Controlling Morphology of Multi-Component Block Copolymer
Based Materials
by
Rafal Adam Mickiewicz
B.A.Sc., Engineering Science
University of Toronto (1998)
S.M., Materials Science and Engineering
Massachusetts Institute of Technology (2001)
SUBMITTED TO THE DEPARTMENT OF MATERIALS SCIENCE AND
ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF
DOCTOR OF PHILOSOPHY IN POLYMERS
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
FEBRUARY 2009
©2009 Massachusetts Institute of Technology
All rights reserved
Signature of Author: ______________________________________________________
Department of Materials Science and Engineering
January 16th, 2009
Certified by: _____________________________________________________________
Edwin L. Thomas
Morris Cohen Professor of Materials Science and Engineering
Thesis Supervisor
Accepted by: ____________________________________________________________
Christine Ortiz
Associate Professor of Materials Science and Engineering
Chair, Departmental Committee on Graduate Students
Controlling Morphology of Multi-Component
Block Copolymer Based Materials
by
Rafal Adam Mickiewicz
Submitted to the Department of Materials Science and Engineering on 16 January 2009
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Polymers
Abstract
The ability of block copolymers to self-assemble into ordered microstructures has
attracted much interest both from a pure scientific perspective and for their potential in
numerous industrial applications. The microphase separation of block copolymers has
been successfully exploited in a wide range of applications, such as templating and
lithography, enhancement of mechanical properties, and nanoreactor schemes.
This thesis focuses on the characterization of the morphology in composite
systems where one or more of the components is a block copolymer. In the first part of
this thesis, binary blends of very high molecular weight diblock copolymers with a low
molecular weight triblock copolymer are investigated. The high molecular weight diblock
copolymers are very strongly segregating, with interaction parameter values, χN, in the
range 470 – 1410. The phase diagram revealed a large miscibility gap for the blends, with
macrophase separation into two distinct types of microphase separated domains and
implied virtually no solubility of the much higher molecular weight diblocks in the
triblock. For certain blend compositions, morphological transitions from the lamellar to
cylindrical and bicontinuous structures were also observed, even though the overall
composition in the blend would be expected to favor the lamellar microstructure. This
was found to result from the compositional asymmetry of the triblock copolymer
influencing the curvature of the inter-material dividing surface (IMDS). Finally, a strong
segregation theory model was used to interpret the observed results.
In the second part of this thesis the microstructure formation in nanocomposites
based on a liquid crystalline side chain block copolymer (LCBCP) and gold nanoparticles
was investigated. The location of the nanoparticles was found to not only depend on the
surface chemistry of the gold nanoparticles, but also on the self-organization within the
liquid crystalline domain of the LCBCP. The nanoparticles were excluded from the liquid
crystalline domains due to the high free energy penalty of disrupting the smectic layering.
The final location of the nanoparticles within the composite was determined by the nature
of the stabilizing surface coating.
The work presented in this thesis revealed a number of interesting tools which are
useful for obtaining a wide range of morphologies in multi-component block copolymer
systems.
Thesis Supervisor:
Edwin L. Thomas
Morris Cohen Professor of Materials Science and Engineering
2
Table of Contents
Table of Contents .............................................................................................................. 3
Table of Figures................................................................................................................. 5
Table of Tables ................................................................................................................ 12
Acknowledgements ......................................................................................................... 14
Chapter 1
1.1
1.2
1.3
1.4
1.5
1.5.1
1.5.2
1.6
Introduction............................................................................................. 15
Scope of Work .......................................................................................... 15
Block Copolymers .................................................................................... 16
Binary Blends of Block Copolymers ........................................................ 17
Nanocomposites........................................................................................ 20
Block Copolymer Nanocomposites .......................................................... 23
Theoretical Work ................................................................................ 23
Experimental Work............................................................................. 26
References................................................................................................. 32
Chapter 2
2.1
2.1.1
2.1.2
2.2
2.3
2.4
2.5
2.6
2.7
Materials and Experimental Methods .................................................. 38
Polymers ................................................................................................... 38
Styrene-Isoprene Block Copolymers .................................................. 38
Liquid Crystalline Side Chain Block Copolymer ............................... 40
Block Copolymer Blends Preparation ...................................................... 42
Nanoparticle Synthesis.............................................................................. 42
Liquid Crystalline Side Chain Block Copolymer Composites ................. 43
Transmission Electron Microscopy .......................................................... 44
Ultra-Small-Angle X-ray Scattering (USAXS) ........................................ 44
References................................................................................................. 45
Chapter 3
3.1
3.2
3.3
Binary Blends of Diblock Copolymers with a Triblock Copolymer .. 46
Results and Discussion ............................................................................. 47
Conclusion ................................................................................................ 66
References................................................................................................. 68
Chapter 4
Influence of Short Block Copolymers on the Morphology of Binary
Block Copolymer Blends: A Modeling Study....................................... 70
Results and Discussion ............................................................................. 70
Conclusion ................................................................................................ 81
References................................................................................................. 83
4.1
4.2
4.3
3
Chapter 5
5.1
5.2
5.3
Liquid Crystalline Side Chain Block Copolymer Nanocomposites.... 85
Results and Discussion ............................................................................. 87
Conclusion .............................................................................................. 106
References............................................................................................... 107
Chapter 6
6.1
6.2
6.2.1
6.2.2
6.3
6.4
Directions for Future Study ................................................................. 109
Block Copolymer Blends in Confined Geometry................................... 110
Block Copolymer Gel and Nanoparticle Composites............................. 116
Block Copolymer Gel and TMV Composites................................... 117
Block Copolymer Gel and Gold Nanoparticle Composites.............. 123
Conclusion .............................................................................................. 127
References............................................................................................... 129
Chapter 7
7.1
7.2
7.3
7.4
7.5
Appendix................................................................................................ 133
Group Contribution Calculation ............................................................. 133
BZL Strong Segregation Theory Model ................................................. 134
Self Consistent Field Theory .................................................................. 137
List of Abbreviations .............................................................................. 138
References............................................................................................... 139
4
Table of Figures
Figure 1.1. Schematic of diblock copolymer morphology. The numbers percentages
indicate the volume fraction of the component shown in dark in the figure. The
morphologies are symmetric beyond 50% volume percent, with the dark domains
becoming the light domains. ............................................................................................. 17
Figure 1.2. Schematic showing how a block copolymer acts to stabilize an immiscible
blend of two homopolymers. The size of the blue micelles is on the order of 1 µm........ 18
Figure 1.3. Calculated interfacial area per volume of particles (in nm-1) assuming a right
circular cylindrical particle shape for different particle diameter d and aspect ratio l/d.
