fraction (¢B) of: fig z Exp(-
[l+s]), assuming the phase separated fullerenes form a pure nanoparticle phase. Using
the experimental value of ¢B =0. 02 yields an insertion enthalpy per fullerene which is of
order s 2 3. The molecular insertion energy per monomer (e) is given by s = za’kBT,
where z is the coordination number, k3, the Boltzmann constant and T, the temperature,
yielding an insertion energy of a 2' 0.02 eV for fullerenes in polystyrene. This relatively
small energy may be rationalized by the fact that favorable molecular contacts between
the aromatic rings on polystyrene and the hexagons on the surface of C60 may occur.
Fullerene dispersion is enabled by use of our technique of rapidly precipitating the

components in a mutual non-solvent 5" ”6

to arrive at a dried powder that is then
thermally aged, allowing melt processing and fiber spinning (Fig. 3.1.a). It is known that
fullerenes have limited solubility in organic solvents,117 of order 5 — 10 mg/mL. Solvent
evaporation from a fullerene/polymer solution will lead to a fullerene supersaturated state
at low overall concentration and likely phase separation (Fig. 3.1.b). Thus, to reach the

thermodynamically favored state the processing procedure for nanoparticle dispersion has

to be carefully controlled to avoid a kinetically trapped condition.

48

 

 

 

Images in this dissertation are presented in color.

Figure 3.1. (a) Rapid precipitation of fullerene/polystyrene blends, followed by drying
and melt processing allows manufacture of fibers. The fibers contains 1 wt% C60
fullerenes that were melt spun into long fibers with a diameter of ca. 1 mm. (b) Fullerene
(1 wt%)lpolystyrene blends developed through regular solvent evaporation produce large,
phase separated domains which are not apparent in the fiber.

A more surprising result is the fact that we observe dispersion of large branched
polyethylene nanoparticles ”2 in polystyrene (see Fig. 3.2). This is surprising since linear
polystyrene/linear polyethylene blends ”8 have an unfavorable mixing enthalpy and are a
classic phase separating system, with complete phase separation occurring at molecular
weights typical of those used here. We have taken TEM images and collected SANS data
for a wide variety of mixtures. The TEM image in Fig. 3.2.b illustrates the dispersion of
dendritic polyethylene nanoparticles in 393 kDa linear polystyrene from which a
nanoparticle radius of 10 — 15nm can be extracted. Moreover, a Guinier analysis of
SANS data '8’ 8‘ fi'om polyethylene nanoparticles in dilute solution yields a polyethylene

nanoparticle radius of 12.8 :t 0.1 nm which is consistent with the TEM measurement.

Neutron scattering data for the same nanoparticles blended with different molecular

49

weight linear polystyrene melts are presented in Fig. 3.2.0. Architecture and size both
make a clear difference in the miscibility of this system as the dendritic polyethylene
nanoparticles are miscible with 393 kDa linear polystyrene (Rg=l7.3 nm) as evidenced by
the non-fractal SANS results at small wave vector ‘8’ 84. However, miscibility does not
occur when the same polyethylene nanoparticles are blended with either 155 kDa
(deuterated) linear polystyrene (Rg = 10.5 nm) or with a smaller protonated 75 kDa
polystyrene (R,g = 7.5 nm) as shown in the figure. The latter experiment demonstrates that
it is not the isotope effect ”9 causing phase separation, rather the relative size of the

nanoparticle and polymer is key.”‘"‘22

50

 

    
  
     

 

Mean Radius: 11.6 1 0.1 nm
Spread: 8.3 3: 0.1 nm _

1000 I

100

a
O
l

.1

1(0) (cm )

__n
l

FittoPowerLaw ..
0 l Exponent= 3.93 i: 0.02

0 PS 393k + dend. PE - 2% blend
0.01 - A PS 75k + dend. PE - 2% blend ‘

Illlll

45678 2 345678

 

 

 

Images in this dissertation are presented in color.

Figure 3.2. (a) Cartoon showing branched, dendritic polyethylene. (b) TEM of a 4 wt%
blend of dendritic polyethylene with 393 kDa linear polystyrene shows the individual
polyethylene macromolecules with a size of order 20-30 mm. The R8 for the linear
polystyrene is 17.4 nm and so is larger than the dendritic polyethylene. The inset shows a
higher magnification. (c) Mixing with a smaller molecular mass polystyrene (75 kDa, Rg
= 7.5 nm) produces phase separation. Power law scattering of intensity (1) versus wave
vector (q) is present at small wave vector for the lower mass polystyrene, whereas the
higher mass system demonstrates miscibility without a power law region. The intensity
profile can be fitted with a polydisperse sphere model yielding a mean radius (11.0 nm)
for the dendritic polyethylene that agrees well with the TEM images.

51

A particularly clear illustration of the importance of the ratio a/Rg on nanoparticle
dispersion is provided by a mixture consisting of crosslinked polystyrene nanoparticles ”
blended with linear polystyrene. We observe phase separation when the nanoparticle size
is greater than the polymer radius of gyration in a manner similar to that observed in the
case of polyethylene nanoparticle mixtures discussed above.

Tightly crosslinked polystyrene nanoparticles, where every fifth monomer unit is
potentially crosslinked ”, were blended with linear polystyrene.8 This system produces a
stable blend even when the interparticle gap reaches surprisingly small distances
suggesting the linear polystyrene molecule is highly distorted.8 The distortion was
directly measured through a SANS Guinier analysis from a sample in which 2 wt%
deuterated linear polystyrene was blended with protonated linear polystyrene of similar
molecular weight and various concentrations of protonated polystyrene nanoparticles
(Fig. 3.3.a). The radius of gyration for the linear polystyrene increases with nanoparticle
concentration and the linear chains remain globular in nature, as determined through
careful analysis using models which distinguish between sphere-like, rod-like and disk-
like shapesm

Chain stretching has been observed in some Monte Carlo simulations '24

though
in many others chain contraction has been noted. '25 Both chain expansion and chain
contraction has been observed in neutron scattering from isotopically labeled
polydimethylsiloxane (PDMS) blends containing silica particles.126 In this system,
nanoparticles of radius ~ 1 nm were blended with linear polymers with a similar radius of

gyration, Rg ~ 3 - 10 nm. It was observed that the polymer mixtures with smaller Rg

experienced chain contraction upon nanoparticle addition, while the polymer mixtures

52

with a larger Rg experienced chain expansion with nanoparticle addition. In our system
the linear polymer R8 was varied between 4 — 11 nm and the nanoparticle radius is
approximately 3 nm, and we observe chain expansion in all cases (see Fig. 3.3.a).
Moreover, excluded volume does not fully account for the radius increase, since if it is
assumed that the individual polymer and nanoparticle densities do not change on mixing,
then the radius of gyration relative to that without nanoparticle incorporation (Rg/Rgo) is
expected to vary as [1+¢]”3. The chain stretching is larger than that suggested by this

relation and is empirically close to 1 + c¢, with c approximately one.

53

 

   

 

 

 

 

T I 1 1 l 1
0 21.0 kDa A
_ I 63.0kDa z
1 15 A 155 kDa A
E
5
C
1 10 8
O ' o’ E
of" I 1+¢'/" e.
‘ i a
DD ’r' 2
C! 1.05 “a; — 3
fl .- 1 _
.. 1
1.00 I1+¢I . a
l
l 1 1 1 1
0.00 0.02 0.04 0.06 0.08 0.10 0 5 10 15
Volume fraction of nanopartides Nanoparticle radius (nm)

 

Images in this dissertation are presented in color.

Figure 3.3. (a) The polymer radius of gyration (Rg), relative to that without nanoparticles
(R30), for three different molecular mass linear polystyrenes: 21, 63, 155 kDa, as a
function of volume fi'action (45) of 52.0 kDa tightly crosslinked polystyrene nanoparticles.
The nanoparticles clearly stretch the polymer chains. The solid line represents the radius
of gyration variation if the polymer density does not change upon mixing, and the
behavior [l+¢l]”3 is expected. Instead, the data obeys 1+c¢, with c about one. (b) A
polymer radius of gyration — nanoparticle radius phase diagram, with the filled circles
representing data where phase separation was detected and the open circles where
miscibility occurs. Open circles with an x represent conditions where some

54

agglomeration was detected by SANS, yet large scale phase separation was not observed.
Squares are the C60/polystyrene system; circles, the polystyrene nanoparticle/polystyrene
system; and triangles, the dendritic polyethylene/polystyrene system. The dashed line
represents the reptation tube radius suggesting phase stability does not depend on the
entanglement structure. The nanoparticle fraction used to generate each data point was 2
wt%. (c) Cartoon illustrating that the attraction between pure nanoparticles is effective
only over a fraction (Ac) of the available surface area (A) due to the limited range (6)
over which dispersion forces operate.

Despite the linear polymer distortion, we found a large miscible region exists for
crosslinked polystyrene nanoparticles blended with linear polystyrene (Fig. 3.3.b). The
data were determined from SANS through the presence or absence of fractal-like
scattering at small wave vector and at nanoparticle concentrations of 2 wt%. Fractal-like
behavior is indicative of a nonequilibrium state consisting of irregular phase separated
aggregates which exist on many length scales, despite the fact that the phase separation is
driven by a gain in equilibrium free energy. Data from the fullerene/linear polystyrene
and polyethylene nanoparticle/linear polystyrene systems are also included in this phase
diagram, indicating that this graph provides a useful guide for a range of nanocomposite
systems. The experimental data clearly demonstrate that if the linear polymer Rg is larger

than the nanoparticle radius then miscibility is promoted. Note that both the polymer R3
and nanoparticle radius were experimentally determined via SANS.

To experimentally determine the Flory I parameter we found the second virial
coefficient for 211 kDa tightly crosslinked polystyrene nanoparticles dissolved in 473
kDa deuterated linear polystyrene to be (5.3 i 3.4) x 10'5 cc-mol/g2 at 127°C and (2.4 :1:
0.6) X 10'5 cc-mol/g2 at 170°C, using SANS data and a Zimm analysis.” 84 A standard

127, 128

analysis, strictly valid for linear/linear architecture blends , yields Flory parameters

of x = - 2.7 X 10'3 (127°C) and - 1.2 x 10'3 (170°C), demonstrating that mixing is

favored at both temperatures. Note that Bates and Wignall ”9 found I to be ~ 10'4 for

55

deuterated polystyrene blends indicating that the negative mixing enthalpy is not due to
isotopic substitution. Furthermore, the z parameter is found to follow ~ + 0.01 — 6/T (K)
confirming that favorable enthalpic interactions, which are geometric in origin, are
responsible for the phase stability.

This unusual behavior is explained by considering the number of molecular
contacts between monomers in the isolated nanoparticle state compared to that of a
nanoparticle in the dispersed state as illustrated in the idealized model given in Fig. 3.3.c.
The energy gain of a monomer-monomer contact is taken to be sup. However, the van der
Waals force operates over an effective distance (6) so that only a fraction of the
nanoparticle area (AC) = [26/4a] X A has this favorable molecular contact. Here 2 is the
average coordination number of the nanoparticle aggregate. The remaining uncovered
surface area of the nanoparticle (AU E A-Ac) does not profit from favorable contacts with
other nanoparticles. Nanoparticles may thus gain enthalpically favorable monomer-
monomer contacts by dispersion in the polymer melt, as has been noted in recent PRISM
calculations. '09 Smaller nanoparticles do not experience this enthalpic driving force since
Ac tends towards A in this limit confirming that Coo fullerenes are miscible solely through
a favorable mixing entropy.

The mixing enthalpy of a nanoparticle, s, can be related to the Flory parameter via
s = AC1+AU (x-anp/kBD E so - s1. Here so = A x, is the insertion enthalpy in the absence
of geometric effects due to uncovered area and s, = AU X enp/koT is the reduction in
enthalpy within the pure nanoparticle phase due to uncovered area. The areas are
expressed in lattice site dimensions and so are dimensionless with so representing the

insertion energy per nanoparticle and 2’ that of a monomer unit. Even though the

56

uncovered area can be quite small on a given nanoparticle the enthalpy gain via
dispersion can be substantial due to their large number given by ¢/v,,p with v,,p being the
nanoparticle volume (4/3 zra3). So, the expected enthalpic stabilization is given by anp X
s, which exhibits a maximum at a nanoparticle radius of 26/2. This is truly a nanoscopic
effect since 6 is of order 1 nm and z, 6 for random packing)” making the optimum radius
for dispersion of order 3 nm, the size scale we have used in the present study. If the
nanoparticles are too small then solubility suffers from too little or no uncovered area to
achieve sufficient enthalpic gain, similar to that experienced by the fullerenes, while a
system containing larger particles has a reduced mixing enthalpy by a reduction in
nanoparticle number for a given volume fraction.

The above argument hinges on uncovered area developed by rigid particles (Fig.
3.3.c) and is related to an increase in the cohesive energy of a material from its pure state.
The dendritic polyethylene nanoparticle system is a liquid at room temperature and so
application of the cartoon to this system is suspect. However, using SANS of thermally
annealed samples we measured the virial coefficient for this molecule dissolved in 393
kDa linear polystyrene to be (2.1 :1: 1.7) X 10'5 cc-mol/g2 at room temperature yielding x
= - (1.7 i 1.3) X 10'3, again a negative mixing enthalpy is found. This result is
rationalized first by noting the density of this material was determined to be quite small,
0.81i0.02 g/cc, compared to the linear polyethylene amorphous density extrapolated to
room temperature '29, 0.86-0.89 g/cc. Secondly, the melt surface tensionm' '3' at 160°C
was measured and found to be : 30% lower than polyethylene of similar molecular
weight (236 kDa). Both these results point to a reduced internal energy in the isolated

nanoparticle melt by using the semi-empirical relation between the surface tension (ST)

57

and the cohesive energy density (CED = internal energy per unit volume); ST ~ CEDZ’3
'32 and is consistent with the enthalpy gain on mixing discussed above (i.e. negative x).
We generalized our observations by using a Flory lattice theory which has proven
useful in interpreting the phase morphology of complex systems such as nanoparticle
dispersion in polymer blends, where reasonable agreement with lattice density functional
theory has been demonstrated (20). The first free energy term considered is the mixing
entropy described by, Fn/VkoT = [¢ Iog(¢)]/vv,, + [(1-¢)10g(I-¢)]/N, where F". is the
entropic gain due to mixing, N, the number of monomers in the linear polymer and V, the
sample volume. Polymer chain expansion (Fig. 3.3.a) yields a loss of entropy and so a

'33“ '34 is included and approximated

“stretching” free energy cost (F3) for each molecule
by F/VkoT = 3/2 [1-¢][Rg2/Rg02 — 1]/N. Previous work ‘2“, '3“ has used a chain stretching
term which is based on the analysis of polymer brushes which does not show as large an
R3 variation with ¢ as we see experimentally. Combining the above terms, including the
enthalpy of mixing discussed above, we find,
opener = s is 11-¢1 + ¢Iogr¢2+t[1-¢110g(1-¢) +3/,.11-¢11R,2/R,.2 — 11 (0
where t = vvp/N, which in terms of experimentally accessible parameters is l =
[a/Rgoj3p/po, where p is the bulk density of the linear polystyrene melt and po is the
density associated with one chain in the bulk polystyrene melt (i.e. the density of a single
chain based on its Rg and molecular weight). The fact that t increases as the cube of the
size ratio a/Rgo implies that the stretching term is very unfavorable for a>Rgo, which is
the basic reason why large nanoparticles do not disperse.

For the case of polystyrene nanoparticles in a linear polystyrene melt, we estimate

the effect of the linear polymer stretch, the third term in Eq. (1), using the data of Fig.

58

3.3.a approximated by Rg/Rgo z 1+c¢. By setting the first and second derivatives of Eq.
(1) with respect to of to zero one finds the binodal at ¢3 = Exp(-[1+s+(3c-l)t]) = Exp(-

{l+s+(3c-l)[p/p1][a/Rgo]3}) and the spinodal at a, = I/[Zs+(6c-3c2-1)t] for small ¢. In

Ginzburg’s work ‘22

an addition non-ideal term, the Camahan-Starling term, is used to
assess interaction effects between nanoparticles which does not alter the binodal at small
concentration. Validity of the model is confirmed by calculating s from the predicted
binodal concentration assuming c is one (Fig. 3.3.a). Further, letting a/Rgo be one, to
delineate the phase boundary (Fig. 3.3.b), and calculating p/po (= 1.7 X \/(M(kDa)) for
polystyrene, M is molecular weight in kDa) then s values of -15 and -64 for molecular
weights of 30 kDa (Rgo = 5 nm) and 320 kDa (Rgo = 15 nm), respectively, are determined.

Dividing these values with the nanoparticle area results in x of order — 3 X 103, in good

agreement with the values determined above via neutron scattering.

Conclusion

We have shown that nanoparticle dispersion in a polymer melt is promoted when
the nanoparticle radius is less than the radius of gyration of the melt chains. In this size
regime, we find that z or s is negative for polyethylene nanoparticles in polystyrene and
also for polystyrene nanoparticles in polystyrene and we present a plausible enthalpic
mechanism for this effect based on packing arguments. Furthermore, as illustrated in the
case of fullerene dispersion into linear polystyrene, the processing procedure must be
carefirlly controlled in order to access the dispersed state, even when it is

thermodynamically favored.

59

CHAPTER 4

NANOSCALE EFFECTS LEADING TO NON-EINSTEIN-LIKE
REDUCTION IN VISCOSITY

 

Introduction

Rheology of particulate suspensions has a long history beginning with Einstein33
who demonstrated that the viscosity increase Brownian particles impart is solely a
function of the particle volume fraction (¢) and suspending liquid viscosity. This

100, 136

prediction has been experimentally confirmed many times when a simple or

monomeric suspending fluid is used. Suspension of particles in polymeric liquids

produces a similar viscosity increase137

even when clay-polymer nanocomposites are
studied.138 In the case of the clay system, the particles are nanoscopic in one direction and
significantly larger than the polymeric liquids’ structural length scale in the other two.
SiegelI39 described how mesoscopic physics or nanotechnology can change the
macroscopic physical properties of materials. Indeed Mayo et al.3" 32 demonstrated how
ceramic materials can change from brittle to ductile through grain boundary sliding when
cluster sizes below 15 nm are present. In a similar vein, Roberts et al.9 blended small
silicate clusters (radius, a ~ 0.35 nm) with linear polymers and observed a viscosity
decrease, again pointing to the unusual effect that nanoscale processes and materials may
provide. However, these particles are almost molecular in size and approach the
monomer length scale, so, interpretation may be clouded by delineating the difference

between a plasticizer molecule and nanoparticle. Indeed Roberts et al. state these small

clusters behave more like a solvent than a particle akin to the function of a plasticizer.