Exfoliated clay (laponite or montmorillonite) particles, spherical nanoparticles, and single
wall carbon nanotubes generate up to four orders of magnitude more interfacial area as
compared to conventional filler materials, like glass fibers, of equal volume filling
fraction. Reproduced from reference 44. .......................................................................... 23
Figure 1.4. Schematic of important parameters for BCP/nanoparticle composites. The
core size, dcore, is the diameter of the rigid particle. The corona is the shell occupied by
the stabilizing surface ligands, and its thickness is tcorona. The effective size of the
nanoparticle is then dcore+2tcorona. The IMDS, or inter-material dividing surface, is the
interface between the A and B type domains. The characteristic domain spacing is given
by L=lA+lB, where lA and lB are the size of the A and B domains, respectively. .............. 24
Figure 2.1. Chemical structure of the poly(styrene-b-isoprene) diblock copolymer. ....... 39
Figure 2.2. Chemical structure of the PS-PVMS block copolymer and liquid crystalline
mesogen. The polymer used is 100% functionalized, giving z = 0. Although there is a
small amount of dimethyl siloxane present, x << y, and the polymer is essentially a
diblock copolymer.5 .......................................................................................................... 41
Figure 2.3. Schematic representation of the LCBCP morphology in an aligned and
oriented fiber. The LC mesogen aligns into interdigitated smectic layers, with the layer
normal parallel to the PS cylinder axis, and a d-spacing of 3.4 nm as determined by
SAXS.4, 5 ........................................................................................................................... 41
Figure 3.1. Bright field TEM micrographs of thin OsO4 stained sections of the neat
diblock copolymers, showing all with lamellar morphologies: a) SI450, b) SI700, c)
SI1000, d) SI1500. ............................................................................................................ 48
Figure 3.2. Bright field TEM micrographs of thin OsO4 stained sections of blends of
SI450 with SIS, with compositions in weight percent (SI450/SIS): a) 5/95, b) 10/90, c)
25/75, d) 50/50, e) 75/25, f) 90/10, g) 95/5, h) the exceptional SI700 5/95 blend exhibits
some cylindrical domains in the minority SI700 phase in addition to thick and thin
lamellar regions. Note that the micrographs were taken from areas containing both the
thin triblock lamellae and thick diblock lamellae, to indicate the coexistence of the two
5
phases, and are not representative of the actual volume percent of each type of domain,
which varies strongly with blend composition. ................................................................ 49
Figure 3.3. Bright field TEM micrographs of thin OsO4 stained sections of blends of
SI1000 with SIS, with compositions in weight percent (SI1000/SIS): a) 5/95, b) 10/90, c)
25/75, d) 50/50, e) 75/25, f) 90/10, g) 95/5. The 10/90 and 50/50 blends exhibit a
disordered morphology with IMDS curvature towards the PS domains, whereas the 25/75
and 75/25 blends reveal a PS cylindrical morphology. According to the scattering data,
the 10/90 blend appears to be disordered cylinders, whereas the 50/50 blend could be
double gyroid, but it is not entirely clear. Nonetheless, micrographs for the latter blend
suggest a bicontinuous morphology.................................................................................. 50
Figure 3.4. Bright field TEM micrographs of thin OsO4 stained sections of blends of
SI1500 with SIS, with compositions in weight percent (SI1500/SIS): a) 5/95, b) 10/90, c)
25/75, d) 50/50, e) 75/25, f) 90/10, g) 95/5. The 5/95, 10/90, and 25/75 blends exhibit a
disordered morphology, which once again appears from the scattering data to be
cylinders. The 75/25 blend appears to exhibit a poorly ordered double-gyroid structure,
and a detail of the structure, showing characteristic serpentine features, is shown in the
inset of (e). Note that while the effective volume fraction of the blends remains in the
lamellar region of the phase diagram ( 0.41 < Φ effPS < 0.44 ), the IMDS is non-flat, with
curvature towards the PS domains.................................................................................... 51
Figure 3.5. USAXS profiles for the SI450 series of blends. The lamellar reflections from
the two different phases are clearly evident, with the intensities of the SIS triblock
reflections increasing with the weight fraction of the triblock in the blend. A single box
outline indicates reflections from the diblock domains and a double box those of the
triblock domains................................................................................................................ 53
Figure 3.6. USAXS profiles for the SI700 series of blends, which are qualitatively similar
to those of the SI450 blends. A single box outline indicates reflections from the diblock
domains and a double box those of the triblock domains................................................. 54
Figure 3.7. USAXS profiles for the SI1000 series of blends. The higher order peaks of the
large diblock are weak or absent, indicating poor long range order. A single box outline
indicates reflections from the diblock domains and a double box those of the triblock
domains. ............................................................................................................................ 55
Figure 3.8. USAXS profiles for the SI1500 series of blends. The change in the scattering
profile going from 25% SIS to 50% SIS is clearly evident, indicating a change in the
morphology from double gyroid-like to cylinders. A single box outline indicates
reflections from the diblock domains and a double box those of the triblock domains. .. 56
Figure 3.9. Domain spacing ( d = 2π q1 ) as a function of the triblock content for the (a)
SI450 and SI700 blend series, and (b) for the SI1000 and SI1500 blend series, obtained
by tracking the position of the first order reflection in the USAXS data. The domain
spacing decreases with increased triblock content and levels off after around 25% by
weight. The error in the measurement was estimated from the broadening of the first
6
order scattering peak, and reflects the higher uncertainty at larger spacing (lower q), due
to the inverse relation between d and q. For the SI1000 and SI1500 blends with
cylindrical morphology, the cylinder radius is directly proportional to the domain
spacing, d, by the relation RCYL = d 2 f 3π , where f is the 2-D area (“volume”) fraction,
based on hexagonal packing. ............................................................................................ 57
Figure 3.10. Morphological phase diagram of the binary blends in the parameter space of
molecular weight ratio, R = M ndiblock 12 M ntriblock , and blend composition, in weight percent SI
(to facilitate comparison with previous studies). The data points for each blend series are
depicted in a unique color. The blue shaded area represents the region where the blends
exhibit lamellar (flat IMDS) morphologies (with one exception at 5% of the SI700
blend). In the yellow shaded area, morphological phase transitions are observed, from
lamellar arrangement to structures with IMDS curvature – cylinders and double gyroidlike, identified by different data point shapes on the graph. The dotted line indicates
where the blends macrophase separate: to the right of the line, the blends are miscible and
exhibit a single microphase separated morphology, whereas to the left the blends are
macrophase separated, with two coexisting microphase separated morphologies. .......... 58
Figure 3.11. Low magnification wide area TEM image of the SI1500 75/25 blend
showing large areas of a distorted gyroid-like structure. .................................................. 61
Figure 3.12. Schematic representation of chain packing of diblock copolymers with an
asymmetric composition. The schematic illustrates the spontaneous curvature implied by
the underlying asymmetry. In the neat block copolymer, this curvature is not expressed,
while the addition of a larger block copolymer of appropriate size (to fill the extra
volume) is capable of stabilizing the curved IMDS morphology. .................................... 63
Figure 4.1. Schematic representation of a binary mixture of two block copolymers of
different lengths for (a) lamellar morphology, and (b) cylinder morphology. It is
important to note that one triblock copolymer chain has been modeled as two diblock
copolymer chains of half the degree of polymerization of the triblock. For the cylinder
morphology (b), the radius of the cylinder is given by rcyl = HAs + HAl........................... 71
Figure 4.2. Reduced free energy plots for the diblock/triblock (SI/SIS) blends
investigated in Chapter 3: (a) SI450 blends, and (b) SI700 blends. The two lines, blue and
red, correspond to the free energy of the lamellar morphology and cylinder morphology,
respectively. ...................................................................................................................... 75
Figure 4.3. Reduced free energy plots for the diblock/triblock (SI/SIS) blends
investigated in Chapter 3: (a) SI1000 blends, and (b) SI1500 blends. The two lines, blue
and red, correspond to the free energy of the lamellar morphology and cylinder
morphology, respectively.................................................................................................. 76
Figure 4.4. Free energy difference between cylinder and lamellar morphology. ............. 77
Figure 5.1. Schematic demonstrating the hypothesis of using a liquid crystal phase
transition to drive nanoparticle location in a block copolymer nanocomposite. .............. 86
7
Figure 5.2. Bright field TEM micrograph of the neat, as cast LCBCP showing a poorly
hexagonally packed, worm-like cylindrical morphology of PS cylinders (light domains)
in a PVMS matrix (dark domains). The image is unstained, with the contrast arising from
the more electron dense siloxane groups in the PVMS. ................................................... 87
Figure 5.3. Chemical structures of the stabilizing ligands used to synthesize the gold
nanoparticles. .................................................................................................................... 88
Figure 5.4. ButSH stabilized gold nanoparticles: TEM micrograph and size distribution
histogram........................................................................................................................... 88
Figure 5.5. HexSH stabilized gold nanoparticles: TEM micrograph and size distribution
histogram........................................................................................................................... 88
Figure 5.6. DodSH stabilized gold nanoparticles: TEM micrograph and size distribution
histogram........................................................................................................................... 89
Figure 5.7. MPS stabilized gold nanoparticles: TEM micrograph and size distribution
histogram........................................................................................................................... 89
Figure 5.8. Bright field TEM micrographs of LCBCP composites as cast from toluene
with 15% wt MPS-functionalized gold nanoparticles. The nanoparticles have aggregated,
creating a poorly dispersed composite. The two images are of the same sample at
different magnifications. ................................................................................................... 91
Figure 5.9. Bright field TEM micrographs of annealed and slow cooled LCBCP
composites cast from toluene with 15% wt DodSH-functionalized gold nanoparticles.
The nanoparticles are again aggregated, creating a poorly dispersed composite. The two
images are of the same sample at different magnifications. ............................................. 92
Figure 5.10. Bright field TEM micrographs of LCBCP composites as cast from
chloroform with 5% wt HexSH-functionalized gold nanoparticles. The nanoparticles are
mainly aggregated, but the higher magnification image on the right appears to show that
the nanoparticles tend to reside near the interfaces of the two domains. The two images
are of the same sample at different magnifications. ......................................................... 93
Figure 5.11. Bright field TEM micrographs of annealed and quenched LCBCP
composites with 5% wt ButSH-functionalized gold nanoparticles. In these films, the
nanoparticles are found to be well dispersed in the PS domain: (a) cast from toluene, (b)
cast from THF. .................................................................................................................. 94
Figure 5.12. Bright field TEM micrographs of the LCBCP composites containing 5% wt
gold nanoparticles initially cast from toluene: (a) as cast film, (b) annealed and quenched
film, (c) annealed and slow cooled film. All films show the nanoparticles preferentially
sequestered in the PS (light) domains. The two annealed films, (b) and (c), appear to
show coarsening of the gold nanoparticles. ...................................................................... 95
8
Figure 5.13. Nanoparticle size distribution comparison for LCBCP nanocomposites
originally cast from THF and containing 5% ButSH functionalized gold nanoparticles: (a)
comparison of the as cast composite with the annealed and quenched composite, (b)
comparison of the as cast composite with the annealed and slow cooled composite. The
nanoparticle size distributions were determined from TEM micrographs using the ImageJ
image analysis software with a grayscale threshold level of 100-125. As mentioned in the
text, nanoparticles with diameters less than 2 nm could not be resolved in the TEM
images, and as a result the histogram is truncated at this level. Even so, “false particles”
are evidently counted even in the 2.5 nm bin. Nevertheless, an increase in particle size is
clear from the histogram, and reflected in the calculated average nanoparticle diameter
(Table 5.2)......................................................................................................................... 96
Figure 5.14. Schematic showing the chemical architecture of the PS-PVMS LCBCP,
indicating that the PVMS polymer backbone is "screened" by the LC side chains. The
ligands on the nanoparticles interact with the alkane terminus of the LC side chain. ...... 97
Figure 5.15. Bright field TEM micrograph of a SI450 composite as cast from toluene
with 5% wt ButSH-stabilized gold nanoparticles. The nanoparticles are seen to be
preferentially dispersed in the PI domains (dark) in this OsO4-stained image. The light PS
domains are free of nanoparticles. .................................................................................... 99
Figure 5.16. Solubility parameter values for the LCBCP and solvents used in composite
preparation. ..................................................................................................................... 101
Figure 5.17. Bright field TEM micrographs of LCBCP composites as cast with 5% wt
ButSH-functionalized gold nanoparticles. In these films, the nanoparticles are again
found to be well dispersed in the PS (light) domains: (a) cast from chloroform, (b) cast
from dichloromethane. .................................................................................................... 102
Figure 5.18. Schematic showing the disruption of the LC side chain smectic layering as a
result of introducing a nanoparticle of comparable size into the ordered domains. ....... 103
Figure 6.1. Density distribution plots for the SI450 blends simulation – dbk refers to the
density of the diblock and tbk refers to the density of the triblock. “A” refers to the
density distribution of the A block of the block copolymer, which in these simulations
corresponds to the PS domains. ...................................................................................... 112
Figure 6.2. Density distribution plots for the SI700 blend simulation – dbk refers to the
density of the diblock and tbk refers to the density of the triblock. “A” refers to the
density distribution of the A block of the block copolymer, which in these simulations
corresponds to the PS domains. ...................................................................................... 112
Figure 6.3. Density distribution plots for the SI1000 blends simulation – dbk refers to the
density of the diblock and tbk refers to the density of the triblock. “A” refers to the
density distribution of the A block of the block copolymer, which in these simulations
corresponds to the PS domains. ...................................................................................... 113
9
Figure 6.4. Density distribution plots for the SI1500 blend simulation – dbk refers to the
density of the diblock and tbk refers to the density of the triblock. “A” refers to the
density distribution of the A block of the block copolymer, which in these simulations
corresponds to the PS domains. ...................................................................................... 113
Figure 6.5. Density distribution plot with line profiles for the SI450 blends simulation.
The image at top displays the density distribution profile of the diblock and the lines
indicate the profile locations. The line profiles indicate that the triblock preferentially
segregates to the IMDS and that the large “pool” of triblock is not microphase separated.
......................................................................................................................................... 114
Figure 6.6. Tobacco mosaic virus: (a) TEM micrograph of a single virus particle,
reproduced from reference 32, (b) schematic of TMV structure reproduced from
reference 31..................................................................................................................... 117
Figure 6.7. Liquid crystalline arrangement of TMV on a carbon coated grid. The TMV
was cast onto the grid from a 10% wt aqueous suspension and allowed to dry. The image
is unstained...................................................................................................................... 118
Figure 6.8. TMV decorated with nickel nanoparticles. The nanoparticles were deposited
on the surface of the TMV using a simple reduction reaction of a nickel salt described in
reference 36..................................................................................................................... 119
Figure 6.9. Chemical structure of PS-P2VP block copolymer. ...................................... 120
Figure 6.10. Quaternization of the P2VP block using bromoethane vapor. ................... 120
Figure 6.11. TEM micrograph of TMV particles in a dried PS-P2VP block copolymer.
The TMV particles are preferentially localized in the P2VP domains, which appear
slightly darker due to staining with iodine vapor............................................................ 121
Figure 6.12. Modes of infiltration of TMV into swollen P2VP domains. In (a) the TMV
axis is oriented perpendicular to the film edge, allowing the virus to penetrate the “forest”
of P2VP chains. In (b) the TMV axis is oriented parallel to the film edge, and the virus
would be “caught” by the chains thus not allowing for its penetration into the film. .... 121
Figure 6.13. Schematic of a suggested implementation of a “tunable plasmonic gel”. Gold
nanoparticles are preferentially localized in the swellable domain of a block copolymer
gel. The swelling of the domain leads to a change in the average spacing between
nanoparticles and possibly a shift in the plasmon resonance.......................................... 123
Figure 6.14. Characteristics of P2VP-stabilized gold nanoparticles: (a) UV-Vis
absorbance spectrum in THF, (b) TEM micrograph....................................................... 124
Figure 6.15. UV-Vis absorbance spectrum of the PS-P2VP block copolymer gel with
15% wt gold nanoparticles.............................................................................................. 126
10
Figure 6.16. TEM micrograph of a PS-P2VP block copolymer containing 15% wt gold
nanoparticles. The slightly darker regions are P2VP domains preferentially stained with
iodine vapor. The nanoparticles are found to localize at the interface between the PS and
P2VP domains................................................................................................................. 126
Figure 7.1. Schematic showing the organization of polymer chains in a cylindrical
domain of a binary blend of diblock copolymers. .......................................................... 136
11
Table of Tables
Table 2.1. Molecular characteristics of the block copolymers: The molecular weights are
in [g/mol]. a MO in toluene at 35οC. b Calculations are based on the equation:
c
SEC in THF at 35οC. d 1H-NMR in CDCl3. The volume fraction is
PDI = M w M n .
1
calculated
based
on
the
H-NMR
values
using
the
equation:
vol %( PS ) = (wt % ( PS ) ρ PI ) [wt % ( PS ) ρ PI + (100 − wt % ( PS ) )ρ PS ] (ρ = 1.06 g/ml, ρ = 0.911 g/ml). e
PS
PI
The total molecular weights for the samples SI1000 and SI1500 were calculated in
combination with SEC/MO (calculating PS) and 1H-NMR (calculating volume fraction of
PS). f The segregation strength was computed based on the equation χ = 33/T - 0.0228
from reference 3. g Only the molecular weight profile of the purchased triblock was
detemined using SEC. The volume fraction of PS is based on the manufacturer’s reported
weight fraction and the PDI is that for the entire triblock copolymer. h R is the molecular
weight ratio for each series of blends containing the respective high molecular weight
diblock, i.e. R = M ndiblock 12 M ntriblock . ......................................................................................... 40
Table 2.2. Molecular characteristics of the LCBCP. wPS is the weight fraction of
poly(styrene) in the block copolymer and Tiso is the smectic-to-isotropic transition
temperature of the LC side chains in the PVMS domain. a The PDI of the LCBCP was
not measured using SEC. The PDI listed is that of the underlying PS-b-PVMS diblock
copolymer, prior to functionalization with the LC mesogen. The molecular weight and
composition, however reflect the entire LCBCP polymer, assuming complete
functionalization of the side chains with the LC mesogen. .............................................. 42
Table 4.1. Polymer characteristics used in the model calculations................................... 73
Table 4.2. Composition ranges for the stability of the cylinder morphology in the blends.
nCYL is the number fraction of the large diblock in the blends ( nCYL = 2n (1 + n ) ), and wCYL is
the corresponding weight fraction, based on the molecular parameters of the experimental
diblock/triblock blends...................................................................................................... 77
Table 5.1. Size characteristics of the nanoparticles. a dcore is the average value of more
than 200 measured nanoparticles and the error is the standard deviation. b tcorona is the
value reported for the ligand length drawn in the Chem3D Pro software from
CambridgeSoft. c deffective = dcore + 2tcorona. ........................................................................ 89
Table 5.2. Average nanoparticle diameter comparison between the three differently
processed LCBCP nanocomposites originally cast from THF with 5% ButSH stabilized
gold nanoparticles. The p value was determined from a student t test on the distributions.