60

To unequivocally investigate this issue, polystyrene nanoparticles were suspended
in linear polystyrene to eliminate enthalpic interactions. Further, since the particles and
polymer are essentially the same material having the same refractive index, dispersion
forces are minimized'oo' ”0 creating a hard sphere system where only excluded volume
forces are apparent. Thus, this is an ideal system to study and delineate nanoscopic

effects without the nuisance of enthalpic or other forces.

Experimental.

Blends of the tightly crosslinked nanoparticles with linear PS were prepared
through co-dissolution in THF and rapid precipitation with methanol followed by drying
in vacuum at 40°C for a least a week to ensure complete solvent removal. The powder
was then compression molded under vacuum in a pellet press to ensure no trapped air
was in a sample. The samples were aged at 120-170°C under vacuum for several hours to
ensure homogeneity. The 8 mm diameter disks were placed on the 8 mm parallel plates
fixture of a Rheometrics ARES rheometer set at a gap of ca. 0.5 mm. Various
temperatures were used and the strain during the dynamic shear test was kept small
enough to ensure all response was in the linear viscoelastic region. Glass transition
temperatures were determined with a TA Instruments modulated differential calorimeter
model Q1000. Sample sizes on the order of 4 mg were used and the instrument was fully

calibrated.

61

Results and Discussion

Here, low polydispersity spherical nanoparticles (a ~ 3-5 nm), synthesized via an
intramolecular collapse methodology,ll are blended with linear polystyrene
macromolecules of approximately the same molecular dimensions. For example, at a
molecular mass of 52 kDa, with every fifth monomer unit crosslinked on average, the
nanoparticles are of order 5 nm in radius and comparable to the linear polymer radius of
gyration (Rg), 7.5-15 nm. Two types of nanoparticles were used, lightly crosslinked (2.5
mol% crosslinker) and tightly crosslinked (20 mol% crosslinker, see Fig. 4.1), that were
synthesized with a variety of molecular weights and hence molecular sizes. The
procedure is relatively simple and robust enough to produce gram quantities of

nanoparticles with controlled size and crosslinking densities from linear precursor chains.

62

12.8 mL/h Linear Chain Precursor

Crosslinking group
Cold benzyl ether
V = 40 mL
c = 0.1 g/mL
added at

A

Hot benzyl ether
250°C
V = 120 mL

   

Nanoparticle
Images in this dissertation are presented in color.
Figure 4.1. Cartoon of the intramolecularly crosslinked nanoparticles produced
from linear chain precursors having pendent crosslinking groups. Varying the
amount of crosslinker allows fabrication of lightly (2.5 mol% crosslinker) or tightly
crosslinked (20 mol% crosslinker) nanoparticles. Nanoparticles were produced by
dripping a solution into hot solvent to activate the crosslinking process. Typical
conditions of volume (V), concentration (c), flow rate and temperature are given.
Crosslinking imposes a particle-like nature to the linear precursor chains that
small angle neutron scattering (SANS) can delineate as shown in Figs. 4.2.a, b. Lightly
crosslinked nanoparticles exhibit very similar scattering behavior to the linear precursor
chains while the tightly crosslinked nanoparticles demonstrate a peak in the Kratky plot,
indicative of particle-like behavior. The similarity of the lightly crosslinked nanoparticles

to the linear polymer, at least in their segment density profile, translates to a likeness in

their rheological properties. This does not invalidate the hypothesis of Antonietti et all“

63

that crosslinked microgels and linear polymers are rheologically alike and indeed may

strengthen it since even light crosslinking will produce cycles within the molecule.

 

 

 

 

 

 

 

 

 

A 0.004 I I V B 0,012 l r I
0.010 - l
0.003
a!" a!" 0.0081135kDa
-< -<
'5 0.002 ~ 'g 0.006 ~ X
9, 3
52.0kDa
‘33 “33 0004+
“001 ' 25.3kDa
0.002 -/ 1
%\Linear
0.000 . . 1 0.000 . e .
0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20
41A") 0(A'1)

Figure 4.2. SANS spectrum for lightly and tightly crosslinked nanoparticles
demonstrating the particle-like nature of the nanoparticles when sufficient
crosslinking is present. a, Kratky plot of SANS intensity (I) multiplied by wave vector
(q) squared as a function of q for solutions of linear precursor polymer or lightly
crosslinked nanoparticle containing 2.5 mol% crosslinker. The lower concentration data
of 2.5 wt% are for the 158 kDa linear chain precursor polymer and nanoparticle while the
higher concentration curves, 5wt%, are for the precursor polymer and nanoparticle with
24.5kDa and 158 kDa nominal molecular masses. These data demonstrate the scattering
from the lightly crosslinked nanoparticles is equivalent to a linear polymer. All data are
in d-THF solvent and at 35°C. The plateau near 0.2 A'1 does not scale linearly with
concentration due to concentration effects. b, Kratky plot for the tightly crosslinked
nanoparticles containing 20 mol% crosslinker of various molecular masses (25.3kDa,
52kDa, 135kDa) compared to the linear chain precursors (curves labeled Linear). These
nanoparticles demonstrate considerably different scattering behavior to the linear
precursors with the curve maxima revealing particle-like behavior. Same solvent and
temperature as in a were used, concentration is 5 wt%. The maximum does not
significantly depend on the nanoparticle concentration.

64

A high wave vector plateau is present for the tightly crosslinked nanoparticles
after a local maximum, unlike the observed behavior for a homogeneous density hard
sphere.84 This phenomenon was seen by Tande et al.142 for poly(benzyl ether) dendrimers
suggestive of both particle and Gaussian chain behavior. The ratio, radius of gyration to
viscosimetric radius (determined from the intrinsic viscosity), call this P, is an important
quantity to delineate segment density profiles and physics.'9 The dendrimer system
displayed values that decreased from the Gaussian coil value (1.2-1.8, depending on
solvent conditions) to the homogenous hard sphere value (0.775 = V(3/5)) with increasing
generation number (molecular mass). The tightly crosslinked nanoparticles show a
similar phenomenon with P-values of: 1.24 (25.3 kDa), 1.15 (52.0 kDa) and 0.93 (135
kDa); in a good solvent (tetrahydrofuran, THF, at 35°C) that approach the hard sphere
value with increasing molecular weight. However, the constant segment density profile is
not achieved which contributes to the plateau in the Kratky plot. Thus, the tightly
crosslinked nanoparticles are intermediate between a polymer chain and homogeneous
density sphere and remarkably resemble the Gaussian soft sphere.I43 Indeed the Gaussian
soft sphere scattering form factor looks very similar to that for the tightly crosslinked
nanoparticles.

A critical feature of these systems is the poor dispersion resulting from
nanoparticle agglomeration and/or interpenetration in the tightly crosslinked nanoparticle
- linear PS blends. Indeed agglomeration may be expected due to depletion flocculation,

however, the results of Cosgrove et al.144

clearly show that 16 nm diameter silica
nanoparticles are stable in poly(ethylene oxide)/water solution up to high polymer and

particle concentrations. In this case, the particle half-separation distance is much lower

65

than the polymer Rg (equal to 10 - 35 nm) in many of their experiments and no evidence
of agglomeration is seen even up to particle concentrations of 18 vol% which must be
due to the nanoparticle size and scale.

The results in Fig. 4.3 for a 50 wt% blend show that the blends are well dispersed
since the intensity profile shows no upturn at small wave vector and no fractal-like
regime at high wave vector, therefore, compact objects are present. A Gaussian plateau
occurs and a fit for a hard sphere model together with a Lorentzian, to account for the
linear polymer conformation, yields an average particle size of 2.7 nm. From the
nanoparticle molecular mass and this radius one can calculate the nanoparticles have
collapsed to a density equivalent to bulk polystyrene. While the model results are not
conclusive it is clear that the 52 kDa tightly crosslinked nanoparticles have collapsed to a
smaller size than in dilute solution where the hydrodynamic radius is 4.8 nm in THF.
Clearly, the SANS results and modeling are suggestive of nanoparticles collapsed to a
density equivalent to bulk polystyrene, yet, a fractal-like nanoparticle network is not
present. Further, a highly contorted linear chain is suggested by the Lorentzian mesh
length of ~ 30 nm. We recognize that a mesh length of 30 nm is extreme and is justified

below.

66

103 1 1

 

102 ~

 

 

101 r

I (cm'1)

 

 

 

 

 

 

 

10° - -
0.00 0.05 0.10 0.15 0.20
-1
q (A )
10'1 ' J
10'2 10'1

q (A‘)

Figure 4.3. SANS spectrum for 52.0 kDa tightly crosslinked nanoparticles blended
with 63 kDa linear d-polystyrene at 50 wt% with the incoherent background
subtracted from the intensity. The solid line represents a hard sphere fit, including

polydispersity, and a Lorentzian (1(0)/[1+52q2], E, = 29.5 i 0.2 nm and [(0) = 623 i 7 cm'
) to account for the deuterated polystyrene chains’ conformation. The mean nanoparticle
phase’s radius from the hard sphere fit is 2.66 nm 3: 0.01 nm, polydispersity (standard
deviation divided by mean) is 0.942 1r 0.001 and the volume fraction is 0.45. Power laws
of 3 and 4 are shown, neither is satisfactory, suggesting that a fiactal network is not
present. The inset is a Kratky plot of the same data (solid line) compared to data for the
same nanoparticles in dilute solution (0.05 wt% in THF at 35°C) demonstrating increased
scatterer size. The intensity is in arbitrary units and the curves were shifted to overlap at
high q.

The (complex) viscosity was measured as a function of frequency as shown in
Fig. 4.4.a. Different temperatures were used and time-temperature superposition was
followed to create a master curve at a reference temperature of 170°C. The neat tightly
crosslinked nanoparticles do not exhibit a terminal viscosity even at very low
frequencies. It is clear that all blends, even up to 80 wt%, show a terminal (zero
frequency) viscosity.

The terminal viscosity was determined from the data and found to decrease upon

nanoparticle addition (Fig. 4.4.b) despite the fact that the pure 52 kDa nanoparticles show

67

no terminal viscosity.m Concentrations of order 50 wt% demonstrate a viscosity
decrease by a factor of 4 while predictions from either the Einstein or Kreiger-
Dougherty145 models suggest a large viscosity increase. For example, utilization of the
Kreiger-Dougherty model estimates the suspension — pure polymer viscosity ratio should
be ~ 10 rather than the measured 0.2-0.3. Further, the 80 wt% nanoparticle blend displays
a terminal viscosity when a gel-like response is expected at such high concentration.100
This result points to nanoparticle shape change and possible agglomeration and polymer
interpenetration. However, if significant agglomeration were present a viscosity increase

should occur.

68

Complex Viscosity / Pa-s

Viscosity ratio u!

0

T9 (°C)

 

107 : TITIIII 'll'lfl‘ Inum' run-'1' llllllI‘ 'llllll‘ 111111" llllll" 1111"

1 111‘

10°

1 1'1"]
1 I 111111]

I l IItlrI]

103

l l Illlll'

1 1|11u1l

T l I runl

 

 

 

 

103 10'2 10'1 100 101 ‘102 103 104 105 10‘5

 

I | r l V l ' l

 

 

 

0.0 0.2 0.4 0.6 0.8 1.0

Mass fraction
108 _ I I I I _‘

 

      

[I'llill'

 

 

96 | l I l
0.2 0.4 0.6 0.8

 

.0
o
.3
0

Mass fraction

69

Images in this dissertation are presented in color.

Figure 4.4. Viscosity and glass transition temperature for 52 kDa tightly crosslinked
nanoparticles, 75 kDa linear polystyrene and their blends. a, Viscosity versus
frequency (measured with a Rheometrics ARES rheometer) for the neat nanoparticles
(NP 52k), neat linear polystyrene (PS 75k) and selected blends containing 10 wt%, 50
wt% and 80 wt% nanoparticles. Note the pure nanoparticle system shows no terminal
viscosity. Various temperatures were used and time-temperature superposition was
followed, the reference temperature was 170°C. b, Terminal viscosity of the blends
divided by neat 75 kDa linear polystyrene viscosity versus 52 kDa tightly crosslinked
nanoparticle mass fraction. c, Glass transition temperature (T g) measured with
differential scanning calorimetry (TA Instruments Q1000) for the blends showing a
general decrease with nanoparticle addition up to moderate volume fractions. Note the T g
for the two pure components are equal.

Slip or inhomgeneous flow could account for the viscosity decrease.98 This was
checked by using different gaps between the parallel plates used to characterize the
viscosity, gaps from 100 — 500 um were utilized with the 10 wt% blend and no gap effect
was seen, thus, slip and inhomogeneous flow is not a factor in the rheological
measurements.

Supplementary testing with the blends shows a concomitant glass transition (T g)
decrease with nanoparticle addition, despite each component having almost identical
Tg’s, see Fig. 4.4.c. It should be noted that Tg does not change when the lightly
crosslinked nanoparticles are added to the linear polystyrene, both have equivalent T g’s,
and the viscosity is intermediate between the two components following a normal mixing

rule based on the weight average molecular mass. Starr et al.'46

show a polymer Tg
reduction near nanoparticles when excluded volume interactions are present, however, if
an attractive potential is present T g is predicted to increase. As discussed above, we have
an ideal system that can only interact via excluded volume. Yet, it is believed our system

is different to the simulations performed by Starr et al. as they do not specifically

simulate confinement effects. However, similar results of a Tg change are seen in

70

confined thin polymer films,147 although it is admitted here that this is a complicated and
rapidly advancing area. It is hypothesized that nanoparticle confinement effects produce
the T g decrease since the interparticle half-gap (h) achieves quite small values. Further,
all the data in this work are at concentrations where h is less than or equal to Rg.

Using a simple relation (h/a z [¢,,/¢]”3 — 1, ¢,,, = 0.638) or an empirical relation
developed from Cosgrove et al.’s dataI44 (h/a z [3.11/¢5]”4‘34 — l, 0.18 > 111 > 0.03) yields h
equal to 0.2 - 1.4 nm for a volume fraction of 0.5. A half-gap of order 1 nm is much
smaller than the linear polymer Rg and approaches the monomer length scale and so
produces severe chain confinement and distortion. Note the above relations do not
include the volume of the interstices between the particles which is substantial thereby
allowing some volume for the polymer to occupy. However, the polymer molecule is
distorted as confirmed through the SANS modeling in Fig. 4.3 where the Lorentzian
mesh length is of order 30 nm. This is an exceptional value and can be rationalized by
realizing the nanoparticle volume fraction is 0.5 making the volume ratio of nanoparticle
(VNp) to linear polymer (V125) equal to unity. The volume ratio is equal to the ratio of
length scales to the third power ([de/dps]3) and the mesh length, if, is de + dps.
Realizing the polymer length scale will be on the order of twice its radius of gyration (~
7nm) one finds ; equal to 28 nm in agreement with the model fitting parameter. This
clearly indicates some degree of distortion.

Both the virgin linear polymer and its blend with tightly crosslinked nanoparticles
follow time-temperature superpositionl3 with similar shift factors. The terminal viscosity
of the pure linear polymer is plotted as a function of temperature above T g in Fig. 4.5.a

and the usual viscosity decrease with increasing temperature is apparent. Graphing the

71

blends’ viscosity in a similar manner, thereby accounting for the T g decrease, shows the
viscosity is a unique function of temperature above the glass transition temperature.
Nanoparticles do not, apparently, contribute to the hydrodynamics of highly
entangled linear polystyrenes with molecular masses of 75 kDa and 393 kDa as shown in
Fig. 4.5.b. If they did then the viscosity would follow Einstein’s model33 at low
concentrations or Batchelor’s correction for moderate concentration148 and it is
graphically shown that these relations are not followed. Larger particle systems in
polymer melts clearly produce a viscosity increase‘37 and so our results are a unique
product of a nanosystem. To expand on this point we measured the viscosity of 1.6 pm
diameter latex microspheres (polystyrene crosslinked with divinylbenzene) blended with
75 kDa linear polystyrene. The results are shown in Fig. 4.5.b and a clear viscosity

increase is seen in agreement with previous results.

72

 

    

 

 

 

 

 
    

 

107 l l I l l I 7
I -0— PS 75kDa
6 e 5%
1° ' e 10%
A e 18%
3 10, _ e 25% _
g I 36%
g“ I 50%
8 104 _ I 65% _
g2 I 80%
103 -
' I?
102 l l I l l l I
20 30 40 50 60 70 80 90 100
B T ’ T9 (K)
I I I I l l
1.4 ~170°c E -
1.2 - -
o Einstein prediction
:5 1.0 - -
E
g 0.8 - -
g PS 393kDa
0.6 — E -
j . ._
' PS 75kDa
02 l l l l l l

 

 

0.00 0.02 0.04 0.06 0.08 0.10
Mass fraction
Images in this dissertation are presented in color.
Figure 4.5 Graphs showing how the viscosity changes with temperature and
nanoparticle concentration. a, Viscosity of 75 kDa neat polystyrene and nanoparticle

blends as a firnction of T-Tg. Open circles are the viscosity for the neat polystyrene while
the other symbols represent data for tightly crosslinked 52 kDa nanoparticles dispersed in

73

the same polystyrene at various mass concentrations (5 - 80%). The measurement
temperature range for all systems was 140 — 190°C with some extending down to 130°C.
There is no clear trend with concentration and it is hypothesized that the viscosity is a
unique function of distance from the glass transition temperature. b, Comparison of the
lower concentration blends containing the tightly crosslinked 52 kDa nanoparticles in 75
kDa linear polystyrene (blue squares) and 393 kDa linear polystyrene (blue circles) at
170°C to the Einstein prediction. It is clear that a hydrodynamic contribution to the
viscosity, in the contemporary sense, is not provided by the nanoparticles. To the
contrary, addition of 1.6 pm diameter crosslinked polystyrene microspheres shows the
conventional viscosity increase with particle addition to 75 kDa linear polystyrene (white
squares).