........................................................................................................................................... 97
Table 6.1. Modeling parameters used in the SCFT simulation, describing the
characteristics of the polymers. The values were chosen to be comparable to the
molecular characteristics of the polymers used in the blend experiments described in
Chapter 3......................................................................................................................... 111
12
Table 6.2. Molecular characteristics of the block polymer used to make the PSP2VP/TMV composites. ................................................................................................. 120
Table 6.3. Molecular characteristics of the polymer used to make the P2VP/Au
nanoparticle composites.................................................................................................. 124
13
Acknowledgements
First and foremost, I wish to thank my thesis advisor, Professor Edwin L. Thomas, for his
committed and constant support throughout my time at MIT, and teaching me that good
research is rarely easy but ultimately rewarding. His dedication, enthusiasm, and
insistence on pursuing pioneering and novel research directions will be a continuing
source of inspiration.
I am grateful to my thesis committee, Professor Alfredo Alexander-Katz, Professor
Caroline Ross, and Professor Francesco Stellacci, for their guidance and advice on
improving the thesis work presented here.
I am also thankful for all my fellow labmates: Joe Walish, Nick Tsui, Taras Gorishnyy,
Chaitanya Ullal, Martin Maldovan, Jongseung Yoon, Ji-Hyun Jang, Taeyi Choi, Neal
Vachani, Rachel Pytel, Henry Koh, Vahik Krikorian, Brian Pate, Naan Wanakomol,
Wonmok Lee, and Youngjong Kang. They have been a pleasure to work with over the
years, always ready to help or offer advice, and a great bunch of people to relax with
outside of work.
I am deeply indebted to my family for their unfailing love and support, which was a
tremendous source of strength through the highs and lows of my doctoral journey. To my
parents for always believing that it was achievable and motivating me to constantly try
harder and do better. To Lulu for her love, encouragement, patience, and desire to see me
succeed. This work would not have been possible without them.
A heartfelt “thank-you” to all my friends whose companionship defined my life outside
of the lab. They have enriched my MIT experience beyond measure and have
continuously been a source of energy for me to renew and refresh my spirit.
This work made extensive use of the various research facilities at MIT, in particular, the
Center for Materials Science and Engineering Electron Microscopy Shared Experimental
Facility and the Institute for Soldier Nanotechnologies. Special thanks to Dr. Jan Ilavsky
of the Advanced Photon Source at Argonne National Laboratory for his invaluable
assistance with the USAXS measurements.
Financial support for this work was provided by grants from the Air Force Office of
Scientific Research (AFOSR) and the National Science Foundation (NSF).
14
Chapter 1
Introduction
1.1 Scope of Work
The main thrust of this thesis is to investigate the morphology and microstructure
formation in multi-component systems containing block copolymers. The aim is to
determine the key parameters that influence the morphology in order to be able to design
functional materials with precisely selected properties. This thesis is divided into six
chapters. The current chapter introduces the reader to the concepts and materials that will
be used in the experimental work described in this thesis. It also provides a survey of the
relevant literature that serves as a backdrop to the work reported here. Chapter 2 details
the materials and experimental methods used during the course of the studies. Chapter 3
reports on the morphological behavior of binary blends of block copolymers. The
systems are comprised of a series of four high molecular weight diblock copolymers
blended with a low molecular weight triblock copolymer. In Chapter 4 a theoretical
model based on the strong segregation limit in block copolymers is used to analyze the
results obtained in Chapter 3, in order to more clearly understand the observed
morphologies. Chapter 5 is focused on the microstructure formation in composites of a
liquid crystalline side chain block copolymer with gold nanoparticles. The main interest
is in exploring the effects that the ordering of the liquid crystalline domains has on the
morphological behavior of the nanocomposite. Chapter 6 details a number of suggestions
for future work that build upon the lessons learned from the work described in this thesis.
15
1.2 Block Copolymers
The simplest block polymers are linear diblock copolymers comprised of two
distinct polymer chains (e.g. A and B) covalently connected at their endpoints to form
one chain. Since block polymers are single-component systems, they cannot macrophase
separate in the melt like a pair of linear homopolymers. Nevertheless, most diblock
copolymers are comprised of incompatible polymer species and as a result, the simplest
AB diblock copolymers segregate on a local scale to form periodic lamellar, cylindrical,
cubic spherical or interconnected network morphologies.1, 2 This microphase separation
arises from the need to balance the two competing requirements of (1) minimizing the
interfacial free energy while at the same time (2) lowering the entropic penalty of
stretching the polymer chains. The specific morphology of a given diblock copolymer is
determined by its composition, i.e. the volume fraction of one of the components, Φ, and
the parameter χN, where χ is the Flory-Huggins interaction parameter and N is the degree
of polymerization of the diblock.3 For example, at the critical value of χN = 10.5, a
lamellar morphology is formed for a symmetric diblock copolymer with Φ = 0.5.4 On
either side of the lamellar range, in specific composition windows, the diblock copolymer
assumes the remaining periodic morphologies, as depicted schematically in Figure 1.1.
In addition to the morphologies obtained from simple diblock copolymers, more
complicated domain structures can be formed by preparing block polymers that have
multiple blocks of varying chemistry, as well non-linear backbone architectures, such as
star block copolymers. In the former case, as a next level of complexity, linear triblock
terpolymers with three chemically distinct domains (e.g. ABC type) have been show to
microphase separate into a wealth of novel structures beyond those of the standard
16
diblock copolymer phase diagram.5-9 Multiple arm star block copolymers, have also been
investigated and have been shown to form original microdomain morphologies which are
dependent on the chain composition and connectivity.10-13 The wealth of morphologies
that can be achieved by block polymer microphase separation makes them appealing for
the preparation of structured materials for a wide range of applications.
Figure 1.1. Schematic of diblock copolymer morphology. The numbers percentages indicate the
volume fraction of the component shown in dark in the figure. The morphologies are symmetric
beyond 50% volume percent, with the dark domains becoming the light domains.
1.3 Binary Blends of Block Copolymers
Commercial polymer based materials are frequently comprised of different
polymeric species blended together. Blending allows not only for a reduction in costs, but
serves also as an inexpensive and facile method to tune and manipulate the properties of
the polymer system for a given application. As a result of their inherent ability to form
microstructured phases, using block copolymers as one of the components in a blend
gives rise to a whole range of possible material properties beyond simple miscibility or
enhancement of a particular physical property. Nonetheless, since most pairs of
homopolymers are immiscible, block copolymers are very often used in blend systems as
compatibilizers.14 That is, an AB-type block copolymer can be used as a surfactant to
emulsify a mixture of A and B polymers. The block copolymer migrates to the interface
17
between the A and B polymer phases, stabilizing the micelles, as shown schematically in
Figure 1.2.
Figure 1.2. Schematic showing how a block copolymer acts to stabilize an immiscible blend of two
homopolymers. The size of the blue micelles is on the order of 1 µm.
Numerous studies have been undertaken on blends of block copolymers with
homopolymers as well as block copolymers with other block copolymers.15 In the latter
category, the bulk of the work has been on blends of two diblock copolymers of moderate
molecular weight (predominantly ~ 1 x 105 g/mol). A series of publications by
Hashimoto et al. examined the morphology and microphase separation behavior of blends
of two A-B type diblock copolymers identical in chemical composition but varying in
degree of polymerization and volume fraction of the respective blocks.16-24 The blends
displayed a rich variety of single microphase or macrophase separated morphologies,
depending on blend composition (volume fraction of the respective diblocks), individual
copolymer composition (volume fraction of the constituent blocks), and molecular weight
ratio (R, defined as the ratio of the degree of polymerization of the larger diblock
copolymer to the smaller copolymer).
Taken together with other studies,25-30 several key findings were established for
the case of symmetric diblock copolymers, where the pure component diblocks form the
18
lamellar morphology. First, the blends displayed complete miscibility (i.e. a single
microphase separated lamellar morphology) when R < 5. For higher ratios of molecular
weights, the blends were found to macrophase separate into nearly pure lamellar
microdomains with different domain spacings, corresponding to the larger and smaller
diblocks. Second, a miscibility gap opened up when the weight fraction of the larger
diblock was less than 0.7 for R > 7 (in the range 5 < R < 7, the miscibility gap was
smaller). That is, at higher loadings of the smaller diblock, the blends showed two
distinct microphase separated phases. Third, morphological transitions to an unexpected
cylindrical morphology were seen upon blending at a particular composition and R
value.23
Hashimoto et al. also studied blends in which the constituent diblocks were not
symmetric, and a range of morphologies was observed that depended on the overall
volume fraction of the A and B blocks in the blend.18 The observation of complete
miscibility for R < 5 was also still valid, unless the composition of each of the two block
copolymers was highly asymmetric. For example, in the case where one polymer forms
A-type spheres and the other forms B-type spheres, the overall morphology was that of a
large grain mixture of the two types of individual morphologies. In addition, lamellar
structures were observed, at certain intermediate compositions, in blends of
complementary cylinder-forming block copolymers, chosen is such a way that the overall
volume fraction in the blend was near 0.5.