Thus, we expect that the nanoparticles affect a physical process within the
polymer melt. Based on the increased free volume silica nanoparticles produce in poly(4-
methyl-2-pentyne)10 and that expanded polystyrene coils have a 45°C glass transition

temperature decrease,149

as well as our results in Fig. 4.5.a, we investigate whether
nanoparticles can induce a free volume increase. It is simple to determine that if a
spherical excluded volume of thickness A exists around each nanoparticle then the
fractional free volume is increased by approximately 3A/aX¢ assuming the continuous
phase’s (i.e. linear polystyrene’s) free volume does not change in the bulk. The fractional
free volume increases by order 0.0], a significant change,13 for a 0.1 nm shell thickness
and the volume fractions used in this study. This free volume increase could explain the
glass transition temperature decrease and apparently the viscosity decrease as well.

Based on the work of Merkel et al.10 it may be expected that free volume is a
critical factor in determining the rheological behavior, yet, the concepts of
entanglements” or reptation"7 have not been addressed. The terminal (zero shear)
viscosity for all nanoparticle concentrations is lower than that of neat polymer as shown
in Figs. 4.4 and 4.5. However, concentrations above approximately 18 wt% have a

viscosity at large frequencies higher than or approaching that of the virgin polymer, the 5

wt% and 10 wt% blends have a viscosity that is always lower than the pure polymer. The

74

80% blend exhibits minimal shear thinning and a large viscosity at high frequencies (see
Fig. 4.4.8), yet, the loss modulus is always larger than the storage indicative of enhanced
dissipation. This is in contrast to the neat nanoparticle system that has an equilibrium
storage modulus at small frequencies. These are unusual effects and could indicate
constrained polymer chains as well as entanglement or reptative changes.

Yet, drawing from the scaling theory presented by deGennes67 and furthered by
Doi and Edwards'50 one finds the terminal viscosity (110) should scale as GNOtRX [M],
where GNO is the plateau modulus, tR, the Rouse time scale, M, the polymer molecular
mass and MC, the mass between entanglements. Further, simple rubber elasticityl3 shows
that the plateau modulus is given by a simple combination of the density (p), gas constant
(R) and temperature (T) as well as the entanglement molecular mass, pRTM. Should the
viscosity reduction be caused by an increase in Me, representing a decreasing number of
entanglements, one would expect both the plateau modulus and the terminal viscosity to
decrease. This does not seem to be the case. No clear trend of plateau modulus with
nanoparticle concentration is seen and its average for all concentrations is approximately
the same as that for the pure polymer. For example, the plateau modulus for 393 kDa
linear polystyrene is (1.7i0.1)X105 Pa, the average values for the polymer-nanoparticle
composites are (l.5i0.3)XlO5 Pa and (1.73:0.2)X105 Pa for 52 kDa and 135 kDa tightly
crosslinked nanoparticle blends, respectively. Further, at constant concentration (5-10
wt%) of the 52 kDa tightly crosslinked nanoparticles, the viscosity scales with the linear
polymer molecular mass to the 3.5 power while neat linear polymer shows a scaling of

3.6 for the molecular masses studied. These are power laws close to that found in the

75

literature for entangled linear polymers,13 if the polymer were completely disentangled a
power law of one is expected.

Thus, entanglement modification does not explain the observed viscosity decrease
and, as shown in Fig. 4.5.a, a free volume increase produces the effect. This manifests
itself through the Rouse time scale and its subsequent relation to the monomeric friction

factor in an unusual manner.

Conclusion

We have discussed how free volume as well as certain configurational changes to
the linear polymer must account for the viscosity decrease. The exact mechanism is
unknown at this point and is a challenge for theoreticians. However, it is clear that
nanoparticles do not contribute hydrodynamically to the viscosity in the traditional sense
predicted by Einstein. Rather they produce a change in the polymer conformation and
free volume to reduce the viscosity. In other words, the system’s properties change with
nanoparticle addition and different physics come into play to produce the viscosity

decrease.

76

CHAPTER 5

EFFECT OF IDEAL, ORGANIC NANOPARTICLES ON THE FLOW
PROPERTIES OF LINEAR POLYMERS: NON-EINSTEIN—LIKE
BEHAVIOR

 

Introduction

The terminal viscosity of polymer melts is an increasing and unique fimction of
molecular mass (M). Below the critical mass for entanglement couplingl3 (MC) the
viscosity scales as M while above M, a much larger power law is evident, approximately

63'“ (see Fig. 5.1, data from Fox and F lory63' 64, Mackay and Henson98 and

3.4-3.8 power
this work are included in the figure). The lower, or Rouse,15 I regime actually occurs over
a relatively small mass range unless correction to constant fiactional free volume (I) is
made. The upper regime has an enhanced power law due to what has been denoted as
entanglements whose physics can be described by reptation.“ '50 Regardless of the
physical process'52 unique flow behavior occurs at MC evidenced by the power law
change. i

The exact mechanism that causes entanglement coupling is not truly known,
however, it is clear that the free volume is essentially constant for masses greater than MC.
Below this critical mass the free volume changes essentially in concert with the specific
volume. This observation does not give a fundamental picture of the complicated

polymer dynamics and merely provides empirical foundation to likely explanations that

incorporate a constant free volume within an entangled polymer melt.

77

An interesting study was performed to elucidate how entanglements, or lack
thereof, affect the flow behavior of polymer melts.153 Polymer molecules were freeze
dried or crystallized from dilute solution then physically compressed and viscosity
measured; no change in viscosity was found after the first 20 mins, the time for the first
data point to be recorded. This is in contradiction to the results of Liu and Morawetz'54
who show that individual polymer molecules take an extraordinary length of time (> 16
h) to reach equilibrium in a melt. However, Farrington155 determined that the storage
modulus (G’) changed significantly within the first 20 mins for samples prepared similar
to above or for microemulsion polymerized polystyrene nanoparticles that were allowed
to interdiffuse upon heating (particle size ~ 40 nm, M ~ 106 Da). This process depended
on temperature and when compared to the relaxation or reptation time (to) approximately
lOXtd was required for equilibrium. Although this study could follow the kinetics of
entanglement formation, the true equilibrium, in accord with the work of Liu and
Morawetz, was not achieved suggesting polymer melts are either never at true
equilibrium and/or flow properties are not sensitive to non-equilibrium structure.

Despite the apparent difficulty in robustly degrading entanglements through
physical means one can eliminate them through flow.‘56 Shear can reduce entanglements
or constraints,157 and as shown in Fig. 5.1, the possible change in viscosity to the fi'ee
Rouse chain limit exemplifies the overall effect of entanglements. If entanglements could
be eliminated by solution precipitation techniques one would expect the Rouse limit to

similarly apply.150

78

 

  
     
    

 

 

 

 

 

 

 

 

 

 

 

 

 

   
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I l I I 1111' I l l l l TIT]
6 ._ 1.51700 , Entangled regime _
10 M3.6810.12
5 _ . -, ., ,, _,
1O . Entanglement
A 4 ‘ change
«1110-- _.
<0
9, 3
g, 10 “' Rouse regime, ’ ' * " -- -- -+
e 1 ;
m . .
° 2 T _
g, 10 l—w - ~~~~~ 3 ~ Mc-32.7kDa-J
>
10 ‘— . ..
O Fox&Flory
100 'r- ’ 0 Mackay&Henson -11
Free volume I This work
-1 © change 7
10 01 4‘! 11111! 4.5 1 11114112 1 E:
2 4 6 8 1 2 4 6 8 2 2 4
10 10

Molecular mass (kDa)

Figure 5.1. Viscosity as a function of molecular mass (M) for polystyrene melts at
170°C. Data from Fox and Flory”, Mackay and Hensons and this work are used to show
how, below the critical molecular mass for entanglement coupling (MC) the Rouse model
is followed, except from deviations caused by a free volume change. Above M; the
entangled regime results with a much larger power law exponent of viscosity with M.
Changes in the entanglement structure or dynamics could reduce the viscosity to the
Rouse limit.

It is conjectured that thin polymer films next to hard surfaces'” '59

change
polymer entanglement160 with minimal change in the radius of gyration (R8) parallel to
the substrate.”" So it was hypothesized by us that nanoparticle inclusion could affect

polymer flow in a more robust manner compared to precipitation techniques discussed

79

above due to the introduction of a vast number of hard surfaces by the nanoparticles. Yet,

addition of particulates to polymer melts demonstrates complicated behavior,137

although
continuum relations provide methods to data correlation. In Einstein’s seminal
manuscript,33 it was shown that the viscosity increase Brownian particles provide scales
with the particle volume fraction, ¢ (r7=r7,[l+2.5¢], where 17 is the solution viscosity and
77, is the solvent viscosity). A viscosity increase has been observed in many systemsloo
even when small (~260 nm) polystyrene latex particles"52 and nanoparticles (~ 56 nm)
made of silica163 were studied. These systems have particle sizes much larger than the
suspending fluids’ molecular size and so continuum expectations introduced by Einstein
are followed.

Of course, when the particle becomes molecular in size it is possible to see

deviations. Edward'64

surveyed the literature to find when the Stokes-Einstein (SE)
relation could not be applied to diffusion of molecular penetrants in simple fluids such as
water and carbon tetrachloride. When the penetrant’s radius (a) became 2-3 times that of
the suspending liquids’ then deviations from the SE relation were evident. This is
equivalent to stating that the numerical factor for the friction coefficient 4 (E 67r r750) is
no longer 6 and decreased in value when very small penetrants were considered.
Deviations from the SE relation have been observed in diffusion of tracer spheres
in polymer solutions.'65 In this case, however, the most significant deviation occurred at
high polymer concentration with large spheres (a ~ 1 pm) rather than smaller (0 ~ 20
nm). The explanation given was that shear thinning influenced the diffusivity. More

recent work has concentrated on this effect to determine the microrheology or local

viscosity of polymer solutions (see e. g. Lu and Solomon'66). This phenomenon is argued

80

as related to local scale heterogeneity of the polymer solution. Further, larger particles
were found to diffuse faster than smaller and this may be akin to the principle of size
exclusion chromatography as the larger particles take a less circuitous route through the
heterogeneous structure.

The situation is different in polymer melts such as poly(dimethyl siloxane) or
PDMS. Roberts et al.'67 showed that a larger silicate nanoparticle (a = 2.8 nm) followed
the SE relation as long as an adsorption layer of PDMS was considered. The 5 kDa
polymer’s radius of gyration (Rg) was 2.0 nm and so the particle and polymer were of the
same size. Of course, the particle is much larger than the PDMS monomer unit. When a
smaller nanoparticle was investigated (a = 0.44 nm), which is closer in size to the
monomer unit and much smaller than the polymer as a whole, anomalous behavior was
observed and the particle appeared smaller than its true size, at least in a hydrodynamic
sense. The authors state that this smaller nanoparticle behaved like a solvent while the
larger as a colloidal particle. Note MC for PDMS is 24.5 kDa13 and so all the studies by
Roberts et al. were conducted in an unentangled polymer melt.

Recently, Zhang and Archer'68

studied the effect of the nanoparticle-polymer
interaction parameter, in blends of poly(ethylene oxide) (PEO) and silica nanoparticles
(~12 nm diameter). Pure silica nanoparticles are strongly interacting (physisorption) with
PEO. It was seen that even a very small addition of nanoparticles caused a large increase
in viscosity of an entangled PEO system, probably by formation of a polymer-

nanoparticle network in the melt. When the nanoparticle surface was chemically modified

by grafting an oligomeric PEO terminated with a trimethoxy silanyl group, no network

81

formation was found. Further, there was no change in the viscosity of the polymer melt
on nanoparticle addition.

The above provides a brief introduction to the complicated dynamics of polymer
melts and highlights that the size and scale of nanoparticles compared to polymer
molecules could yield interesting behavior. The nanoparticles used in this work have a
size between 5 — 10 nm which is much larger than a monomer unit (~ 0.3 nm). Polymers
in contrast to simple fluids, like water, have an equilibrium configuration that spans 10 —
20 nm and so the nanoparticles are smaller than the polymer molecules. Further, the size
associated with entanglement coupling is approximately 5 — 10 nm and is of the same
size as the nanoparticles. Clearly, the nanoscopic size chosen here could disrupt the
polymer dynamics.

In our previous study,8 we investigated the effect of polystyrene nanoparticlesll
on the flow properties of entangled polystyrene melts. This is an ideal system since the
particle and polymer are chemically equivalent, and have a similar refractive index,
thereby reducing if not eliminating dispersion forces.169 Thus, the system was equivalent
to hard spheres dispersed in an entangled polymer melt.

The terminal (zero shear) viscosities of the systems were always found to
decrease upon nanoparticle addition, paralleling the reduction of the glass transition
temperature (T g). The plateau modulus (Go/0) was not affected and so it was argued that

the entanglement densityl3’ '50

was not affected. Further, a graph of the terminal viscosity
with temperature (7) above T , or T -T , resulted in a master curve suggesting that the

nanoparticles caused a glass transition temperature decrease and the viscosity reduction

related to a free volume change. Evidently the free volume change of unentangled melts,

82

concomitant with the excess viscosity reduction below the Rouse limit, is translated to
entangled melts (see Fig. 5.1).

Free volume could be readily incorporated by nanoparticles through their high
surface area to volume ratio.10 Assuming an excluded volume layer of thickness A exists
around each nanoparticle, the fractional free volume (f) within the linear polystyrene
matrix is increased by ~ 3¢A/a. The free volume increase can be quite large for
nanoparticles; assuming a volume fraction of 0.1, exclusion layer thickness of 0.1 nm and
radius of 3 nm results in an f increase of 0.01 which is a 10-20% increase in free volume
at typical melt temperatures. A colloidal scale particle (a ~ 300 nm) produces a much
smaller fractional free volume increase, 0.0001.

It was anticipated by Mackay et al.8 that the viscosity decrease was a much more
complicated phenomenon than a mere free volume increase. This became evident when
the average interparticle half gap (h) was determined. Twice this distance represents the
average distance separating particles and is approximated by

Ma = [MW — 1 (5.1)
where ¢m is the maximum random packing volume fraction (~ 0.638). Since the half gap
scales with nanoparticle radius, this variable can become quite small at modest loadings.
For example, a 3 nm radius nanoparticle at a volume fi'action of 0.1 suspended in a liquid
results in an average half gap of ~ 2.5 nm and is much smaller than the entangled linear
polymer’s Rg. Thus, it appears easy to confine linear polymers between nanoparticles at
moderate volume fractions as long as they don’t agglomerate (depletion flocculation).
The systems discussed by Mackay et al. were all confined (i.e. h < Rg) and the linear

polymer had masses above MC.

83

We were able to confirm through small angle neutron scattering (SANS) that our
system did not significantly agglomerate even at volume fractions of 0.5. This result
agrees with Cosgrove et al.’s study144 for a poly(ethylene oxide) - water system
containing silica nanoparticles (a = 8 nm). They found that negligible particle clustering
was evident possibly because the nanoparticles are smaller than the linear polymer (Rg ~
10 -— 35 nm). It can be hypothesized that continuum argumentsI70 are no longer valid in
nanosystems and when Rg/h approaches and exceeds one that phase separation and
agglomeration does not occur.

In the present study we extend our results to gain further insight into this unique
phenomenon of a viscosity reduction when nanoparticles are added to polymer melts. The
ratio Rg/h was greater than one in the previous study8 indicating that the linear
macromolecules in the continuous phase were always confined. Here the ratio is made
less than one to determine the effect of this variable under different conditions. In
addition, a wider range of nanoparticle sizes and polymer molecular masses are used to
elucidate the effect of size and molecular architecture on the flow properties of polymer

melts.
Experimental

Materials and synthesis. Linear polystyrene (PS) was purchased from Scientific
Polymer Products at molecular masses of 19.3, 31.6, 75.7 and 393.4 kDa. Details of these

polymers are given in Table 5.1. The radius of gyration was determined by a relation

developed fi'om data of Cotton et al.17' (Rg(nm) = 0.87 \/ M(kDa), a deuterated polymer

84

has a prefactor of 0.84) The nanoparticles (NPs) were synthesized by intramolecular
crosslinking, details of the process are provided elsewhere.ll All the nanoparticles used in
this work were tightly crosslinked (20 mol% intramolecular crosslinking). It should be
pointed out that the solubility parameter for the polystyrene nanoparticles matched that
for linear polystyrene (9.1 - 9.2 (cal/cm3)”2) determined by measuring the hydrodynamic
radius in various solvents via dynamic light scattering. The solvent producing the largest
radius is assumed to have the same solubility parameter as the polymer. All solvents were

purchased from Sigma-Aldrich and used as received.

Table 5.1. Polystyrene materials used in this study.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample Mw (kDa)'l Mn (kDa)" Condition
PS l9kDa 19.3 18.1 Linear
PS 3lkDa 31.6 28.9 Linear
PS 75kDa 75.7 64.7 Linear
Ps 393kDa 393.4 339.1 Linear

d-PS 155kDa 155.8 130.9 Linear
25 kDa NP 27.3“ 25.3“ Crosslinked
52 kDa NP 61.3“” 52.0“ Crosslinked
135 kDa NP 162.0“ 135.0“ Crosslinked

 

a MW is the weight average mass and Mn is the number average molecular mass.
b Based on the assumption that a single chain collapses to give a single nanoparticle. The
masses for the linear chains were determined by GPC.

Sample Preparation. Blends of the PS nanoparticles with linear PS were
prepared through co-dissolution in THF and rapid precipitation with methanol} ”6

followed by drying in vacuum at 50°C for at least a week to ensure complete solvent

removal. The powder was then molded by compression, under vacuum, in a pellet press

85

(8 mm diameter) to ensure that no trapped air remained in the sample. The samples were
aged at 130—170°C, under vacuum, for several hours to ensure homogeneity.

Rheology measurements. The 8-mm diameter discs obtained from the pellet
press were placed on the 8-mm parallel plates fixture of a Rheometrics ARES rheometer
set at a gap of approximately 0.4 mm. Measurements were done in the dynamic
(oscillatory) mode. Frequency sweeps in the range 0.1-100 rad/sec were performed at
various temperatures. These were then combined using time-temperature superposition87
to yield a master curve at 170°C (all quoted temperatures refer to the surface temperature
of the lower plate). The strain during the dynamic shear test was kept small enough to
ensure that all response was in the linear viscoelastic region. A dwell time of 8-10 mins.
was allowed at each temperature for the samples to attain a uniform melt temperature,
before commencing measurements.