Several theoretical studies have looked at the behavior of binary diblock
copolymer blends in an effort to map out a phase diagram of these systems. Lyatskaya et
al. used a strong segregation limit (SSL) theory and one of their findings was of a lower
19
free energy for the cylindrical morphology in a narrow composition window with wlarge ≤
0.4 for two lamellar forming diblock copolymers.31 The self-consistent field theory
(SCFT) study by Matsen32 focused on selected values of χN and R, and demonstrated the
macrophase separation into two coexisting lamellar phases for R > 5. Shi and Noolandi
utilized the SCFT to map out a phase diagram (“phase cube”) for a pair of diblocks of
equal length (i.e. R = 1) and found interesting changes in the phase diagram, but their
work did not predict phase transitions to curved interface structures, such as cylinders,
when the effective volume fraction of the blends was near 0.5, unless one of the diblocks
was highly asymmetric (i.e. nearly a homopolymer).33 In another study, Shi and Noolandi
investigated the effects of short diblocks (effectively non-ordering surfactants, since χN <
10.5) on the phase behavior of strongly segregated long diblocks (R = 10).34 They
determined that when their composition was near 0.5, a sizeable proportion (~ 20%) of
the short diblock chains tended to segregate to the interface between the large diblock
domains. They also found that the chain end distribution of the long diblock was found to
deviate from the analytical SSL theory of Semenov,35 with the chain end density
increasing gradually from the interface to the center of the domain. This hints at the
possibility of chain end effects playing a role in determining the microstructure. In the
case of the SSL theory of Lyatskaya et al., the chains are presumed to be highly stretched
and the long diblock chain ends are explicitly excluded from folding back and mixing
with the short diblock segments near the interface.31
1.4 Nanocomposites
Composite materials that consist of a matrix (metal, polymer, ceramic) with
embedded reinforcement (filaments, whiskers, particulate) comprise many of today’s
20
high performance engineering materials.36, 37 Currently, one of the fastest growing areas
of materials research is in composite systems where the characteristic length scales of the
filler material are in the nanometer range, i.e. nanocomposites. Research in polymer
nanocomposites has expanded beyond simple polymer-nanocrystal dispersions for
refractive index tuning, or clay-filled homopolymers primarily pursued for mechanical
reinforcement, barrier properties, and flame retardancy, to include high performance
systems containing a wide range of variable aspect ratio nanoscale fillers (e.g. carbon
nanotubes (CNTs)) for diverse applications such as EMI-shielding, conductive coatings,
self-passivation, sensors, catalysis, and photonics.38, 39 In many of these applications the
control of the composite architecture, i.e. location and orientation of the nanoscale
inclusions, is a prerequisite to enable maximum performance and function of the material.
Key challenges are thus to provide both synthetic and processing strategies towards
ordered heterogeneous materials and then to study the basic structure-property
relationships in nanocomposites, enabling the rational design of the next generation of
these materials.
Nanometer-sized filler materials are particularly interesting, since their inherently
large surface area-to-volume ratio, allows less of the additive to be used in order to
achieve a desired property or level of property enhancement. Moreover, due to the small
size of the filler, certain properties may be modified while unaffecting others, e.g.
mechanical enhancement while maintaining optical transparency. The exploitation of
nanometer-size specific properties of matter, e.g. luminescence of semiconductor
nanocrystals, due to quantum confinement,40-42 also offers access to a host of new types
of functional composites. Beyond enhancement of static properties, there is a wealth of
21
opportunities for future applications that arise from the dynamic response of
nanocomposite materials to external stimuli. For example, in composite materials for
actuation processes, since switching speed is primarily diffusion limited and scales as the
square of the feature size, it could be significantly reduced when nanoscopic diameter
fibers are used.43
In order to understand the extraordinary properties of nanocomposite materials, it
is instructive to consider the characteristic differences of nanometer-sized and traditional
filler composites. Six characteristic features may be associated with nanocomposite
materials: (1) particle-particle correlation arising at low concentrations (< 0.1 vol%), (2)
ultra low percolation thresholds (~ 1 vol%), (3) large particle number densities up to ~
1020 /cm3, (4) extensive interfacial area per volume of particles (~107 cm2/cm3), (5) small
particle-particle distances, and (6) comparable length scales between the particle size, the
distance between particles, and the typical relaxation volume of a polymer chain (~ Rg3,
where Rg is the polymer radius of gyration, and Rg ~ 10 nm for typical polymer molecular
weights).
The interfacial area per particle volume increases by several orders of
magnitude as the filler size shrinks to the nanometer length scale. This is demonstrated in
Figure 1.3, where the interfacial area per particle volume, A/V ~ 1/d + 1/l, is shown as a
function of the particle radius, d, and aspect ratio, l/d (with l the particle length). Since
the static and dynamic characteristics of a polymer chain in the vicinity of a surface are
influenced by the surface, the properties of polymer chains less than a few Rg away from
the particle surface differ from those of the bulk polymer material. The response of
nanocomposite materials to mechanical forces will therefore be determined by the
collective properties of a “communicating” network of nanoscopic inclusions, rather than
22
an effective property of discrete inclusions embedded within a bulk matrix material as
found in “classical” composite materials.44
Figure 1.3. Calculated interfacial area per volume of particles (in nm-1) assuming a right circular
cylindrical particle shape for different particle diameter d and aspect ratio l/d. Exfoliated clay
(laponite or montmorillonite) particles, spherical nanoparticles, and single wall carbon nanotubes
generate up to four orders of magnitude more interfacial area as compared to conventional filler
materials, like glass fibers, of equal volume filling fraction. Reproduced from reference 44.
1.5 Block Copolymer Nanocomposites
1.5.1
Theoretical Work
Theoretical models developed to predict block copolymer (BCP)/nanoparticle
phase diagrams and to understand the relevant parameters that govern the equilibrium
23
microstructure formation, have spurred recent empirical studies in the field. The detailed
behavior of the particles in a BCP matrix of a specific morphology and dimension
depends on many factors, such as particle core size, size and chemistry of the stabilizing
surface ligands, size of the corona region, and interaction (χ) with the polymer host. The
chemistry of the block copolymers themselves can also be varied to include domains with
diverse properties (glassy, rubbery, crystalline, liquid crystalline) and a range of
processing methods can be used to influence the morphology of the composites. Some of
the key parameters mentioned above are depicted schematically in Figure 1.4.
Figure 1.4. Schematic of important parameters for BCP/nanoparticle composites. The core size, dcore,
is the diameter of the rigid particle. The corona is the shell occupied by the stabilizing surface
ligands, and its thickness is tcorona. The effective size of the nanoparticle is then dcore+2tcorona. The
IMDS, or inter-material dividing surface, is the interface between the A and B type domains. The
characteristic domain spacing is given by L=lA+lB, where lA and lB are the size of the A and B
domains, respectively.
Much of the oft-cited theoretical modeling of BCP/nanoparticle composite
behavior has been done by the Balazs group, using a combined density functional (DFT)
and self-consistent field theoretical (SCFT) approach, though some recent simulation
work on these systems by Fredrickson et al., has questioned the applicability of this
combined methodology.45 Nevertheless, important insights can be gained from this work,
and Huh et al. and Thompson et al. were the first to study by computer simulation the
24
structure formation process in BCP-particle blends.46, 47 In these studies, the effect of the
corona regions, comprised of the surface grafted ligands, was ignored and replaced by an
effective interaction parameter. The chemical affinity of a particle P to a polymer domain
X was expressed by the Flory-Huggins interaction parameter χPX, that quantifies the
enthalpic interactions between the particle and the respective monomeric units of block
X. In their studies, Thompson et al. assumed a neutral interaction of the particles with
respect to one of the blocks, i.e. χPA = 0 and χPB > 0. For a 2-D system, representing a
mixture of spherical nanoparticles within a lamellar BCP in the intermediate segregation
regime, they showed that interfacial segregation of particles (i.e. at the boundary between
domains of blocks A and B) is expected to occur in the limit of small particle sizes (d/L =
0.2, where L = lA + lB is the lamellar spacing, d the particle diameter, and hi the thickness
of polymer domain i). Concentration of the particles at the center of a particular domain
was predicted for somewhat larger particle diameters (d/L = 0.3). The results were
interpreted as a compromise between (a) the penalty in conformational entropy of the
polymer, which has to deform in order to accommodate particles in its vicinity, and (b)
the gain in translational entropy of the particles for free dispersion throughout the
domain.