Differential scanning calorimetry (DSC) measurements. A TA instruments Q-
1000 DSC was used to perform all glass transition measurements. Each sample was
subjected to at least three heating - cooling cycles, where each cycle consisted of heating
the sample from 0°C - 200°C, at a rate of 5°C / min, followed by cooling back to 0°C,
also at 5°C / min. The inflection point for the heat flow as a function of temperature was
taken as the glass transition temperature for a particular cycle. The glass transition
temperatures reported in this work are the mean of the glass transition temperatures
obtained from the second and the third run cycle.

Relaxation spectra. The RSI Orchestrator software available with the ARES
rheometer was used to evaluate the continuous relaxation spectra, using both the 0’

(storage modulus) and G” (loss modulus) data. An algorithm developed by Meadm' '73

86

was used to model the relaxation modulus as a discrete N element Maxwell line
spectrum. In such a case the storage and loss moduli for a system are given as

' N t 2
0(a)) =§G 1-(——’——a()w :1), (5.2.a)

N

G"(a) -2G,

.-1 1+(wt [)2 (5.2.b)

where (0 is the frequency, t. are the time constants and G. the corresponding
moduli. The discrete relaxation spectra are converted to a continuous relaxation spectrum
based on the work of Baumgaertel and Winter.174 They developed the ‘parsimonious’
model to mimic a continuous relaxation spectrum, based on the idea that the discrete
relaxation times should be freely adjustable so as to converge to the characteristic
relaxation values for the material under study. Then, for a system having equally log-
spaced time constants, the continuous H(t,~) and the discrete spectra are related by a

simple scale factor
G. = H (t.)log(R) (5.3)
where R is the ratio of successive time constants.
Small Angle Neutron scattering (SANS). The SANS experiments were

performed on the compression molded samples at the SAND instrument of IPNS at

Argonne National Laboratory.‘75 Neutrons are produced at IPNS with a pulse frequency
of 30 Hz and wavelengths (71.) in the range 1.4 - 14 A. The instrument has a fixed detector
distance of 2 m, which results in an instrument q range of 0.005-0.6 A" (q=47r//1 sin( 61/2),
where 6 is the scattering angle). The instrument detector was a 40 X 40 cm2 area sensitive

3He detector with 128 X 128 channels. The scattering time for the samples was 2 hours.

87

The raw data were absolutely calibrated using a silica standard, following the
described procedure at IPNS.176 All samples were also run in transmission mode for 15
minutes to aid in the calibration.

Kratky plots. The description of scattering from polymer chains in their theta
condition (second virial coefficient, A2 = 0) was first postulated by Debye.” For a
Gaussian distribution of segment density within the coil the scattering firnction (or

differential cross-section)1(q) is given as””‘77

I(q) = is x mm“ {2(exp1—(qR. )“1 + <ng )“ —1)/(qR.>“ } (5.4)
Here, ¢ is the volume fraction of scattering centers, V, the volume of a single
scattering center and (21p)? the difference in the scattering length densities between

solvent and scatterer (or the contrast). In the high q limit (practically q > 5R8," ),18 eq. 5.4

reduces to

I(q)><q2 = 2¢>< V(A10)2 /(Rg2) (5.5)

The plot showing the variation of I(q) qu with q is known as a Kratky plot. For
any given sample, ¢, V, 21p,Rg are constant, thus, from eqs. 4 and 5, for an ideal,
Gaussian coil the Kratky plot should asymptotically approach a constant value (plateau)
at high q values.

The Kratky plot is a good indicator of the polymer’s inherent molecular
architecture as it reflects the short-range interactions acting along the polymer chain from
neighbor to neighbor, such as bond forces and hindrance of rotation. Deviations from the
asymptotic behavior (as observed for a polymer coil) in the Kratky plot indicates non-

ideal arrangement of the polymer segments. A constant density sphere has no plateau and

88

a series of ever decreasing peaks is seen. Both ring and star polymers have a peak
(maximum) prior to the asymptote revealing different distributions than linear

polymers.84

Results and Discussion

SANS serves as an important tool to determine the degree of dispersion as well as
the molecular architecture of polymer nanoparticles, both in solution and melt states. This
technique is especially useful for this system as there is no optical or mass contrast
between the PS nanoparticles and linear PS, eliminating the possible use of light or x-ray
scattering, as well as electron microscopy, for characterization.

Fig. 5.2.a shows the Kratky plot for a 2% blend (by mass) of the 52 kDa NP in
deuterated-155 kDa linear polystyrene. The background was deuterated-polystyrene, and
hence the data shows scattering from the nanoparticles. The peak in the Kratky plot is
immediately apparent, indicating that the intramolecular crosslinking induces a particle
like nature to the molecules.142

Fig. 5.2.b shows the scattering intensity from the same sample as a function of the
wave vector q. It can be seen that the intensity is not a power law function of q, instead
the intensity goes to a plateau in the low q regime, confirming the absence of phase
separation (depletion flocculation) of the nanoparticles, which has been a common

problem with other nanoparticle-polymer blendsm’ ”9

89

 

 

5x10 TIIITTIIIIIIITIIIIIII fjrI TIIIIIII""I II1II

     

 

 

 

 

(a) 52kDa NP in d-PS 155 koaj 10 (b) 52kDa Np in d.ps 155 kDa
PA 4 — Polydisperse sphere—
.E 2 form factor
0 ’ ‘ ~-" 1
‘1‘ 3 _ “ 'E
< I 1 0
Z: . Sphere form factor - v
g 2 -_ Parameters from Guinier fit; 9 0.1
N— . - x
c' _ _
1 f ‘ 0'01 Fit to polydisperse sphere forTn fact-or
Mean radius 2.3 t 0.02 nm
: Radius spread. 0.8 :t 0.03 nm
0 I'll I 1111 , 1L4 0.001 1.1 1 111414I..111 I1 I411
0.00 0.05 0.101 0.15 0.20 2 4 6 “0, 2 4 6 8
q (A ) q (A4)

Figure 5.2. (a) Neutron scattering intensity (I) multiplied by the wave vector (q) squared
as a fimction of wave vector (Kratky plot) for 2 wt% 52 kDa NP blended with d-PS 155
kDa. The peak is associated with globular objects and the associated Schulz polydisperse
hard sphere fit reasonably represents the data (mean radius of 2.3 :h 0.02 nm with a radius
spread of 0.8 :1: 0.03 nm). The other curve is the result of a simulation assuming a
monodisperse system of spheres with a radius given by the Guinier result (4.0 nm = ‘1
(5/3) X 3.1 nm). (b) Log-log graph of intensity versus wave vector for the same system
and the associated polydisperse hard sphere fit.

Also, shown in Fig. 5.2.a, is the Kratky profile for a monodisperse hard sphere
system having the same radius of gyration as the nanoparticles determined with the

Guinier technique. The Guinier approximation is applied in the low q scattering regime,

when q X Rg is small and can be written as

 

log I (q) = log 1(0) -

R 2
(q 33) (5.6)

where 1(0) is given by ¢V(Ap)2. The Guinier plot,86 log(I(q)) versus q), allows
determination of Rg and, further, can be used as a concentration check through the

neutron intensity at zero wave vector, which we have done.

90

The parameters determined from the Guinier fit do not represent the data well due
to the slight sample polydispersity. This becomes apparent when the scattering data are
fitted to a polydisperse hard sphere model by assuming a Schulz distribution'80 arriving at
a mean radius (<a>) of 2.3 :1: 0.02 nm and a radius spread of 0.8 :1: 0.03 nm; the fit is
shown in Fig. 5.2 to be reasonably representative of the data. These values yield a radius
polydispersity index (rPDl) of 1.12 and polydispersity parameter of 8.3 (k, rPDI =
[k+1]/k). The z-average radius can be found to be 2.9 :t 0.6 nm ([k+2]/k X <a>) while the
radius found from the Guinier analysis is 4.0 d: 0.9 nm (for a hard sphere a = 31(5/3) X 3).
Since the Guinier technique yields the z-average size, agreement between these two
values is expected, while deviations between them may occur from errors in either
regression and/or because the polydispersity is not accurately described by the Schulz
distribution. Polydispersity is expected through the nature of the polymerization reaction
as well as the crosslinking process itself which may produce molecular dimers, trimers,
etc. We use a radius calculated from the expected number average molecular mass for the
NPs (Table 5.1) assuming a density (1.04 g/cc) equivalent to bulk polystyrene.

Since homogeneous blends can be produced, different molecular mass
nanoparticles were blended with linear polystyrene having molecular mass below MC
(unentangled), near MC and above MC (entangled). Fig. 5.3.a shows the ratio of the
terminal (zero shear) viscosity of the nanoparticle blends with PS 19.3 kDa to the
terminal viscosity of pure PS 19.3 kDa, as a function of Rg/h (see eq 5.1). When the ratio
Rg/h is less than 1, the interparticle separation between the nanoparticles is greater than
the radius of gyration of the linear polymer coil. With increasing particle loading, the

interparticle gap becomes less than the radius of the polymer, causing confinement. It is

91

important to point out that none of the viscosity data discussed here show a master curve

when correlated with particle volume fraction (see appendix).

 

 

      

  

 

  

 

 

 

 

 

4_0 r r. 1 l r 1 l l 1 T
(a) l'mear PS 19-3 kDa Blends 1 4 _(b) Linear P8 31.6 kDa Blends _
3.5 -
l l
3.0 - ' 2 1.2 ' .-
l —e— 25 kDa NP '
8 25_ l +52kDaNP 8310
E ' | ---- 25 kDa NP -Theory 5 ‘ -
"' , —52 kDa NP-Theory *7 1
2.0 l- ~
0.8 — —e- 25 kDa NP —
1 5 J —I— 52 kDa NP
' ---- 25 kDa NP -Theory
0-5 ’ — 52 'kDa NP -Theory ‘
1-0 1 1 ‘3 1 1 1 1 1
0 1 2 3 4 0.0 0.5 1.0 1.5 2.0
Rgl h Rgl h

Figure 5.3. Viscosity ratio of the nanoparticle blends with respect to pure polystyrene,
with polystyrene below (19.3 kDa) (a) and near (31.6 kDa) (b) the critical entanglement
molecular mass at 170°C. The curves labeled theory are the values predicted by
Batchelor’s relation for this system, ending at the limit of the relation’s applicability (111 ~
0.1). It can be seen that the blend viscosity is much greater than the predicted value for
the blend below MC, however, when the polymer is near Me, the viscosity hardly varies
with addition of nanoparticles, again contradicting the Einstein and Batchelor predictions.

From Fig. 5.3.a it can be seen that addition of both the 25kDa and the 52kDa
nanoparticles causes a sharp increase in the viscosity of the polymer melt. The curves
labeled ‘theory’ are predictions from Batchelor’s relation,148 which is a modification of

Einstein’s relation, and includes the effect of hydrodynamic interactions in the system

with increasing concentration,

77 = o,(1+2.5¢+6.2¢“) (5.7)
The 412 correction improves the limit of applicability of Batchelor’s relation to ¢~

0.1 as compared to Einstein’s relation whose limit is {11 ~ 0.02. From Fig. 5.3.a, it can be

92

seen that addition of nanoparticles increases the viscosity of unentangled polymers and
this increase is much greater than predicted by either Einstein or Batchelor. Also, the
increase in viscosity caused by the addition of 52 kDa NP’s is greater than caused by the
25 kDa NP’s, suggesting that the viscosity increase in the polymer is affected by
nanoparticle size.

Fig. 5.3.b shows the effect of nanoparticle addition on linear polystyrene near Me.
In this case it can be seen that there is essentially no change in the viscosity of the linear
polymer on the addition of nanoparticles, even with particle volume fractions as high as
0.1 (the standard deviation in the measured viscosity for all samples was < 5%). This
surprising result holds true for both the 25 kDa and 52 kDa nanoparticles. It was also
seen that the complex viscosity (77*), storage modulus (G’) and loss modulus (G ”) curves
(not shown here) for all the nanoparticle blends completely overlaid with the pure linear
polymer curve at all frequencies. This observation is in stark contrast to what is seen for
the unentangled and the entangled polymers, as will be shown below.

Entangled polystyrene samples with molecular mass 75 kDa and 393 kDa, were
blended with the nanoparticles at various concentrations, and as shown in Fig. 54.3, the
viscosity ratio for PS 75 kDa is a complicated function of Rg/h. It is immediately apparent
that the behavior of the entangled system is different to the previous two cases that were
considered. For both the 52 kDa and the 135 kDa NP it can be seen that when Rg/h is less
than 1 (no confinement), the viscosity increases sharply. Here the increase in viscosity is
much greater than that predicted by either Einstein’s or Batchelor’s relation. However, as
soon as Rg/h is greater than 1 (confinement), there is an abrupt decrease in viscosity. For

example, the 52 kDa nanoparticle system has a viscosity ratio change from 1.6 to 0.6 as

93

the Rg/h value changes from 0.9 (¢= 0.01) to 2.1 (¢= 0.05). In all the different
nanoparticle systems, for values of Rg/h greater than one, it can be seen that the viscosity
ratio is either close to l or is greatly reduced. Thus, the confinement of the linear chain
leads to a reduction in the melt viscosity, even as the particle volume fraction is
increased. It is also important to point out the reduction in viscosity does not scale with
the volume fraction (see appendix for this chapter) of the added nanoparticles, as
mentioned above. This suggests that the mixing rule for viscosity is not applicable for

this system.

 

 

  

   
   

 
  
  

 

      

 

 

 

 

 

 

1.8 4 l ' ‘ ' - 1 l l 1 l
(a) ' 12382:: 1.241211 Linear PS 393 kDa Blends
1.6 _ + 135 kDa NP 1 l -'
----25kDaNP-Theory 10 ..... +2510”?
—52kDaNP-Theory ' +5210”?
/ ,r’ 0,3 ---- 25 kDa NP -Theory .
2 Linear PS 75 kDa Blends g3 — 52 kDa W - Theow
: 1.2 .,.’ ’2’ ‘1 C ........ 135 kDa NP-1heory
\: I ‘ \ 0.6 '- —r
r " c
1.0 I
0.4 — | —
I
0.8 | 0.2 - :
— l
06 1 1 ' l 0.0 l 1 1 1 1 -
0 1 2 3 4 5 0 2 4 6 8
R9, h Rg/ l'l

Figure 5.4. Viscosity ratio of the nanoparticle blends with respect to pure polystyrene for
two different entangled systems, PS 75 kDa (a) and PS 393 kDa (b) at 170°C. The curves
labeled theory are the values predicted by Batchelor’s relation and these end at the limit
of the relation’s applicability (0 ~ 0.1). The viscosity falls precipitously when the radius
of gyration is greater than the inter-particle half-gap for the entangled systems.

The viscosity variation for the PS 393 kDa blends is shown in Fig. 5.4.b. In this

case all the blends considered had an Rg/h value >1, and as was seen for the PS 75 kDa

blends, the viscosity is decreased for all the nanoparticle blends at all concentrations. It is

94

interesting to note addition of just 1% (Rg/h = 2.8) of the 25 kDa NP causes an 80%
reduction in the melt viscosity. It was difficult to produce a blend with Rg/h <1 for this
system because of the very low concentration of nanoparticles required.

The complex viscosity profiles for the pure polystyrene (PS 393 kDa), pure 52
kDa nanoparticles, as well as their blends, as a function of frequency, are presented in
Fig. 5.5.a. It is observed that the pure nanoparticle system does not have a terminal
viscosity and instead behaves like a yield stress material, having an infinite viscosity at

zero shear rate (frequency). This behavior is similar to the rheological behavior of some

 

 

  
     
  

 

 

 

 

 

intramolecularly crosslinked polystyrene microgels studied by Antonietti et. al.14l'm
7 ’ F I I I I I I I
e ' 10 (b) “a
10
I 6
5 ~ 10 1
A10 _ 5 :
3 : . $10 '5
m 4 _ ‘ a =
'h 10 E 3 .V 4 ‘
$ E 3 (9 10 'g
iir: 3 " ‘ o Puresz kDaNP I
10 103 0 PS 393 kDa pue 1
:o PS 393 kDa pure I PS 393 kDa + 52 kDa M3 -o.5%5
2 1 PS 393 koa+52|oa Np.o,5 2 '0 A PS 393koa+52IoaN=.8% .
10 5- PS 393 kDa + 52kDa NP-8% '- ~ 10 . vV tzv PS 393 kDa + 52 kDa MD 40%:
:v PS 393 kDa + 52103 NP—10% : g
” l l L i J 4 l l ‘ l J l l l l l l l
-3 -1 1 3 5 -3 -1 1 3 5
1 O 10 1 0 10 1 0 1O 10 1 0 10 1 0
Frequency (rad Isec) Frequency (rad Isec)

Figure 5.5. (a) Complex viscosity as a function of frequency for PS 393 kDa, 52 kDa NP
and their blends at 170°C. It can be seen that the pure nanoparticles display a gel like
behavior with an infinite terminal viscosity. All the blends however have a distinct
terminal viscosity which is lower than the pure component. (b) Storage modulus variation
with frequency for the same systems at l70°C. Blends with a nanoparticle concentration
below 10% have a plateau modulus equivalent to the virgin polymer while the 10% blend
has a reduced modulus and complex viscosity at all frequencies.

95

In contrast, both the pure linear polymer and the nanoparticle blends have a finite
terminal viscosity. From Fig. 5.5.a, it can also be seen addition of nanoparticles at low
concentrations (up to ¢ ~ 0.08), only affects the terminal region, demonstrated by a lower
zero shear viscosity. Above a critical frequency (~ 10'1 rad/s in this case) the viscosity
curves for all the blends merge with the pure polystyrene curve. However, further
addition of nanoparticles causes a viscosity reduction at all frequencies, as can be seen
with the 10% blend.

The same trend is observed for the storage modulus curves of the pure
components and the blends (Fig. 5.5 .b). Traditionally the storage modulus for the
polymer blends relates directly to the storage modulus of its componentsm’ ‘83 In this
case, however, 0’ variation for the blends is governed by the G’ for the linear polymer,
with the nanoparticles providing a reduction in the terminal region. As was seen earlier,
after a frequency ~10" rad/s, all the 6’ curves (up to ¢ ~ 0.08) merge with the pure PS
393 kDa curve.

For all the blends discussed above, the minima in G"/ ’ (tan 6) occurred near a
frequency of 10 rad/s. The value of G ’ corresponding to the minima in tan 6 is taken as
the plateau modulus (GNO‘).99 As all the G’ curves overlay near this frequency, it was
concluded that the plateau modulus of the polymer is unaffected by addition of
nanoparticles, up to ¢ = 0.08 (the GNU values are listed in Table 5.2). This observation is
contrary to the rule of mixing for athermal systems as postulated by both Tsenoglou184
and Wu,185 where the plateau modulus for the blend scales with the plateau modulus of its

components .

96

Table 5.2. The plateau modulus for pure PS 393 kDa and its blends with various
nanoparticles at 170°C

 

 

 

 

 

 

 

 

 

 

 

Sample Plateau Modulus (MPaL
PS 393 kDa 0.167i0.015
PS 393 kDa + 25kDa NP -0.5% blend 0.165zt0.019
PS 393 kDa + 25kDa NP -1% blend 0.078zt0.009a
PS 393 kDa + 52kDa NP -0.5% blend 0.1712t0.009
PS 393 kDa + 52kDa NP -1% blend 016110.020
PS 393 kDa + 52kDa NP -8% blend 0.] 80:t0.014
PS 393 kDa + 52kDa NP-lO% blend 0.103i0.005°
PS 393 kDa + l35kDa NP-O.5% blend 019210.016
PS 393 kDa + l35kDa NP-l% blend 0.184i0.014
PS 393 kDa + l35kDa NP-20% blend 0.0612t0.015 a

 

 

 

 

' The viscosity for these blends was reduced at all frequencies on nanoparticle addition,
as compared to the neat polymer.

It is interesting to compare the effect of nanoparticle size on the complex
viscosity profile for PS 393 kDa. Addition of 52 kDa NP (Rg = 3.1 nm; Fig. 5.5.a) caused
an effect only in the terminal region at low volume fractions with a decreased viscosity at
all frequencies at higher volume fractions (4) ~ 0.1). In comparison, the addition of 25
kDa NP (R8 = 2.2 nm) causes a decrease in viscosity at all frequencies with particle
volume fractions as low as 0.01, as shown in Fig. 5.6.21. The addition of 135 kDa NP (Rg
= 4.0 nm, Fig 5.6.b), again affects only the terminal region at low volume fraction, while
at higher volume fractions (4) ~ 0.2), the viscosity is decreased at all fiequencies. Note the

polymer is confined for all these systems, i.e. Rg/h > 1.

97

 

 

 
  
   
 

 

 

 
   
  
 

 

 

 

 

 

—r F I
106 10° ‘
105 " 105 _
’6 4 _ ’8 ‘
$ 10 $10 —
8 £
V 3 —. v
, 10 * 1o3 -
C C
102 _- -1 102 Pure PS 393 kDa _
0 PS 393kDa l PS393kDa+135kDa NP-O.
1 P8393kDa+25kDaNP-O.5° A P8393kDa+135kDaNP-1%
10 [P811393 ltDa+l25lea NIP-1% l 101 IPSIngfiDa +113511<Da|1lP-20% 1 2T
10'3 10‘1 101 103 105 10.3 10.1 101 103 105

Frequency (rad / sec) Frequency (rad I sec)

Figure 5.6. (a). Complex viscosity as a function of frequency for pure PS 393 kDa and its
blends with 25 kDa NP at 170°C. In this case, the viscosity is decreased at all
fi'equencies. A large viscosity reduction is apparent with just 1% addition of the
nanoparticles. (b) Complex viscosity as a function of frequency for the blends of 135 kDa
NP with PS 393 kDa also at 170°C. Here, only the terminal viscosity is reduced with
nanoparticle addition until the concentration reaches 20%.

This differing viscosity behavior can be related to the total number of
nanoparticles present in the blend, at least to first order. As the molecular weight of the

nanoparticles decreases, for the same volume fraction, the total number of nanoparticles
in the blend increases. For (I) = 0.01, the number of 25 kDa NP is 2.3x10'4NP/ mg; for the
52 kDa NP, with o = 0.1, the number of nanoparticles is 9x10'4NP/ mg, while for the 135
kDa NP, at (I) = 0.2, the number of nanoparticles is 8.6x10l4 NP/mg. Thus, when the total
number of nanoparticles present in the blend are below a certain threshold (~ 1015
NPs/mg), only the zero shear viscosity is reduced; however on the addition of more
nanoparticles, a reduction in viscosity at all frequencies is seen. We find that the number
of polymer chains in these blends are also ~ 10'5 chains/mg and so by this empirical

observation the data suggests that the chain dynamics are severely affected and the

98

viscosity is decreased at all frequencies when the number of polymer chains
approximately equals the number of nanoparticles.

The complex viscosity and the storage modulus for the blends of PS 19.3 kDa and
52 kDa NP as a function of frequency are shown in Fig. 5.7. It can be seen that both the
viscosity and storage modulus increase at all frequencies on the addition of the
nanoparticles. Also, the increase in these properties scales with the concentration of the
added nanoparticles. The effects observed here may be due to a density increase (Fig.
5.8.a) and free volume decrease (Tg increases, Table 5.3) provided by the nanoparticles.
Interestingly, a zero shear viscosity can be observed for all the blends measured, even
though the pure nanoparticles behave as a gel (as seen in Fig. 5.5). On comparing the data
in Fig. 5.7 with the data shown in Fig. 5.5 for an entangled polymer, the importance of

chain entanglements in the polymer is again emphasized.

 

 

 

_ __w__“w ‘:
(a) : (b)

. ‘ ~ 1

105 r -=

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d: 10 : M. ' . ,6 10 E i

9: ‘ ' ‘ 9; 7- 3

V - - r- ‘ ..

‘C u ' 0 3 I. .1."

J' ‘ 10 r J F

o PurePS19.3koa a": d E ff 5

I PS 19.3 kDa+ aware-1% blend " : .. o I

' A P8193 kDa+ 52kDahP-10% blend g? - ‘ o -2 -

v 9519.3 kDa+ 52kDahP-30% blend . 2 " ._.

C 10 .- ‘ a

I _ .

1o1 102 1o3 10‘ 1o1 102 1o3 10‘
Frequency (rad / sec) Frequency (rad / see)

Figure 5.7. Complex viscosity (a) and storage modulus (b) data for pure PS 19.3 kDa and
its blends with 52 kDa NP at 170°C. Both these properties increase at all frequencies
upon nanoparticle addition. Same symbols used in each graph.

99

The molecular mass between chain entanglements, Me, for narrow dispersity
polymer melts can be estimated by using the equation,”‘ '4
Me = pRT/GN (5.8)
where p is the bulk density of the material at temperature T, and R is the ideal gas
constant. The bulk density values for the various PS 19.3 kDa and PS 393 kDa blends are
shown in Fig. 5.8. It can be seen that the addition of the nanoparticles may cause a very
small reduction in the bulk density for PS 393 kDa blends, particularly for the smaller
nanoparticles (Fig. 5.8.b). From Table 5.2, it is observed that the plateau modulus is
unaffected by the 52 kDa and 135 kDa nanoparticle addition at lower volume fractions.
Hence, for those samples, the relation in eq. 5.8 implies that M. remains unaffected by
nanoparticle addition. From Fig. 5.4.b, it can be seen that for the 52 kDa NP at ¢=0.08,
the terminal viscosity decreases by about 60% with nanoparticle addition. Thus, even
with this large reduction in viscosity, the polymer entanglements are not affected, at least
in the way entanglements are thought of traditionally. This is surprising behavior, as the
effects on viscosity produced by nanoparticle addition are strongly dependent on the

presence or absence of entanglements (Fig. 5.1).

100

 

 

 

 

 

 

 

 

 

 

1.06 4 I I I I 1-1 106 .I I I I I L
(a)
1M_ A1m
’6 §
3 9 1.04
g 1 02I — g;
'5 2 1.03
5 8
o 1'00 _ 1 02 - + PS 393 kDa + 25kDa NP blend
-c— P8 19.3 kDa + 25 kDa NP bIend °
”WWW IS§£§:3::?§§‘:S."£:L°$I
0.98 L I I g l 1- 1.01 I I I l r
0.00 0.02 0.04 0.06 0.08 0.10 0.00 0.02 0.04 0.06 0.08 0.10
Mass fraction nanoparticles M355 fIaction nanoparticles

Figure 5.8. Bulk density variation as a function of nanoparticle concentration for PS 19.3
kDa blends (a) and PS 393 kDa blends (b) at 25°C. For polymer molecular below Me, the
density increases, and when it is above M, the density decreases or remains constant, on

nanoparticle addition.

In Figs. 5.9.a and 5.9.b, the G”(a)) data was used to obtain the continuous
relaxation spectrum for PS 393 kDa and its blends with the 52 kDa NP (up to 11> = 0.1), as
described in the experimental section. It can be seen that the relaxation spectra for pure
polystyrene as well as the blends, have a peak near 1 z 30secs indicative of a narrow
molecular mass distribution in the polymer sample.‘86 It should be noted that the pure
nanoparticles have an infinite terminal relaxation time, suggesting that the relaxation
properties of the nanoparticle-polymer blend are distinct and not a distribution of the
individual relaxation times of its components. This observation is in contrast to what is
generally observed for blends of low and high molecular mass polystyrene.186 In addition,
as no separate relaxation times are seen for the pure nanoparticles, there is no
nanoparticle structure formation within the polymer melt as has been seen in a few

PYCVIOUS nanoparticle-polymer systems.“ '87

lOI

 

 

    
  
  
 

 

 

 

 

 

 

 

r
105 — (b) n
4
10 F ‘
PlateauRegime
A A 3 — -1
III III 10
9; Ll, 2
a 910 .— _‘
I 101 I- J I 101 _ TeminalReglme -1
0 _ _. 0 _
10 —0— PS 398 kDapuIe 1O _._ 133393”)an
+ PS 393 kDa+PS 52 kDa NP-10% + ps 393kDa+PsszkoaM=.o,5%
10'1r I 10'1 +P3393koa+Pss2koaM=-8%
l l l l 4 I l l l l l l A l l l
-4 - -
1o 102 10° 102 10“ 102 10° 102
t(sec) t(sec)

Figure 5.9. Relaxation spectra for pure PS 393 kDa and its blends with 52 kDa NP up to
concentrations of up to 8% (a) and for a concentration of 10% (b). The Rouse, Plateau
and Terminal regimes are also shown. It can be seen that the nanoparticles only affect the
terminal regime, by reducing the longest relaxation time, at lower concentrations while at
higher concentrations, a reduction occurs at all relaxation times.

For 4) = 0.1 (Fig. 5.9.b), it can be seen that the relaxation modulus for the blends is
reduced, when compared to the relaxation modulus for the pure polymer, at all relaxation
times. This could be attributed to a dilution effect with the nanoparticles acting as
plasticizers.9’ 188490 However, addition of the nanoparticles at low volume fractions (up to
(b = 0.08, Fig. 5.9.a), quite unexpectedly, does not significantly affect the Rouse or the
plateau regime of the relaxation spectra. Instead, nanoparticle addition reduces only the
longest relaxation times (terminal region) for the polymer chain, causing a fall in the

'5' 67 of a polymer

terminal viscosity. These are the relaxations caused by the reptation
chain in the polymer melt.
There are several mechanisms that may cause this curious behavior. We

hypothesized in our previous publication that a reduction in viscosity is produced by an

increase in free volume, for a given temperature, due to a reduction in the glass transition

102

temperature found in many of the blends discussed here. This is part of the reason for the
viscosity decrease, however, as seen in Table 5.3 a clear correlation between glass
transition temperature and viscosity reduction is not apparent with this expanded data set.
Further, there is no clear glass transition reduction when Rg/h is greater than one, see Fig.
5.4.a, and a viscosity reduction is evident. Thus, another mechanism must exist to explain

the viscosity reduction and possibly operate in tandem to the free volume change (see fig.

5.8.b).

103

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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104

l9l, 192

We hypothesize that these phenomena are related to the double reptation or

constraint release35

phenomenon introduced by the nanoparticles. In this model,
constraints are released due to movement of surrounding molecules constituting the
entanglement mesh (tube67). This has the effect of reducing the relaxation time, yet, not
the modulus, as we observe experimentally.

The physics of the mechanism introduced by the nanoparticles will certainly
depend on the relative diffusion time scales of the nanoparticle and polymer. As evident
from Fig. 5.9, the pure 393 kDa polymer relaxation time is of order 10-50 3. Assuming
the nanoparticles follow the SE model one can estimate a diffusion time, through a
distance a, as ~ 50 s (= 4' azlkBT, k3 is Boltzmann’s constant) which is the same order as
the polymer relaxation time. One may expect a viscosity reduction if the nanoparticles
diffuse much more rapidly than the linear polymer so they can not contribute to the
entanglement mesh. So, the continuum SE relation may not be valid for nanoparticles
diffusing through the polymer (temporary) network to allow this hypothesized
mechanism. Diffusion of neutrally interacting NPs in entangled melts is certainly worthy
of further study and here we merely (tentatively) hypothesize that the NPs invoke
constraint release noting inconsistencies of this model with some of the data.

Yet, once there are approximately the same number of nanoparticles and polymer
molecules per unit volume the viscosity falls at all frequencies. Clearly, under this
condition, the entanglement network or tube of constraints has suffered to great extent
and the plateau modulus is seen to decrease. However, this curious phenomenon occurs

in the high frequency Rouse regime that is not affected at all until this nanoparticle

concentration. So, once the entanglement network is severely affected, to reduce the

105

plateau modulus and viscosity at all frequencies, the Rouse regime is similarly affected.
We find all these observations remarkable and postulate that what we interpret as
independent free volume and constraint release mechanisms in fact operate in concert to

generate the flow property modification.

Conclusion

We have shown that addition of polystyrene nanoparticles to linear polystyrene
produces peculiar and unique behavior with a viscosity reduction only when the polymer
molecule is entangled and confined. In fact, there appears to be critical behavior at the
characteristic molecular mass for entanglements where the viscosity does not change,
within experimental error. Further, when there is approximately one nanoparticle present
for each polymer molecule, an abrupt viscosity decrease is present at all frequencies.

In our previous study,8 we demonstrated that the increase in free volume, signaled
by a glass transition temperature decrease, accounted for the viscosity reduction at a
given temperature. Here we have extended the data set to realize the phenomenon is
much more complicated with a viscosity increase present when the polymer molecule is
not confined then a precipitous drop occurs upon molecular confinement. Further, the
plateau modulus is not initially affected suggesting no change in the number of
entanglements. We hypothesize that the nanoparticles induce constraint release affecting
the longest relaxation modes thereby producing a terminal viscosity decrease without
reduction in the plateau modulus. However, as the nanoparticle concentration is

increased, until there is approximately one nanoparticle for every polymer molecule, the

106

viscosity at all frequencies falls, as does the plateau modulus, suggesting a drastic change
in the entanglement structure. Yet, the Rouse regime is similarly affected promoting the
idea that the single molecule as well as the entanglement dynamics are similarly changed.

In Fig. 5.1 we showed that when no entanglements are present then the viscosity
can deviate from the Rouse prediction due to free volume effects, while reduction of
entanglements above the critical molecular weight can yield a viscosity change. It
appears this explanation where the two regimes are considered separately may be too
simple. Above the critical molecular weight one may have free volume and entanglement
changes induced by nano-objects which are not easily reconciled under existing
theoretical considerations. It is clear, however, that this is a nanoscale effect and larger

particle sizes will not produce any of this behavior.

Appendix for Chapter 5
Here we present the viscosity ratio for the blends given in Figs. 5.3 and 5.4 as a

function of volume fraction in Fig. 5.10. It is clear there is no scaling with volume
fraction as expected for suspensions.

107

 

     
  

 

 

 

 

 

 

 

 

 

 

I’T'TTI' . r*' ‘1
3.5 ~ b
1.4 — +
3.0 —
1 2 o Theo -«
3 8 N
g 2.5 — e
8 '5 1.0 fi _
g 2.0 . g
>
1.5 — 0.3 - .
+25k03NP +25kDaNP
+ 52 kDa NP
Theory + 52 kDa NP
1'0 1 1 1 1 1 I 0.6 1 1 m 1 1 H
0.00 0.10 0.20 0.30 0.00 0.02 0.04 0.06
Nanoparticle volume fraction Nanoparticle volume fraction
I I I I T I I I I I
1.6 _ _
1.4 Theory d

1.4 _ 1.2

1.0

  
  

1.2 — oa
' +25 kDa NP "

-I- 52 kDa NP

1.0 . +135kDaNP

._4

0.6

VIsoosly ratio
Viscosity raio

0.4

 
   

 

 

 

 

 

 

0.8 ‘ 4
-o— 25 kDa NP p
-I— 52 kDa NP 0.2 “ “t
0.6 _ + 135 kDa NP -
1 1 1 1 0.0 *1 1 1 1 r
0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20

Nanoparticle volume fraction Nanoparticle volume 1186th

Figure 5.10. Viscosity ratio of the nanoparticle blends with respect to pure polystyrene as
a function of nanoparticle volume fraction, with different molecular weight linear
polystyrenes’ at 170°C: (a) 19.3 kDa, (b) 31.6 kDa, (c) 75 kDa, (d) 393 kDa. The curves
labeled theory are the values predicted by Batchelor’s relation for this system, ending at
the limit of the relation’s applicability ((1: ~ 0.1).

108

CHAPTER 6

BREAKDOWN OF THE CONTINUUM STOKES-EINSTEIN
RELATION FOR NANOSCALE INCLUSIONS IN POLYMER
MELTS

 

Introduction

The assembly of inorganic nanoparticles in polymer matrices and block
copolymers has been widely studied with the aim of tailoring their magnetic, mechanical,

electrical or optical properties.”* ”38

Other nanoparticles found in nature
(bionanoparticles) including tobacco mosaic virus and cowpea mosaic virus have also
now been functionalized with various synthetic polymers with the objective of directing
them into self assembled ordered structures to tailor vehicles for drug delivery.” 40 In
addition, the movement of proteins, DNA and other naturally occurring nanoparticle —
like systems, either inside or outside the cell are expected to emulate the nanoparticle -
polymer matrix interaction. So, any study targeting the assembly or diffusion of
nanostructures requires an understanding of the nanoparticle dynamics, spatial
arrangement and ordering kinetics within the polymer matrix. Moreover, with many
important experimental techniques moving towards smaller length scales and sample

41, 42

volumes, such as microrheology which uses the generalized Stokes - Einstein (SE)

relation to determine the shear modulus and viscosity, an accurate description of

48, 49

nanoscale dynamics becomes essential for data interpretation. Further,we and

others'88 found that addition of nanoparticles to polymer melts causes an unexpected

109

reduction in their viscosity, contradicting Einstein’s prediction for a viscosity increase
and so it is suspected that the nanoparticle dynamics contributes to this phenomenon.