Further theoretical studies by Lee et al. and Buxton et al., using the same hybrid
SCFT/DFT approach, suggest that by tuning the particle/polymer interaction (i.e. χPX),
the distribution of particles in the matrix can be varied and a phase transition to a new
microdomain geometry within the microphase separated structure can be induced, by
effectively changing the volume fraction of the minority block. This suggests an even
wider parameter space in the morphology of BCP/nanoparticle composites, depending on
25
the particle size and volume filling fraction.48, 49 Recently, Thompson et al. extended the
SCFT/DFT approach to study the influence of particle sequestration on the mechanical
properties of BCP/nanoparticle composites, however, their simulations were restricted to
the melt state.50
When applying the results of the numerical studies mentioned above to the
interpretation of experiments, it should be noted that neglecting the particles’ corona
region on the miscibility and rigidity of the sequestered particles, will render the model
less applicable in situations where high molecular weight polymers are grafted to a
particle’s surface (i.e. dcore/tcorona < 1, see Figure 1.4). In fact, the behavior of polymer
chains grafted to a curved surface, in which the radius of curvature is on the order of Rg
of the host block, is just beginning to be explored.51
1.5.2
Experimental Work
The experimental work on BCP/nanoparticle composites has followed two major
approaches for the preparation of BCP/nanoparticle composite materials, distinguished by
the sequence of microstructure formation and particle synthesis; (1) the in-situ synthesis
of inorganic particles within a BCP domain that has been preloaded with a precursor, and
(2) co-assembly, where ex-situ synthesized nanoparticles, surface-tailored in order to
allow preferential sequestration within a target domain, are blended with the BCP matrix
(usually in the presence of a volatile solvent, e.g. by means of solution casting).
The first experiments on nanoparticle formation within BCP microdomains
followed the former method, with the synthesis of gold or silver nanocrystals in lamellar,
cylindrical, and spherical domains of a phosphine-functionalized BCP, in which the
monomers were preloaded with metal salt.52,
26
53
A similar approach was used for the
synthesis of semiconductor particles within the domains of a norbornene-derived BCP
that was preloaded with lead salt.52-54 While this work provided an early proof of concept,
the complex synthesis of suitable BCP compositions resulted in a shift towards the
‘nanoreactor scheme’. Here, amphiphilic BCPs that contain polar groups (usually derived
from poly(ethylene oxide), poly(acrylate), or poly(vinyl pyridine)), are first microphase
separated and subsequently immersed in a salt solution. Due to its chemical affinity, the
salt selectively infiltrates the hydrophilic copolymer domain. The nanocrystals then form
selectively upon reduction of the precursor within the pre-loaded domains.55-58 Following
this approach, monolayer thin films with 2-D hexagonal patterns of metal particles in a
BCP matrix were produced by Bootongkong et al., by infiltrating the polar hydrophilic
domains of a spherical-microstructure-forming poly(styrene-b-acrylic acid) copolymer
with a silver salt that is reduced in a subsequent reaction step. The authors demonstrated
that the BCP nanoreactor scheme might be applied to a wide variety of metal (e.g. Pd,
Cu, Au, Ag) as well as semiconductor (e.g. PbS) nanocrystals.59 Nevertheless, the
relatively poor control of the particle size, as well as the limited possibilities to control
the surface chemistry and architecture of the embedded nanocrystals, are major
drawbacks of the in-situ approach for applications that rely on specific electronic, optical,
or magnetic properties of individual nanocrystals, which are intimately related to particle
size, shape, and architecture.60, 61,62
The ex-situ approach allows precise control of the structural characteristics of the
sequestered component, since it moves the particle synthesis step from inside the BCP
matrix to a well controlled chemical reaction environment. The strategy is to synthesize
nanocrystals of desired size, shape, or core-shell architecture, and to tailor the particles’
27
surface chemistry, such that chemical affinity to one of the blocks of the copolymer will
drive the particles into the respective target polymer domain during the self-organization
process. Selective chemical compatiblization of the nanoparticles into an AB-type BCP is
typically achieved by attaching an oligomer or polymer to the particle surface that will
favorably interact with the target copolymer domain (say domain A). Depending on the
chemistry of the core materials and the type of corona, grafting-to, grafting-from, as well
as micelle-based nanoreactor schemes have been developed for grafting compatiblizing
agents to a particle’s surface.63-65
The first mention of the ex-situ approach was made by Hamdoun et al., who
synthesized iron oxide nanocrystals with surface grafted poly(styrene) (PS), that were
subsequently solublized in the PS domain of a lamellar poly(styrene-b-butyl
methacrylate) diblock copolymer.66 Although the periodicity of the lamellar
microstructure was too small (L ~ 32 nm) to clearly resolve the particles within the
domain microstructure, the samples were studied by small angle neutron scattering and it
was suggested that smaller particle sizes (d = 4 nm) tended to localize close to the
interface, whereas larger particles (d = 6 nm) tended to locate at the center of the BCP
domain.67
Bockstaller et al. demonstrated that the preferential sequestration of PS-coated
gold nanocrystals within a high molecular weight (Mw ~ 800 kg/mol), lamellar-forming
poly(styrene-b-ethylene propylene) (PS-PEP) block copolymer facilitates the preparation
of metallodielectric Bragg-reflector-type structures, that exhibit significantly enhanced
reflectivity as compared to the neat BCP material.68 The PS coated nanocrystals (d = 3
nm) were found to preferentially and uniformly sequester within the PS domains of the
28
copolymer. The enhanced reflective properties could be attributed to the increase in the
effective dielectric contrast between the alternating particle-loaded PS domains and the
particle-free PEP domains. This interpretation was supported by Buxton et al., in their
studies based on finite difference time domain (FDTD) modeling of the optical properties
of BCP/nanoparticle composite materials.49
In recent studies, Wei et al. succeeded in preferentially sequestering surface
modified
TiO2
and
CdS
nanoparticles
within
lamellar
poly(styrene-b-methyl
methacrylate) and poly(styrene-b-ethylene oxide) copolymers.69,
70
These studies
demonstrate the feasibility to pattern a wide range of dielectric, semiconducting, and
metallic materials on the nanometer length scale by simultaneous self-organization of
BCPs in the presence of ex-situ synthesized particles. The experimental evidence also
supports the theoretical conclusion that entropic effects, related to the characteristic
length scales of the materials, are relevant parameters that determine the location of the
nanoscale particles within the domain microstructure. Bockstaller et al. prepared a series
of samples by blending aliphatic-modified gold (d = 3 nm) and silica (d = 22 nm)
nanoparticles with a lamellar PS-PEP BCP.71 Since the PEP domains are essentially
aliphatic, a chemical affinity of the nanoparticles towards the PEP domain was expected
in both cases. Gold nanocrystals were found to segregate to the inter-material dividing
surface (IMDS) that separates the PS and PEP domains, whereas the larger silica
nanocrystals were preferentially located at the center regions of the PEP domains.
Interestingly,
the
morphological
characteristics
of
the
two
different
binary
BCP/nanoparticle mixtures are retained in the ternary (particle 1)-(particle 2)-BCP
mixture, and result in autonomous particle separation and organization into a stack-like
29
structure comprising alternating sheets of silica and gold nanocrystals. It should also be
noted, that particle sizes larger than d/L ~ 0.3 could not be homogeneously mixed with
the BCP but rather were found to aggregate and macrophase separate. This presumably
arises as a consequence of the increasing energy penalty, due to increased chain
deformation, curvature, and elastic bending deformations of the layered structure as
larger particle sizes are included within lamellae. Since the energy of an inclusion is
proportional to the square of the local surface curvature, macrophase separation of the
additives will eventually occur.
Besides the particle core diameter, the grafting density, as well as the molecular
weight of the surface grafted ligands, were shown to affect the particle distribution in
BCP matrices. Blending experiments on PS-functionalized fullerenes (C60) with a
lamellar poly(styrene-b-isoprene) block copolymer demonstrate that with increasing
molecular weight and increasing number density of the surface bound PS, the particles
tend to localize at the center of the PS domains of the BCP, as opposed to a more
homogeneous distribution in the case of a less dense, low molecular weight
functionalization. This indicates that a dense packing of a high molecular weight surface
bound polymer acts to increase the effective size of the particle, similar to an increase of
the particle core diameter.72 Kim et al. also showed that grafting density plays a
determining role in the partitioning of the nanoparticles in a block copolymer matrix.
Using PS-coated nanoparticles dispersed in a poly(styrene-b-2-vinylpyridine) (PS-P2VP)
copolymer matrix, the nanoparticles tended to segregate near the interface when the
grafting density was low (less than 1.3 chains/nm2). This was an indication that part of
the gold surface was being exposed, and the affinity of the bare gold nanoparticle surface
30
to the pyridine groups in the P2VP domain was responsible for the distribution of the
nanoparticles at the IMDS.73 Using the same polymer system (PS-P2VP), the researchers
also tested the effect of the size of the stabilizing ligand (i.e. its molecular weight) on the
behavior of the composites. They found that there is an interplay between ligand size and
areal chain density on the nanoparticle surface. A critical chain density for nanoparticle
segregation to the IMDS was found that decreased with increasing ligand molecular
weight, and was described by a simple scaling relationship which took into account the
curvature of the nanoparticle.74 In addition, the researchers also looked at mixed ligand
gold nanoparticles, containing both PS and P2VP oligomers. The behavior of the mixed
ligand nanoparticles indicated that the stabilizing ligands were mobile on the gold surface
and tended to phase separate to form a “Janus” particle, with one side covered in PS
ligands and the other with P2VP ligands. As a result, segregation of the nanoparticles to
the interface between the PS and P2VP domains was found in a very broad range of
composition (10% - 90% mol PS).75
As a final note, when blending polymer-coated nanoparticles with block
copolymers, the addition of the particles acts to increase the effective volume fraction of
the surface-grafted polymer species in the blend. This induces a phase transition of the
equilibrium microdomain structure if the amount of particles exceeds a threshold value,
according to the phase diagram of the block copolymer. In line with previous theoretical
studies,48 this effect has been demonstrated empirically by Kim et al., who reported a
lamellar-to-cylindrical phase transition upon blending PS-coated gold nanocrystals with a
PS-P2VP BCP, when a critical particle filling fraction was exceeded.76
31
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32
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B. Hamdoun. "Effect of nanoparticle size on the internal structure of copolymernanoparticles composite thin films studied by neutron reflection." Physica BCondensed Matter, 241, 1092-1094 (1997).
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36
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weight on polymer-coated nanoparticle location in block copolymers."
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37
Chapter 2
Materials and Experimental Methods
This chapter outlines the experimental techniques and protocols, as well as the
materials and their preparation, that were used for the investigations described in this
thesis. Most of the work described in this thesis (Chapters 3 and 5) relied heavily on
transmission electron microscopy to characterize the morphology of the multi-component
polymeric materials. Ultra-small-angle x-ray scattering was used to gain further insights
on the nature of the block copolymer blends (Chapter 3), and to corroborate the electron
microscopy results. The poly(styrene-b-isoprene) block copolymers are used in the
blends studies described in Chapter 3. The liquid crystalline side chain block copolymer
is utilized, along with the gold nanoparticles, in the studies on nanocomposites described
in Chapter 5.
2.1 Polymers
2.1.1
Styrene-Isoprene Block Copolymers
The high molecular weight poly(styrene-b-isoprene) (SI) diblock copolymers were
synthesized by Eleftherios Ntoukas in the labs of Prof. Apostolos Avgeropoulos at the
University of Ioannina, Greece. The polymers were prepared by anionic polymerization
under high-vacuum techniques, using glass reactors equipped with break-seals for the
mixing of the reagents and constrictions for the removal of the products; the details may
be found in references 1 and 2. Briefly, a typical synthesis began with the polymerization
of styrene using sec-BuLi in 500 mL of benzene at room temperature for at least 24 h,
38
followed by the addition of the appropriate amount of isoprene and left to react for
another day. The polymerization was terminated by adding a small amount of MeOH (1
mL). The molecular weight and polydispersity of the copolymers were characterized by a
combination of size exclusion chromatography (SEC) and membrane osmometry (MO),
while the copolymer composition was determined through 1H NMR spectroscopy. The
poly(styrene-b-isoprene-b-styrene) (SIS) triblock copolymer is a commercially available
thermoplastic elastomer, sold under the trade name Dexco 4411. The volume fraction of
poly(styrene) (PS) is ∼0.41 with a number-average molecular weight of 62 000 g/mol,
which translates into a central poly(isoprene) (PI) block of 35 000 g/mol and two PS end
blocks of 13 500 g/mol each. The block copolymer characteristics are summarized in
Table 2.1 and the chemical structure is shown in Figure 2.1.
CH 2
CH 2
CHCH 2
CH3
n
m
Figure 2.1. Chemical structure of the poly(styrene-b-isoprene) diblock copolymer.
39
Sample
(M )
n
PS
× 103 a
(M )
n total
× 103 a
(M )
w total
× 103 b
PDI c
ΦPS d
χΝ f
Rh
SI450
212
438
460
1.05
0.47
470
14
SI700
351
715
751
1.05
0.49
760
23
SI1000
443
944e
1001e
1.06
0.44
1010
30
SI1500
613
1318e
1437e
1.09
0.43
1410
43
SISg
13.5
62
65
1.05
0.41
34
-
Table 2.1. Molecular characteristics of the block copolymers: The molecular weights are in [g/mol]. a
MO in toluene at 35οC. b Calculations are based on the equation: PDI = M w M n . c SEC in THF at
35οC. d 1H-NMR in CDCl3. The volume fraction is calculated based on the 1H-NMR values using the
equation: vol %( PS ) = (wt % ( PS ) ρ PI ) [wt % ( PS ) ρ PI + (100 − wt % ( PS ) )ρ PS ] (ρPS = 1.06 g/ml, ρPI = 0.911 g/ml). e
The total molecular weights for the samples SI1000 and SI1500 were calculated in combination with
SEC/MO (calculating PS) and 1H-NMR (calculating volume fraction of PS). f The segregation
strength was computed based on the equation χ = 33/T - 0.0228 from reference 3. g Only the
molecular weight profile of the purchased triblock was detemined using SEC. The volume fraction of
PS is based on the manufacturer’s reported weight fraction and the PDI is that for the entire triblock
copolymer. h R is the molecular weight ratio for each series of blends containing the respective high
molecular weight diblock, i.e. R = M ndiblock 12 M ntriblock .
2.1.2
Liquid Crystalline Side Chain Block Copolymer
The liquid crystalline side chain block copolymer (LCBCP) was synthesized by
Eric Verploegen in the labs of Prof. Paula Hammond at MIT, and the details of the
polymerization and structural characterization of the polymer can be found in references
4, 5, and 6. The LCBCP is comprised of a poly(styrene-b-vinylmethylsiloxane) (PSPVMS) backbone, with liquid crystalline mesogens attached to functional groups in the
PVMS domain (Figure 2.2). The PS-PVMS block copolymer was synthesized by anionic
polymerization using standard glove box techniques under a nitrogen atmosphere. A
typical synthesis was performed at room temperature in cyclohexane, using n-butyl
lithium as the initiator, with the styrene monomer polymerized first, followed by the
vinylmethylsiloxane.4 The liquid crystalline mesogen was attached to the PVMS
backbone by means of a hydrosilation reaction.6 Though an entire series of block
40
polymers containing various amounts and sizes of the liquid crystalline mesogen were
prepared, in this thesis work only the LCBCP with 100% functionalization of the PVMS
domain with the liquid crystalline mesogen was used, having a composition that yielded a
morphology of PS cylinders in a liquid crystalline side chain PVMS matrix. From the
structural characterization, it was found that the liquid crystalline side chains form
smectic layers, with the layer normal parallel to the long axis of the PS cylinders, as
depicted in. The molecular characteristics of the LCBCP are outlined in Table 2.2.
Si
w
R=
CH3
HSi
O
CH3
CH3
Si (CH2)n O
CH3
Si
O
xR
Si
O
y
Si
O z
O
O
O
O
H3C
O
Figure 2.2. Chemical structure of the PS-PVMS block copolymer and liquid crystalline mesogen. The
polymer used is 100% functionalized, giving z = 0. Although there is a small amount of dimethyl
siloxane present, x << y, and the polymer is essentially a diblock copolymer.5
Figure 2.3. Schematic representation of the LCBCP morphology in an aligned and oriented fiber.