The observed reduction in viscosity for many systems required that the
nanoparticles diffuse faster than the prediction fi'om the SE relation (D = k3T/61ma , here
D is the diffusion coefficient, k3 is the Boltzmann constant, 1] is the bulk polymer melt
viscosity, T is the temperature and a is the radius of the particle) for the system.49 In this
work, we report the results for the first successful, measurements to our knowledge of the
diffusion coefficients of nanoparticles in polymer melts, using X-ray photon correlation

spectroscopy (XPCS or dynamic X-ray scattering) 43' 44

and to directly determine the
nanoparticle diffusivity. The measured diffusion coefficients were found to be dependent
on the molecular mass of the polymer, but were independent of the temperature.

However, for all the different cases studied, we found that the diffusion coefficient was

larger than the prediction from the SE relation by up to a factor of 100.

Results and Discussion

Recently, addition of quantum dots (QD) to polymers has received the attention of
a number of research groups, mainly because of their extraordinary range of potential

'93' '94 and biosensors.'95’ '96 Most synthesized

applications, including electronic materials
quantum dots have a covering of tri-n-octylphosphine oxide (TOPO) ligands on their
surface. However, the dispersion of these quantum dots in various polymer matrices has

proven to be quite difficult, unless the TOPO ligands are replaced by either the matrix

polymer or another polymer that is miscible with the matrix polymer.

110

In our recent work 34 we showed that dispersion of organic nanoparticles is
possible in various polymer matrices despite chemical dissimilarity, as long as the radius
of the nanoparticle is less than the radius of gyration (Rg) of the matrix polymer. That
work is extended here for dispersing inorganic nanoparticles i.e. oleic acid covered CdSe
quantum dots ‘97 in polystyrene (PS) as shown in Fig. 6.1.a. The radius of the quantum
dots is 6 nm (as determined through dynamic light scattering in Toluene at 35°C), with a
QD core radius of 2 nm, as can be seen from the TEM micrograph; while the RE of the
polystyrene is ~ 17 nm. The quantum dots are miscible up to a very high mass fraction (~
38 wt% in Fig. 6.1.a) and the dispersion of the quantum dots within the polymer matrix
has been achieved without any chemical modification of the oleic acid covered surface.
Indeed linear oleic acid is expected to have an unfavorable interaction with the
polystyrene matrix causing phase separation. However, it is believed that this unfavorable
process is offset by an enthalpy gain due to an increase in molecular contacts at dispersed
nanoparticle surfaces.34 It should be pointed out that the method of blend preparation
(rapid precipitation here) is quite critical to ensure the dispersion of nanoparticles.34 A
picture of the as prepared PS-QD blend can be seen in Fig. 6.1.b. The blend is colored
pink because of the dispersion of the quantum dots, in comparison, pure PS is white.

Also, as was the case with the organic nanoparticles,48' 49

the addition of the quantum dots
to polystyrene also causes a large reduction (~ 60%) in the melt viscosity (Fig. 6.1.c) of

the nanocomposite, even at this high mass fraction.

111

 

     

21. PS393kpure
I PS 393k+CdSe QDots
50 nm r1 1 1 1 1 1 1

0.001 0.1 10 1000

 

 

 

 

 

 

 

 

 

Frequency (rad/sec)
105 _e I l l I I
105 - -
6‘
i 104 - -
e 103 1 -
c 102 r
0 PS 393k pure
101 . I PS 393k + Fe304 _
I L41 1 l l 1
0.001 0.1 10 1000
Frequency (rad / sec)

Images in this dissertation are presented in color.

Figure 6.1. Inorganic nanopartich can be dispersed in polymer matrices by the
process of rapid precipitation and cause a large reduction in the polymer melt
viscosity. a. TEM micrograph of a 38wt.% blend of oleic acid capped quantum dots
dispersed in polystyrene (molecular mass 393kDa). Based on the nanoparticle
concentration and size, as well as the sample size, there should be several thousands of
nanoparticles visible in the micrograph, as seen. The dispersion of inorganic
nanoparticles is possible in polymers as long as the RE of polymer > radius of
nanoparticles. b. An optical picture of the QD-PS blend, showing the pink color of the
blend. c. The complex viscosity as a fimction of frequency for pure PS and the PS-QD
blend. The melt viscosity reduces by ~ 60% on the addition of quantum dots even at this
high weight loading, contradicting Einstein’s prediction for a viscosity increase. d. A
TEM micrograph of the 5 wt% blend of the magnetite nanoparticles in PS (molecular
mass 393kDa). There should be several tens of nanoparticles in this micrograph, as is
clearly seen. e. The complex viscosity as a function of frequency for pure PS and the PS-
magnetite nanoparticle blend. The addition of just 5 wt% of the magnetite nanoparticles
causes ~ 90% reduction in the melt viscosity of pure polystyrene.

112

see methods in Chapter 7 for more details) in polystyrene. The magnetite nanoparticles
are quite polydisperse with a radius varying between 5-10 nm (as obtained from dynamic
light scattering in Benzene at 35°C), and can be readily dispersed in the high molecular
weight polystyrene (Rg ~ 17 nm), as shown in Fig. 6.1.d (the PS-magnetite nanoparticle
blend is yellow in color as compared to the pink PS-QD blend). The addition of ~ 5 wt.%
of the magnetite nanoparticles causes an ~ 90% reduction in the melt zero shear viscosity
(Fig. 6.1.00e).

The mechanism for the unusual and important decrease in viscosity on the
addition of nanoparticles, first seen for the ideal case of polystyrene nanoparticles in
linear polystyrene 48 and observed here again for the addition of quantum dots as well as
the magnetite nanoparticles, has not been understood so far. However, from our previous
work, it was clear that the reduction in viscosity was only seen in entangled systems,
while for the unentangled systems, addition of nanoparticles causes a viscosity increase.
It was postulated then that the nanoparticles must diffuse faster than predicted by the
continuum SE relation and hence not contribute to the entanglement network, to cause the
observed reduction in viscosity.49

Deviations from the SE relation have been observed before, especially when the
particle radius came close to the size of the solvent molecules. The continuum SE relation
is ideally applicable only for a >> I; (correlation length for a polymer, generally taken as
the size of a monomer / polymer segment). However, there have been differing findings
on the region of applicability of the SE relation. Edward ‘64 reviewed the literature and
found that the SE relation could not be applied to diffusion of molecular penetrants’ in

simple fluids such as water and carbon tetrachloride. Indeed, when the penetrants’ radius

113

became 2-3 times that of the suspending liquids’ then deviations fiom the SE relation
were quite evident. Similarly, Somoza et al. '98 found the local viscosity for rotation of
dissolved anthracene (~ 0.6 nm in radius) to be orders of magnitude lower than the bulk
viscosity for PDMS. However, previous simulations report the applicability of the SE

199
l.

relation on the atomic love More recently, Vergeles et. al. 200 showed that the SE

relation can serve as a qualitative approximation for particle sizes comparable to the

solvent; while simulations from Heyes et al. 20'

predicted that the translational diffusion
coefficients for nanoparticles in polymer solutions are lower than the SE predictions,
while the rotational diffusion coefficients are higher than the predictions from the SED
(Stokes-Einstein-Debye) relation. Also, XPCS, the technique used in this work, was used
to measure the translational diffusion coefficient of ~ 70 nm PS spheres in glycerol for
various volume fractions of the particles.43 The measured diffusion coefficient in this
case was found to match well with the predicted value from the SE relation. However, as
we stated before, direct measurement of the diffusion coefficient of nanoparticles in
polymer melts has not been performed before. It is also important to note that in this
work the nanoparticles are larger than the correlation length but smaller than the Rg of the
polymer.2°2’ 203

Our XPCS measurements were carried out at the 8-ID-I beamline at the Advanced
Photon Source (APS). Both the nanoparticle systems used in this work (quantum dots and
magnetite nanoparticles) were ideal for the study as they provided a large contrast for the
X-ray diffraction. XPCS is a relatively new technique for the determination of condensed

matter dynamics, and is in essence the extension of dynamic light scattering into the X-

ray regime.204 The primary requirement for the technique is the availability of a high

114

brilliance synchrotron radiation source and the x-ray beam has to be made partially
coherent with the detector size matched to the size of the coherent speckles scattered by
the sample.205 Fluctuations in the speckle intensity are then directly related to the sample
dynamics as discussed elsewhere.43

Dynamical properties of the melts were characterized via autocorrelation of
sequences of CCD images, like the one shown in Fig. 6.2.a, and normalized to the
circular average of the CCD scattering at each wave vector. This allowed for the
determination of the normalized intensity — intensity autocorrelation function, g; (q,t),
which is related to the field autocorrelation function, g1 (q, t), by

g2 (c1, t)= 1 +01 (15 (q,t))2 (6.1)
here t is the delay time, q is the wave vector (= 47W» sin (6/2), A is the wavelength of the
X rays and 0 is the scattering angle) and a is the setup dependent instrument contrast (~
0.15 for these measurements), with

151 (q, t) = em (4111) (6.2)
where t, = l / (qu).

Typical data obtained for the intensity-intensity autocorrelation function as a
function of the delay time is shown in Fig. 6.2.b. This data could be well fitted to a single

exponential (the solid blue lines in Fig. 6.2.b) with or and 1:r as the two fitting parameters.

By definition, a plot of l/tr versus q2 is a straight line, whose slope gives us the diffusion

coefficient. This was found under all conditions demonstrating normal Brownian motion.

115

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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: 393kDa Ps+CdSeQDotsg~ 5nm): 393 kDa S+Fe30,(5-10nm) 1
: Rouse viscosity (501) c - E Rouseviscosity(501) d _
2 2 -
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\1 ~ It. ~ 1
s x ‘ s .' ..............................
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10° _ . . 2 10° : . . _
_ True VIscosrty (1.0) : : True VISCOSlty (1.0) 3
, V -;1__L__l—l: hi 1 1 I 1 1 IT
130 140 150 160 150 160 170 180
Temperature (°C) Temperature (°C)

Images in this dissertation are presented in color.

116

Figure 6.2. The diffusion coefficients of quantum dots and magnetite nanoparticles
in PS (molecular mass 393 kDa). a. A single frame (CCD image) obtained from the X-
ray diffraction of the 5 wt% magnetite nanoparticles in PS. For each sample, 400-500
such frames were taken at each temperature, at intervals of 0.1 secs. b. Each fiame was
divided into equally spaced q regimes, based on their angular distance from the upper
right hand comer of the frame (the centre of the X-ray beam). The scattering from these
regimes was used to calculate the intensity-intensity autocorrelation function (g; (q,t))
using the mean q value from each regime. The data from 6 of those q values can be seen
here (a is the radius of the nanoparticle = 5 nm; the sample is at 160°C). Each data set has
been offset with respect to the previous data set by 0.2, starting from q X a = 0.370, to
allow for easier visibility (so the data set for q x a = 0.370 has been offset by 0.2, while
the data set for q X a = 0.998 has been offset by 1). The data is then fitted to a single
exponential (the solid blue line), to obtain 1, as a function of q c. The ratio of the
measured diffusion coefficient to the diffusion coefficient calculated from the SE relation
for the quantum dots in PS. d. The same ratio for the magnetite nanoparticles in PS.

Fig. 6.2.c and Fig. 6.2.d show the ratio Dmeasmd / D35 for the CdSe Quantum dots
and the magnetite nanoparticles in linear PS as a function of temperature (it should be
noted that the glass transition temperature for PS is 106°C). This ratio would be 1 if the
measured diffusion coefficient matched the prediction from the SE relation based on the
viscosity of pure PS. Because the addition of the nanoparticles causes a reduction in the
melt viscosity, the red dotted line shows the value of the ratio if the blend viscosity is
used to calculate D33 instead of the viscosity of pure PS. If the polymer had no

151 and

entanglements then the viscosity would be equal to the so called Rouse viscosity,
the system should follow the solid green line shown on the graph. It should be pointed
out here that for the calculation of D35 for the magnetite nanoparticles, we have used a
radius of 5 nm, which is the size of the smallest particles and gives the highest value for
D35, while a radius of 5 nm was used for the QD’s, yielding the highest value of D313.

It is immediately clear that both the nanoparticle systems diffuse almost a 100

times faster than the prediction from the SE relation based on the viscosity of pure PS,

117

contrary to MD simulations for the system.” This is equivalent to stating that the local
viscosity experienced by nanoparticles is much less than the viscosity macroscopically
measured.

The size and shape of the particles are expected to be critical 206 to their diffusion.
For example, the nanoparticles are about the same size as the tube diameter or the
entanglement mesh length,14 in entangled polystyrene (~ 8-9 nm). In fact, the quantum
dots are smaller than the tube diameter, while some of the magnetite nanoparticles are
larger, however, for both cases, the measured difiusion coefficients are much faster than
the SE prediction. Clearly, both the systems diffuse regardless of the entanglement
network and their size, leading to this extremely high diffusion coefficient. Quite
significantly, the diffusivity ratio is almost independent of temperature for both the
systems, suggesting that an activated process other than that associated with the polymer
melt is not present. The XPCS measurements were repeated for the addition of these
nanoparticles to a lower molecular weight PS matrix (molecular mass of 115 kDa), as
discussed below, to find Dmeasured/ D35 was approximately 10 for all temperatures tested
suggesting a molecular mass dependence.

The nanoparticles’ fast diffusion suggests that the physical mechanism for the
viscosity decrease seen in nanoparticle-polymer blends is through the constraint release
phenomena.” 35 In this model, constraints are released due to movement of surrounding
molecules constituting the entanglement mesh or tube 67. This has the effect of reducing
the polymer blend viscosity, yet, not the modulus, as we observe experimentally 49. This
hypothesis is clearly dependent on the relative time scales of diffusion for the linear chain

and the nanoparticles. From our calculations and experimental data 49 the relaxation time

118

for the PS linear chain is ~ 10-50 secs., which is about 10-100 times slower than the
diffusion time for the nanoparticles through a distance equivalent to their radius or the
tube diameter. Thus, we hypothesize that the nanoparticles diffuse rapidly, without
participating in the entanglement mesh and their occupied volume provides the constraint
release. However, this would suggest a simple dependence of viscosity on the
nanoparticle concentration, which we do not see, suggested that complicated polymer and
nanoparticle dynamics contribute to the observed reduction in viscosity.

To confirm our hypothesis that constraint release contributes to the viscosity
decrease, we extend our work to study the effect of nanoparticle addition on the viscosity
of star polymers. Star polymers do not relax by reptation or constraint release but only by

'5' 207 since the star cannot move back and forth as a whole.'50

primitive path fluctuations,
If constraint release is the cause of the viscosity decrease in linear polymers, the viscosity
of star polymers should not decrease on the addition of nanoparticles, which is what we
observe.

A TEM micrograph is shown in Fig. 6.3.a, for the 2 wt% dispersion of magnetite
nanoparticles in a 3 arm PS star (molecular mass of each arm ~ 108 kDa), clearly
demonstrating that the magnetite nanoparticles are well dispersed. The complex viscosity
as a function of frequency for the pure 3 arm star as well its 2 wt% blend with the
magnetite nanoparticles is shown in Fig. 6.3.b, showing a viscosity increase. In fact a
60% increase in the zero shear viscosity can be observed, even at this low weight fraction
of the nanoparticles. Significantly, XPCS measurements on this sample indicate that the

diffusion coefficient of the nanoparticles, even in this case, is almost 10 times the larger

than diffusion coefficient predicted from the SE relation based on the pure 3 arm star

119

viscosity (Fig. 6.3.c). Since the viscosity of the blend is greater than the viscosity for the
pure 3 arm star, the ratio of diffusion coefficients obtained by using the blend viscosity is
less than one, as shown in the figure. It should be noted that the ratio obtained by using
the measured diffusion coefficient still lies within the limits of the ratios obtained by
using the pure 3 arm star viscosity and that obtained by using the Rouse viscosity, based
on the arm length. Also, the diffusion occurs at the same rate as a linear polymer with
mass equal to that of an arm (Fig. 6.3.c) demonstrating that the star architecture does not
influence the diffusion, rather it is the lower molecular mass of the arm which is

important.

120

 

 

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130 140 150 160 170

Temperature (°C)

Images in this dissertation are presented in color.

Figure 6.3. Addition of magnetite nanoparticles to 3—arm PS stars. a. A TEM
micrograph showing the dispersion of magnetite nanoparticles (2 wt% or 0.4 vol%) in a 3
arm PS star (molecular mass of each arm ~ 108 kDa). Based on the nanoparticle
concentration and the sample size there should be 5-10 nanoparticles in this figure, as can
be seen here. b. The complex viscosity as a function of frequency for the pure 3 arm star
as well as its blend with the magnetite nanoparticles. It can be seen that the addition of
the nanoparticles causes a large increase in the viscosity of the star, in contrast to the
viscosity decrease seen on the addition of the same nanoparticles to linear PS. c. The ratio
of the measured diffusion coefficient (from XPCS data) to the diffusion coefficient fi'om
the SE relation for the magnetite nanoparticles dispersed in the 3 arm star and linear PS
with molecular mass of 115 kDa. Even though the addition of the magnetite nanoparticles
causes an increase in the melt viscosity, their diffusion coefficient is almost an order of
magnitude higher than the prediction fiom the SE relation.

12]

Conclusion

With this work we have shown that it is possible to disperse inorganic
nanoparticles in polymer matrices at high mass fractions without surface modification, as
long as the Rg of polymer > radius of the nanoparticles. We also, for the first time,
successfully measured the diffusion coefficients of different nanoparticles in an entangled
polystyrene matrix. The diffusion coefficients of the nanoparticles were found to be as
much as 100 times faster than the predictions form the continuum Stokes — Einstein
relation based on the bulk viscosity, in contrast to previous simulations. This suggests
that the local viscosity in the case of nanoparticles is much lower than the bulk viscosity,
as the nanoparticles do not feel all of the entanglements in the system. The faster
nanoparticle diffusion coefficients lead to an overall decrease in the bulk viscosity of the
polymer melt, contradicting Einstein’s century old prediction and common observation of
a viscosity increase on the addition of particles to solutions and melts. This unusual
decrease in viscosity can be explained by a faster mode of polymer relaxation as
compared to reptation, constraint release, introduced by the fast diffusion of the
nanoparticles. The importance of constraint release was tested by studying the dynamics
of nanoparticle addition to 3 arm stars, which can only relax by primitive path
fluctuations. As anticipated, the addition of nanoparticles increases the melt viscosity of
the 3 arm stars, in spite of the fact that the nanoparticles diffuse almost 10 times faster

than the SE prediction for the system.

122

CHAPTER 7

DESIGNING MULTIFUNCTIONAL NANOCOMPOSITES

 

Introduction

Nanomaterials hold the promise of providing new properties that far exceed
traditional material performance. However, in many instances, significant improvements

in material properties of nanocomposites have not yet been achieved} 45' 46

mainly
because the factors affecting nanoparticle dispersion are poorly understood. In our recent
work, we demonstrated various strategies for the dispersion of organic nanoparticles in
polymers.208 Here we extend that work and define the dispersion techniques as well as the
polymer and nanoparticles parameters, including the polymer molecular mass (Mp), its
radius of gyration (Rg), nanoparticle shape, concentration as well as its radius (a),
required to cause simultaneous enhancements in multiple material properties and hence
produce truly multifunctional nanocomposites, with both organic and inorganic
nanoparticles.

Recently, fullerenes (C60 or bucky balls, diameter ~ 0.7 nm) have received much

attention as nanofillers, with pure fullerenes and their derivatives being used to impart

fascinating photonic, electronic and biomedical properties, which could prove useful for a

28, 209 210, 211

gamut of fiIture applications, including solar cells, superconductive materials
and drug delivery.212 However, the dispersion of fullerenes in polymers has proven quite

difficult.“ 28' 2'4 To improve the compatibility of fullerenes with bulk polymers, various

123

techniques, including the modification of fullerene structure and direct attachment of

fullerenes to the polymer backbone by covalent bonds, have been tried. These methods,

apart from being resource intensive, can not be used to produce fully miscible blends.47
To determine whether dispersion of fullerenes is possible, a reasonable estimate

26, 208

of the ultimate solubility in polymers can be made with the Flory theory to arrive at

the solvent binodal volume fraction (¢3) of: — In(¢3) 2 1+3”, in the limit of small
nanoparticle concentration. Since the chi parameter (1) is related to the molecular

insertion energy on a lattice (s) and given by: x = za’kBT, where z is the coordination
number, k3, the Boltzmann constant and T, the temperature; one expects its value to be of
order 1 — 10, allowing one to predict soluble concentrations of up to ~ 10 vol%. Even
with the basic Flory theory suggesting the possible dispersion of fullerenes, previous

studies in the literature have been unsuccessf‘111.24'2'3'214

Experimental

Nanocomposites of fullerenes and polystyrene were prepared through co-
dissolution in toluene followed by precipitation into methanol. The solids were filtered
from methanol and dried in vacuum at 50°C for at least a week to ensure complete
solvent removal. For rheological measurements, 8-mm diameter discs were pressed under
vacuum in a specially designed pellet press and were used with the 8-mm parallel plates
fixture of a Rheometrics ARES rheometer set at a gap of approximately 0.4 mm.
Frequency sweeps in the range 0.1-100 rad/sec were performed at various temperatures

and then combined using time-temperature superposition to yield a master curve at

124

170°C. The strain during the dynamic shear test was kept small enough to ensure that all
response was in the linear viscoelastic region. The magnetite (Fe3O4) nanoparticles were
obtained from the Ferrotec Corporation. The particles are coated with a stabilizing
dispersing agent (surfactant) to enable their solubility in organic solvents. The disks
obtained from the pellet press were also used to make films by compression in a Wabash
compression molding press at 160°C. Steel spacers were used to obtain the desired film
thickness. After compression the films were aged at 170°C for 3-4 hours to ensure
homogeneity and then samples were cut from the film for dynamic mechanical analysis
with a Rheometrics RSA III. The phase separated films were produced by co-dissolution
of polystyrene and fullerenes in toluene followed by casting onto a glass slide. All these
films were then used as samples for dynamic mechanical analysis, wide angle X-ray
diffraction and electrical conductivity tests. Thermal analysis was performed using a TA
instruments Q1000 DSC. Samples were heated and cooled at 5°C/min.
Therrnogravimetric analysis (TGA) was carried out using a TA instruments Q50 TGA.
Here, the samples were heated at 20°C/min from room temperature to 330°C and held

isothermally for up to 24 hours.
Results and Discussion

In our previous work,208 we showed that the polymer radius of gyration (Rg) must
be greater than the nanoparticle radius (a) to ensure nanoparticle dispersion. However,

even when the dispersed state is thermodynamically stable, it may be inaccessible unless

the correct processing method is employed for nanoparticle dispersion. We find that rapid

125

precipitation (see methods for details) can be used to produce miscible fullerene —
polystyrene nanocomposites up to a maximum concentration of ~ 2 vol% in linear,
monodisperse polystyrene. In comparison, gradual solvent evaporation (a method
typically employed for nanoparticle dispersion by various researches) leads to large scale
phase separation (Fig. 7.1.a) of the bucky balls. The formation of these phase separated
structures relates directly to the difference in solubility between the linear polymer and
the fiIllerenes which causes the fullerenes to precipitate from solution before the linear
polymer. However, using rapid precipitation, a more homogeneous blend can be
obtained} ”6 as the nanoparticle and the polymer separate out of solution together. These
nanocomposites can then be drawn into fibers, Fig. 7.1.b, and no large scale aggregates
are apparent. They can also be compression molded to form thin films, as shown in Fig.
7.1.c and 7.1.d. A color shift from light to dark brown with increasing concentration of
fullerenes can be clearly seen in these pictures. In comparison, the pure polystyrene film

is colorless.

126

- utters.“-
PS 1 wt%; 20 Wt%C

l l

10 wt% Q",
l
l

 

Images in this dissertation are presented in color.

Figure 7.1. It is possible to disperse fullerenes in polystyrene by rapid precipitation.
Fullerene-polystyrene nanocomposites developed through solvent evaporation produce
large phase separated domains a, while rapid precipitation yields homogeneous blends
that allow melt spinning of fibers b. The nanocomposites can also be compression
molded to prepare free standing thin films as shown in the optical micrographs c, and d.
Markings on the films are from the platens.

At this point, it is important to consider the average interparticle half gap (h)
between the dispersed fullerenes. Twice this distance represents the average distance

between particles and is approximated by; h/a = [¢,,,/¢]w

— 1, where ¢,,. is the maximum
random packing volume fraction (~ 0.638). At a fullerene weight fraction of 0.0], the
average interparticle half gap is ~ 1.3 nm which is much smaller than the 393 kD

polystyrene’s radius of gyration (Rg) (~ 17 nm), considered above, in Fig. 1.17' Thus, it

127

can be imagined that the linear polymer would be severely distorted from its equilibrium
conformation because of confinement caused by the presence of fullerenes.95 Higher
particle loadings would probably enhance this distortion considering that the interparticle
gap would decrease to ~ 0.4 nm at a fullerene weight fraction of 0.1. At this volume
fraction, the interparticle gap is comparable to the fullerene equilibrium separation in a
single crystal215 and the polystyrene monomer size! And so it is quite remarkable that we
get good dispersion of fullerenes in polystyrene up to ~ 2 vol% or ~ 3.5 wt%.

From differential scanning calorimetry (DSC) measurements, a first order
transition from simple cubic structure to face centered cubic structure around —15°C was
observed for pure fullerenes.215 This transition is clearly visible in Fig. 7.2.a and is also
apparent in the 10 wt% blend produced by solvent evaporation (the inset shows an
expanded view of the DSC data obtained for the 10 wt% blend prepared by solvent
evaporation). Note the glass transition for polystyrene is also apparent at ~105°C. In
contrast, the 10 wt% blend prepared by rapid precipitation shows a single transition near
the glass transition temperature of pure polystyrene, suggesting the absence of large
phase separated fullerene domains or that the simple cubic to face center cubic transition
does not occur in this case.

In Fig. 7.2.b, we show the intensity (obtained from wide angle x-ray scattering,
WAXS) as a function of d spacing, for the various nanocomposites prepared by rapid
precipitation, where d = 27r/q, q is the wave vector defined as 47:01 >< sin(19/Z) with 2., the
X-ray wavelength (1.54 A) and 6, the scattering angle. No peaks are present in the
WAXS intensity profile for the 1 wt% nanocomposite, confirming the absence of phase

separated fullerene domains,2'6 however, at higher concentrations, peaks in the WAXS

128

intensity can be clearly seen. These match well with those seen for fiIllerene single

crystals,”5

as shown in the figure, and are probably the result of scattering from phase
separated crystallites in the higher concentration blends.

The same WAXS intensity data is plotted as a function of the wave vector in Fig.
7.2.c, together with the data for the 10 wt% blend prepared by solvent evaporation. It can
be seen that the blend prepared by gradual solvent evaporation displays a large degree of
low q scattering, clearly indicating large scale phase separation,18 which is absent in the
blends prepared by rapid precipitation. Subsequent TEM experiments on the blends
prepared by rapid precipitation did, however, uncover some phase separated regions
approximately 200 — 300 nm in size (Fig. 7.2.d) for concentrations above 1 wt%.
However, it is clear that the ubiquitousness of the phase separated regimes is greatly
reduced by employing the rapid precipitation method as evidenced by the lack of low q-
vector scattering. It should be noted that all of the samples were annealed for ~ 24 hrs, at
170°C, before performing the TEM and WAXS experiments, to make sure that rapid
precipitation does not lead to a kinetically trapped metastable state. These aging
conditions are above the glass transition temperature of polystyrene (106°C) and the
relaxation or reptation time is about 40 sec. at 170°C, ensuring the polymer molecules
have explored many configurations; while the RMS diffusion distance of the
nanoparticles is on the order of 100’s nm also ensuring that they have explored sufficient
space within the sample to achieve an equilibrium.

To ascertain whether the transition in the fullerene packing (seen for the pure

fullerenes around — 15°C) occurs in these phase separated structures, electron diffraction

patterns at different temperatures from the fiIllerene crystallites produced by both solvent

129

evaporation and rapid precipitation were obtained. Fig. 7.2.e shows the diffraction pattern
for the fullerene crystallites produced by solvent evaporation at room temperature. It can
be seen that the diffraction pattern has hexagonal symmetry, as expected. A clear change
in the diffraction pattern and hence the crystal structure can be observed on lowering the
temperature to -50°C (Fig. 7.2.f), which can be related to a transition from face center
cubic packing to simple cubic.

The much smaller crystallites present in the 5 wt% and 10 wt% samples produced
by rapid precipitation also showed a diffraction pattern with hexagonal symmetry at room
temperature (similar to Fig. 7.2.e); however, quite surprisingly no change was observed
in the diffraction pattern on lowering the temperature to as much as --70°C2'7 (which was
the limit of temperature control in the TEM). Thus, rapid precipitation provides, in
essence, a method for ‘freezing’ the crystal structure of the fullerene crystals, which
could prove to be very important for future electronic application of both fullerenes and
their derivatives.217 We suspect the transition does not occur as the small crystallites are
tightly encased by the surrounding polystyrene not allowing an expansion to the simple
cubic structure. It should be noted here that for the 1 wt% blend and regions where there
are no crystallites for higher concentration samples, there was no equivalent electron
diffraction pattern. Thus, long range order in the homogeneous blend, or in the regions

outside the nanocrystals, is not present.

130

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131

Images in this dissertation are presented in color.

Figure 7.2. Dispersion of 1 wt% fullerenes is possible, however, higher
concentration mixtures tend to have slight phase separation with small crystallite
formation. a, Dispersion of 10 wt% fullerenes in 393 kDa polystyrene via rapid
precipitation leads to a single (glass) transition of the nanocomposite (PS — 10 wt% C60
RP) with a glass transition that is slightly greater than that for pure polystyrene (Pure 393
kDa PS). Pure fullerenes have a crystal structure transition around -15°C (Pure C60)
which is absent in the nanocomposite produced by rapid precipitation, but is present in
the phase separated film produced by solvent evaporation (PS —- 10 wt% C60 SE), as can
be seen more clearly in the inset. b, The change in the polystyrene WAXS intensity
profile (Pure 393 kDa PS) with the addition of fullerenes for mixtures produced with
rapid precipitation can be significant. At 5 and 10 wt% fullerenes (5 wt% RP and 10 wt%
RP) evidence of a crystalline structure becomes clear while the amorphous halo for
polystyrene is only slightly changed through addition of 1 wt% fullerenes (1 wt% RP).
The lines at an intensity of 2000 are positions of the structure peaks seen for a fiJllerene
single crystal plotted as a function of d-spacing. c, The WAXS intensity profiles, as a
function of q-vector, for 10 wt% fullerene — polystyrene mixtures produced via rapid
precipitation (PS -— 10 wt% C60 RP) and solvent evaporation (PS — 10 wt% C60 SE) are
vastly different with the latter showing low q scattering indicative of large scale phase
separation. The data for the sample prepared by rapid precipitation agrees well with that
for pure polystyrene (Pure 393 kDa PS) at low q-vector. d, A TEM micrograph for the 10
wt% fiillerene mixture produced by rapid precipitation shows some phase separated
crystallites. e, An electron diffraction pattern from a crystallite (present in a blend
prepared by solvent evaporation) at room temperature demonstrating six-fold symmetry.
f, Electron diffiaction pattern from another crystallite, from the same sample, at -50°C.

In our previous work,8 we reported for the first time that the addition of
intramolecularly crosslinked polystyrene nanoparticles to linear polystyrene, quite
surprisingly, caused a decrease in the polymer melt viscosity, contradicting Einstein’s
century old relation. It was postulated that the viscosity decrease observed in these
nanocomposites was directly related to the increase in the melt free volume caused by
nanoparticle addition.lo However, subsequent experiments95 revealed that a change in
fiee volume does not account for all of the effects observed in this system, with a

viscosity decrease only present for entangled and confined (h < Rg) systems. Indeed,

addition of nanoparticles led to a viscosity increase in unentangled polymers. This

132

provides us two design parameters to cause a viscosity reduction in nanocomposites: the
polymer must be entangled (M, > MC, where Mc is the critical molecular mass critical
mass for entanglement coupling”) and the interparticle half gap h < R8 of the polymer. It
should also be pointed out that the shape of the nanoparticles is extremely important as so
far only spherical nanoparticles have been shown to provide a viscosity decrease, with

other nanofillers like nanoclaysI38 and carbon nanotubesm'219

producing a large increase
in the viscosity of the polymer melt, leading to more challenging processing conditions.
From Fig. 7.3.a, it can be seen that the unusual viscosity decrease first seen in the
ideal polystyrene nanoparticle - linear polystyrene system is repeated here for the
fullerene - polystyrene system. The addition of fullerenes, at all the mass fractions
considered, causes a large decrease in the terminal viscosity of polystyrene as shown in
Fig. 7 .3.a (PS 393 kD is entangled, R3 of polymer ~ 17 nm hence Rg > a, and for all these
nanoparticle concentrations h < Rg). Indeed an 80% reduction in the melt viscosity can be
observed by addition of 10 wt% fullerenes! This is one of the largest reductions in
viscosity on the addition of nanoparticles reported in the literature. It is known that phase
separated structures (crystallites) are present with the 5 and 10 wt% samples (Fig. 7.2), at
least at room temperature, and so it is interesting that the viscosity continues to decrease
even under this condition. However, it can be seen that the viscosity does not change at
the same rate at concentrations above 1 wt% and so, apparently, the small, phase
separated, crystallites, should they be present in the melt, slow the viscosity decrease.
Due to the gradual color change in the nanocomposites (Fig. 7.1) we suspect there

may be more fullerenes dissolved in the polystyrene phase for the 10 wt% rapidly

precipitated blend than at the initial concentration where phase separation was detected (~

133

2 vol%). This may account for the continued viscosity decrease despite the potential
introduction of crystallites. Note, the 10 wt% fullerene phase separated system prepared
via solvent evaporation (Fig. 7.1.a) shows a large viscosity increase above pure
polystyrene and in fact no terminal (zero shear) viscosity is observed for the system.
Viscoelastic materials are also fast gaining popularity in damping applications,220
however, issues like poor thermal stability, reliability and high weight penalty have

1.22' showed addition

severely affected their large scale development. Recently, Suhr et a
of multiwalled carbon nanotubes (MWNT) to epoxy can greatly improve its mechanical
damping properties.222 This unique observation of increasing the damping properties,
without any detrimental effects on the polymer strength, was expected to be related to the
large surface area to volume ratio present in these nanoscale fillers.221

The MWNT’s have a interfacial contact area of ~ 100 m2/g, in comparison, the
fullerenes have an interfacial contact area of ~ 1300 mz/g (a high interfacial area is
expected for all spherical nanofillers). It was hypothesized by us that this large fullerene
contact area would allow for large frictional dissipation of energy, leading to excellent
damping properties. From Fig. 7.3.b, it can be seen that this is indeed the case. A five
fold increase in the loss modulus (E ’) of the fullerene — polystyrene nanocomposite can
be observed without significantly affecting the elastic modulus (E ). Indeed a slight
increase in the elastic modulus is observable. We note that Suhr et al. used 50 vol% of
MWNT to achieve ~ 3-times enhanced damping while the loss modulus we have

measured with the 50 wt% (~ 37 vol%) firllerene nanocomposite shows ~ 5 fold increase

and a similar increase in damping is expected. It should be pointed out that this is the first

134

example of a spherical nanoparticle causing significant improvements in the damping
properties of polymers.

The weight loss with time for the various fullerene - polystyrene nanocomposites
prepared by solvent evaporation and rapid precipitation are shown in Fig. 7.3.c. All the
samples were kept isothermally at 330°C under a nitrogen atmosphere. It can be seen
addition of fullerenes causes a significant reduction in the degradation rate of
polystyrene, suggesting their usage as possible fire retardants (other experiments under an
air atmosphere also show a significant improvement in thermal stability on fullerene
addition). It should be noted here that the weight fraction of the samples remaining at the
end of each experiment equals the weight fraction of fullerenes in the nanocomposites, as
fullerenes do not degrade at 330°C.

Nanocomposites have shown great promise as effective fire retardants for some
types of materials.223 Typically, research on the thermal stability of nanocomposites has

4 and layered silicates,225 where the spacing

focused on the use of graphite sheets22
between the layers is in the nanometer range. It has been proposed that enhanced barrier
properties are related to the observed improvement in thermal stability. Barrier properties
take into consideration both the thermal barrier, which reduces the polymer temperature,
as well as mass transport barrier which makes it difficult for the degradation products to
leave the polymer, and for oxygen to diffirse into the polymer. However, such a
mechanism for thermal stability might not extend to our case as unusual permeability
results have been reported in the case of nanoparticle filled polymers. It was seen that

nanoscale, fumed silica particles when blended with poly(4-methyl-2-pentyne)

simultaneously and rather surprisingly enhance both membrane permeability and

135

selectivity for large organic molecules over small permanent gases.10 Such an effect in
our case would probably enhance the thermal degradation of the polymer by decreasing
the mass transport barrier.

In more recent work, it has been postulated that the formation of a jammed
network of nanofillers is essential for causing an improvement in the thermal degradation

properties of nanocomposites containing nanotubes and carbon black.219

However, in our
case we see significant improvements in the thermal properties coupled with a large
viscosity decrease (Fig. 7.3.a), clearly indicating the absence of a jammed or gel-like
network of nanoparticles within the polymer melt. Indeed the formation of a gel-like
network in the case of carbon black particles would indicate their phase separation from
the polymer, especially if the radius of the carbon black particles is greater than the radius
of gyration of the linear polymer (Rg < 0).208

Improvement in thermal stability for our case may then be related to the overall
free energy of the system. It can be imagined that a large increase in the system’s
entropy, because of the firllerene dispersion, leads to a negative overall free energy for
the system (this is the reason why the fullerenes stay dispersed).208 Removal of the linear
chain through thermal degradation (the fullerenes do not degrade at 330°C) in this case
would lead to a gain in the overall free energy (make it positive) of the system and could
be the reason for slowing down the degradation of the composite. In other words, the
polymer and its degradation products might condense within the nanoparticles’ interstices
and on their surfaces to remain thermodynamically stable until the overall entropy is

increased by the low molecular mass degradation products leaving the system. It should

be pointed out that this gain in free energy on the dispersion of particles is truly a

136

nanoscale phenomenon since addition of larger particles leads to an adverse free energy
effect.208 So again Rg must be greater than a to cause improvements in the thermal
stability of the nanocomposite.

The electrical conductivity of the fullerene-polystyrene nanocomposites was also

determined. As has been seen before with the addition of nanoscale fillers to

226, 227 228

therrnoplastics and polymer electrolytes, addition of fullerenes (with the rapid
precipitation technique) also causes an increase in the conductivity of polystyrene (Fig.
7.3.d). It is interesting that this increase in conductivity, even though small, is much
greater than Maxwell’s predicted increase50 for an infinitely conductive spherical filler.
This unusual increase in conductivity is expected to be related to the small interparticle
gap (2h) in the nanocomposite. This small gap would allow charge transfer by electron

h0pping between electronegative fullerenesm' 230

(if they are close enough) and may
even allow for ballistic electron transfer?“ Indeed the formation of small fullerene
nanoclusters (in the higher fullerene concentration samples) may enhance the
nanocomposite conductivity even more.231 In comparison, the nanocomposite prepared
by solvent evaporation has a lower conductivity than neat polystyrene (Fig. 7.3.d).

Thus, we have successfully designed a truly multifunctional7 nanocomposite with
enhanced damping properties, better thermal stability, greater electrical conductivity
coupled with a much reduced melt viscosity allowing for easier melt processing and the
development of finer features, using existing industrial technologies like injection

molding and extrusion. It is also the first time that all of these improvements in the bulk

properties have been shown to occur simultaneously in any nanocomposite.

137

 

 

   
    
    
 
 
  
    
 

 

   
    
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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1.0 10 ET .5
2.5 '— ‘ : b 2
PS 19.3k + Cc,o ; 3
08 2'0— prlems : Dice-ooooooooo000".. '. -‘
-.‘-3 ' 1-5 " ‘ 610° _- \ 1:
9 _0 Theoryl _ Ll, : VA": ,5
€06” 00 “1010” E”- r- I
8 . . m 7
§ 1° 2‘ i
04 — T _ 1700C -‘ : — ELPS 33k NIB
' - - - . E'oPS swoon-50 wt% RP
' — E"-PS 393k ptre
0" ' PS 393k + c,0 RP blends " ‘06 E ' ° ' BPS 393k+c°°5m RP
I l I l I " I l ! I
0.00 0.02 0.04 0.06 0.08 0.10 40 60 80 o 100 120
Fullerene mass fraction Temperature ( C)
1 I I I I g
100 d I
1.6 '— -1
a 1.4 ’- . .1
80 '12; 1.2 l- . ._
if g 1 0 Maxwell Model _
E, 60 g 0.8 - -
—P8393k ‘ g 0.6— . 1o"...z _
40 --- Ps 393k +0,o - 5wt% RP 0% — 0‘41 ‘ 105112 S°"’°"t Evapaamm
- -P3393k+c,,-10m%RP 0.2- \ .
°""’?393"t°eo“9“‘%915 1 - 1 - .4.
0.0) 0.02 0.04 0.06 ON 0.10
0 50 100 150 200 250 .
Falerene mass fractIon

Time (mins)
Images in this dissertation are presented in color.

Figure 7.3. Addition of fullerenes to linear polystyrene has multifunctional effects on
the properties including a viscosity reduction, increase in dissipation, increase in
degradation time and increase in conductivity. a, The addition of fullerenes to
polystyrene leads to a sharp decrease in the melt viscosity as long as the samples are
prepared by rapid precipitation. This behavior directly contradicts Einstein’s prediction
(theory) of a viscosity increase in such a system. The inset shows the effect of fullerene
addition on the viscosity of unentangled polystyrene (Mw= 19.3 kDa). The blend was
prepared by rapid precipitation. b, Minimal changes are seen in the storage (E’) modulus
on the addition of fullerenes while a five fold increase is observed in the loss (E”)
modulus, indicating a significant improvement in the damping properties of the
composite. The samples are pure 393 kDa polystyrene (Pure 393 kDa PS) and the same

138

polystyrene containing 50 wt% fullerenes produced by rapid precipitation (PS- 50 wt%
C50 RP). c, The addition of fullerenes, when well dispersed, greatly reduce the rate of
thermal decomposition of the nanocomposite as shown by weight loss curves obtained by
heating the samples to 330°C, under a nitrogen atmosphere. The samples containing 1
and 10 wt% C60 samples were produced by rapid precipitation (labeled RP) and when
compared to pure 393 kDa polystyrene (Pure 393 kDa PS) have a much greater time to
degrade. For comparison, phase separated fullerenes perform much worse and a 10 wt%
blend prepared by solvent evaporation (PS — 10 wt% C60 SE) only slightly increases the
degradation time. d, Conductivity of C60 - 393 kDa polystyrene nanocomposites, relative
to pure polystyrene. When fullerenes are well dispersed in polystyrene, prepared by rapid
precipitation the conductivity rises above the Maxwell model prediction for an infinitely
conducting particle. In comparison a sample containing phase separated structures
produced by solvent evaporation has a relative conductivity that is ~ 90% lower than pure
polystyrene. Conductivity was measured at a variety of frequencies and only the 10", 102
and 105 Hz data are shown.

To test if our design parameters (spherical nanoparticle, entangled polymer, Rg >
a, h < Rg and using rapid precipitation for dispersion; the various design parameters and
the properties they affect have been summarized in Table 7.1) can be used to produce
multifunctional nanocomposites with inorganic nanoparticles as well, we study the
effects of adding magnetite nanoparticles (see methods) to polystyrene (Mw = 393 kD). A
picture of the nanocomposite prepared by rapid precipitation, attracted to a permanent
magnet, is shown in Fig. 7.4.a, showing that the incorporation of the nanoparticles has
made the nanocomposite ferromagnetic. Again, rapid precipitation and the condition that
R8 is larger than 0, enables good dispersion of the nanoparticles as evidenced by the TEM
image shown in Fig. 7.4.b. Image analysis shows that the nanoparticles are quite
polydisperse with their radius varying between 5-10 nm. The good dispersion 'of the
magnetic nanoparticles, at this high density, opens up plethora of possible future
applications including electro-magnetic shielding, high density memory, magnetic

232-234

recording, drug delivery and separation aids (this is an additional benefit which was

of course not seen with the fullerenes). Again, as was the case with fiillerenes, solvent

139

evaporation leads to large scale phase separation (Fig. 7.4.c, note the change in the scale
bar compared to Fig. 7.4.b) due to the large difference in solubility between the
nanoparticles and the polymer in the common solvent (benzene). The incorporation of the
ferromagnetic nanoparticles using rapid precipitation also improves the thermal stability
(Fig. 7.4.d) of the nanocomposite. Again the thermal stability of the rapidly precipitated
blend is better than the blend prepared by solvent evaporation. The initial, rapid weight
loss for time less than 100 see is most likely due to the steric stabilizing layer leaving the
system. The magnetite addition also simultaneously causes a massive reduction in the
melt viscosity (Fig. 7.4.e). It is quite surprising that just 5 wt% (or ~ 1 vol%) of the
magnetite nanoparticles can cause an ~ 90% reduction in the polymer melt viscosity,
which is again one of the largest viscosity decreases reported on the addition of
nanoparticles. It would thus appear that the improvement in thermal stability and the
viscosity decrease seen in the fullerene - linear polystyrene blends can transcend to other
nanoparticle - polymer systems and is not the result of some peculiar chemical or

physical interaction.

140

Table 7.1. Design parameters for nanoparticle dispersion and producing multifunctional
nanocomposites.

 

 

 

 

Parameter Parameter values to enhance bulk properties
Method for Rapid precipitation provides a better technique for
nanoparticle dispersion nanomrticle dispersion.

Polymer molecular Mp > MC for nanoparticles to cause a reduction in viscosity;
mass (M) M, also determines Rg.
Polymer R3 Rg > a for nanoparticle dispersion and for improving thermal

stability; Rg > h for viscosity reduction.
So far, only spherical nanoparticles have been shown to
cause a viscosity decrease; spherical nanoparticles also have

 

 

 

Nanoparticle shape higher interfacial contact area leading to better damping
properties.

Nanop article radius (a) :2 1;“; for nanoparticle dispersmn and Improvmg thermal

Nanoparticle Determines the interparticle half gap, h; Rg > h for viscosity

 

 

 

concentration reduction.

 

141

[Milt/swam» ‘>

PS 393k+Fe NP—
5wt% RP

      

PS 393k + Fe NP—
5wt% SE

   

 

 

 

 

 

 

 

 

 

100 -I—PS:I393kpuie ' I ‘ 2+
—— P3393k+FeNP-5wt%RP
80~ PS393k+FeNP-5M%SE_ _
i 60 _ T = 330°C _ _
.C

'% 4o _
g d

20 L _

1 0 PS 393k pure
0* I I i 10 "u P8393k+FeNP-5wt% ‘
0 200 400 600 8001000 _3 o 3
Time (mins) 10 10 10
Frequency (rad / sec)

Images in this dissertation are presented in color.

Figure 7.4. It is possible to disperse ferromagnetic nanoparticles in linear
polystyrene (393 kDa) to make a ferromagnetic polymeric material. a, Polystyrene is
slightly colored by the dispersed magnetite nanoparticles which cause the sample to be
attracted to a permanent magnet. b, A TEM micrograph showing the nanoparticle
dispersion with gross phase separation. c, Nanoparticle - polystyrene blends developed
through solvent evaporation produce large phase separated domains. Also, as shown for
the fullerene nanoparticles, the magnetite nanoparticles at 5 wt% reduce the amount of
degradation (d) and the melt viscosity at all frequencies (e). The degradation experiment
was performed at 330 °C under a nitrogen atmosphere and the viscosity was measured at
multiple temperatures and shified to a reference temperature of 170 °C.

I42

Conclusion

In conclusion, as long as we follow certain critical design parameters (spherical
nanoparticle, entangled polymer, Rg > a, h < R8 and using rapid precipitation for
dispersion), we can create multifunctional nanocomposites with both organic and
inorganic nanoparticles having the desired electrical or magnetic properties, coupled with
enhanced mechanical damping, greater thermal stability and a much reduced melt

viscosity.

143

CHAPTER 8

CONCLUSION

 

In this work we aimed to provide a better understanding of nanoparticle-polymer
blends. There were some significant findings through the course of the project which not
only helped us proceed with the project but will also prove useful to other researchers
working in the area. Some of those findings and their implications have been detailed
below.

First, we started out by comparing the various methods used in the literature for
nanoparticle dispersion. One of the most common methods in the literature was solvent
evaporation,24 which entailed the mixing of the polymer and the nanoparticle in a
common solvent, followed by the evaporation of the solvent. Differences in the
solubility’s of the nanoparticles and the polymer typically led to phase separation in this
case. To overcome this difficulty, we used the ‘rapid precipitation’ technique“ 48
(Chapters 4 and 7). In this case, as both the nanoparticles and the polymer are insoluble in
the non-solvent, they precipitate out together.

With the understanding of the importance of the technique used for nanoparticle
dispersion, we studied the various parameters responsible for the miscibility or phase
stability of nanoparticles in linear polymers. One of the most important findings of this
work is the establishment of a thumb rule for phase stability in nanoparticle-polymer

blends. In Chapter 3 we showed that it is possible to disperse chemically dissimilar

nanoparticles in various polymer matrices as long as the Rg of the polymer > radius of

144

nanoparticle. This simple parameter has allowed us to disperse both organic (like
polyethylene in polystyrene or polystyrene in poly(methylmethacrylate)) and inorganic
nanoparticles (like magnetite nanoparticles or Cd-Se quantum dots in polystyrene) in
dissimilar polymer matrices.

Another important finding highlighted in Chapter 3 is that linear chains get
stretched on the addition of nanoparticles. This has been an extremely controversial

'24' 23”” and some experimental studies'26’

subject in the literature. Multiple simulation
243 have tried to provide a conclusive answer to the issue. However, their findings are
almost equally divided, with half of the studies suggesting that there should be an
increase in the chain dimensions on nanoparticle addition while the other half concluding
that the nanoparticles do not affect the chain dimensions at all. Our experimental work,
using SANS, conducted on the ideal system of polystyrene nanoparticles in linear
polystyrene, conclusively shows that linear chains do indeed get stretched on the addition
of nanoparticles, and that the chain stretching is directly proportional to the volume
fraction of the added nanoparticles.

Another objective of this work was the study of the effects of nanoparticle
addition on the flow properties of polymer melts. This work has been detailed in chapters
4 and 5. It was seen that the addition of nanoparticles to unentangled polymers led to a
sharp increase in their viscosity, in comparison, the addition of nanoparticles to a
polymer near its critical molecular weight for entanglement had almost no effect on the
viscosity of the polymer melt. When extended to entangled polymers, it was seen that the

addition of nanoparticles to a constrained (Chapter 5) and entangled polymer melt caused

a large decrease in the viscosity of polymer melts. This unusual viscosity decrease was

145

seen for various inorganic and organic nanoparticle — polymer systems (Chapters 5 and
6). In certain cases as much as 80 - 90% reduction in the polymer melts’ viscosity was
observed with just 1-5% by volume addition of the nanoparticles. This surprising
behavior has recently been confirmed for a variety of nanoparticle — polymer systems by
various other research groups.“‘ 244448

To understand the reasons for the viscosity reduction caused by the addition of
nanoparticles, we recently measured the diffusion coefficients of various nanoparticles in
an entangled polystyrene matrix (Chapter 7). It was seen that in certain cases the
diffusion coefficient of the nanoparticles was almost 100 times larger than the diffusion
coefficient calculated from the Stokes-Einstein relation based on the bulk polymer
viscosity. We hypothesize that this fast nanoparticle diffusion provides another mode for
polymer relaxation based on the mechanism of constraint release. To confirm this
hypothesis we also measured the viscosity of a nanoparticle — 3 arm star blend. Stars can
only relax by primitive path fluctuations, and as expected, the addition of nanoparticles
caused an increase in the melt viscosity of the stars.

The final objective of this work was to build up materials utilizing the various
important findings in this work. We have taken the first steps in that direction by creating
one of the first ‘multifunctional’7 polymer — nanoparticle composites (Chapter 7). It was
seen that the addition of fullerenes (C60) and magnetite nanoparticles can impart specific
electrical or magnetic properties to the polymer coupled with simultaneous improvements
in the mechanical, thermal and rheological properties.

It is clear in the end that the addition of nanoparticles to polymers can create some

unexpected property enhancements like miscibility despite chemical dissimilarity and a

146

reduction in the polymer melt viscosity, which are not expected with the addition of
micron or colloidal scale fillers. It has to be expected then that there still remain a lot of
fascinating discoveries to be made in this area, which should definitely provide impetus

to a future batch of researchers.

147

LIST OF PUBLICATIONS

The following publications were made as a direct result of the research carried out for

this project.

Published and accepted journal articles:

I)

2)

3)

4)

“Nanoscale effects leading to non-Einstein-like decrease in viscosity”, Michael E.
Mackay, Tien T. Dao, Anish Tuteja, Derek L. Ho, Brooke van Horn, Ho-Cheol
Kim, Craig J Hawker, Nature Materials, 2003, 2(11), 762-766.

“Effect of ideal, organic nanoparticles on the flow properties of linear polymers;
non-Einstein-like behavior”, Anish Tuteja, Michael E. Mackay, Brooke van Horn,
Craig J. Hawker, Macromolecules, 2005, 38, 8000-8011.

“General strategies for nanoparticle dispersion ”, Michael E. Mackay, Anish
Tuteja, Phil M. Duxbury, Craig J. Hawker, Brooke van Horn, Zhibin Guan, R.S.
Krishnan, Science, 2006, 311, 1740-1743.

“The molecular architecture and rheological characterization of novel
intramolecularly crosslinked polystyrene nanoparticles”, Anish Tuteja, Michael E.
Mackay, Brooke van Horn, Craig J. Hawker, Derek L. Ho, 2006, Journal of
Polymer Science — Part B — Polymer Physics, 44, 1930-1947.

Journal articles submitted for review or in preparation:

1) “Multifunctional nanocomposites: nanoparticle induced enhancements in the

thermal, mechanical, magnetic, electrical and rheological properties of polymers.”
Anish Tuteja, Michael. E. Mackay.

2) “Nanoparticles induced expansion in linear polymer coils”, Anish Tuteja, Michael

E. Mackay, Brooke van Horn, Craig J. Hawker.

3) “Breakdown of the Stokes-Einstein relation for nanoscale inclusions in polymer

melts”, Anish Tuteja, Michael E. Mackay, Suresh Narayanan, Michael Wong.

148

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