The LC mesogen aligns into interdigitated smectic layers, with the layer normal parallel to the PS
cylinder axis, and a d-spacing of 3.4 nm as determined by SAXS.4, 5
41
(M )
n total
× 103 [g/mol]
184
PDI
wPS
Tiso [°C]
1.21 a
0.33
89
Table 2.2. Molecular characteristics of the LCBCP. wPS is the weight fraction of poly(styrene) in the
block copolymer and Tiso is the smectic-to-isotropic transition temperature of the LC side chains in
the PVMS domain. a The PDI of the LCBCP was not measured using SEC. The PDI listed is that of
the underlying PS-b-PVMS diblock copolymer, prior to functionalization with the LC mesogen. The
molecular weight and composition, however reflect the entire LCBCP polymer, assuming complete
functionalization of the side chains with the LC mesogen.
2.2 Block Copolymer Blends Preparation
A series of blends were prepared for each of the high molecular weight diblock
copolymers with the lower molecular weight triblock. The films were cast in ceramic
crucibles of 1.3 mL nominal volume from 1.4% (w/v) toluene solutions. The solutions
were covered with glass coverslips and placed under a bell jar and then allowed to slowly
evaporate over a period of about 2 weeks, yielding bulk films of ∼0.2 mm thickness. In
order to promote near-equilibrium structures, the films were subsequently annealed at
125°C for 72 h under vacuum. Certain films were annealed up to one week to check the
stability of the observed morphologies.
2.3 Nanoparticle Synthesis
The nanoparticles were prepared using a one phase modification of the BrustSchiffrin method7 of reduction of a gold salt.8 In a typical synthesis 20 mg of gold
tetrachloroaurate trihydrate (HAuCl4·3H2O) (Aldrich, 99.9%) was dissolved in 10 mL of
tetrahydrofuran (THF, Aldrich, anhydrous). An appropriate amount of a thiol ligand
(butanethiol, Aldrich, hexanethiol, Fluka, or dodecanethiol, Alfa Aesar) to achieve a gold
to thiol molar ratio, [Au]/[SH], of 0.641 was then added to the solution. Using this molar
42
ratio was empirically found to produce nanoparticles with average diameters of
approximately 3 nm.9 The solution was transferred via syringe to a round bottom flask
that had been previously evacuated and purged with argon. The flask was equipped with
a transfer arm having a Teflon stopcock and sealed with a rubber stopper in order to
minimize contamination with air. After stirring the solution for 15 min, approximately
0.5 mL Superhydride (Aldrich, 1M in THF) was added dropwise via syringe in a similar
fashion, under vigorous stirring. The reaction was allowed to proceed overnight at which
point the reaction vessel was exposed to air and diluted with methanol or acetone
(Malinckrodt), depending on the nature of the ligand. The suspension was then
centrifuged at 15000g to isolate the nanoparticles. The process was repeated, washing
with methanol or acetone and centrifugation, several times to ensure removal of excess
ligands and unreacted precursors.
2.4 Liquid Crystalline Side Chain Block Copolymer Composites
The LCBCP/nanoparticle composites were prepared by casting 5% solutions (w/w
polymer) of LCBCP in a suspension of gold nanoparticles onto Teflon coated aluminum
foil. The samples were covered with a petri dish and the solvent allowed to evaporate
slowly (drying times varied from about an hour to several hours, depending on the
casting solvent), yielding films approximately 0.1 mm thick. The films were subsequently
annealed at 140°C overnight, whereupon a piece of each film was quickly quenched in
liquid nitrogen, while another piece was allowed to initially cool to 90°C (slightly above
the melting temperature (89°C) of the smectic liquid crystalline side chains), held at this
temperature for 1 hour, and finally allowed to cool slowly to room temperature. Films
43
were prepared with both 5% and 15% by weight loading of nanoparticles (~ 0.3% and 1%
by volume, respectively).
2.5 Transmission Electron Microscopy
Thin film cross sections, in the range of 50-100 nm thickness, were obtained by
sectioning at -100°C on a Leica EM UC6 microtome equipped with the EM FC6
cryogenic stage. The SI and SIS blend samples were then exposed to osmium tetroxide
(OsO4) vapor, which preferentially stains the PI domains and is used as a contrast agent.
The LCBCP samples were imaged without staining, since the more electron-dense, Sicontaining PDMS block, provides adequate contrast. In order to mitigate against the
effects of electron beam damage, the cross sections were coated with a thin layer of
carbon prior to imaging. The cross sections were imaged in bright field on a JEOL 2000
or JEOL 2011 transmission electron microscope (TEM) operating at 200 kV.
2.6 Ultra-Small-Angle X-ray Scattering (USAXS)
Scattering profiles for the blend films were collected using an advanced Bonse-Hart
instrument on the 32ID-B beamline at the Advanced Photon Source at Argonne National
Laboratory using high intensity X-rays with a wavelength λ = 0.10419 nm. The data,
consisting of absolute intensity as a function of scattering vector q (q ≡ (4π/λ) sin(θ/2),
where θ is the scattering angle), were corrected for background and analyzed by fitting
model slit-smeared data to the intensity profiles. The data were also analyzed by
desmearing the slit-smeared scattered intensity using an implementation of the standard
method of Lake10 included in the data reduction tools (“Indra”) provided by Dr. Jan
Ilavsky of the Advanced Photon Source.
44
2.7 References
[1]
A. Avgeropoulos, N. Hadjichristidis. "Synthesis of model nonlinear block
copolymers of A(BA)(2), A(BA)(3), and (AB)(3)A(BA)(3) type." Journal of
Polymer Science Part a-Polymer Chemistry, 35(4), 813-816 (1997).
[2]
D. Uhrig, J. W. Mays. "Experimental techniques in high-vacuum anionic
polymerization." Journal of Polymer Science Part a-Polymer Chemistry, 43(24),
6179-6222 (2005).
[3]
T. P. Lodge, C. Pan, X. Jin, Z. Liu, J. Zhao, W. W. Maurer, F. S. Bates. "Failure
of the Dilution Approximation in Block-Copolymer Solutions." Journal of
Polymer Science Part B-Polymer Physics, 33(16), 2289-2293 (1995).
[4]
E. Verploegen, L. C. McAfee, L. Tian, D. Verploegen, P. T. Hammond.
"Observation of transverse cylinder morphology in side chain liquid crystalline
block copolymers." Macromolecules, 40(4), 777-780 (2007).
[5]
E. Verploegen, T. Zhang, N. Murlo, P. T. Hammond. "Influence of variations in
liquid-crystalline content upon the self-assembly behavior of siloxane-based block
copolymers." Soft Matter, 4(6), 1279-1287 (2008).
[6]
A. Moment, R. Miranda, P. T. Hammond. "Synthesis of polystyrene-polysiloxane
side-chain liquid crystalline block copolymers." Macromolecular Rapid
Communications, 19(11), 573-579 (1998).
[7]
M. Brust, M. Walker, D. Bethell, D. J. Schiffrin, R. Whyman. "Synthesis of
Thiol-Derivatized Gold Nanoparticles in a 2-Phase Liquid-Liquid System."
Journal of the Chemical Society-Chemical Communications, (7), 801-802 (1994).
[8]
C. K. Yee, R. Jordan, A. Ulman, H. White, A. King, M. Rafailovich, J. Sokolov.
"Novel one-phase synthesis of thiol-fuctionalized gold, palladium, and iridium
nanoparticles using superhydride." Langmuir, 15(10), 3486-3491 (1999).
[9]
P. A. Buining, B. M. Humbel, A. P. Philipse, A. J. Verkleij. "Preparation of
functional silane-stabilized gold colloids in the (sub)nanometer size range."
Langmuir, 13(15), 3921-3926 (1997).
[10]
J. Lake. "An iterative method of slit-correcting small angle X-ray data." Acta
Crystallographica, 23(2), 191-194 (1967).
45
Chapter 3
Binary Blends of Diblock Copolymers
with a Triblock Copolymer
In this chapter, the morphology of a series of binary blends of block copolymers
is studied using transmission electron microscopy and ultra-small-angle x-ray scattering.
The main aim is to investigate the behavior of blends where the mismatch in size, i.e. the
molecular weight ratio, R, between the two block copolymers is large (R > 15). In the
present study we build and expand upon earlier work. Specifically, we focus on blending
lamellar-forming, high molecular weight diblock copolymers with a lamellar-forming,
low molecular weight triblock copolymer. Only two previous studies have looked at
blends containing triblock copolymers,1,2 but with lower molecular weights and
molecular weight ratios, R < 4. Here we employ diblock copolymers with molecular
weights Mn > 1 x 105 g/mol. This, coupled with the assertion that the triblock copolymer
behaves morphologically as a diblock of half the molecular weight,3 enables us to access
molecular weight ratios in the range 14 < R < 43 (here we define R = M ndiblock
1
2
M ntriblock ),
which are well beyond those previously reported (R < 15).
Binary blends of four different high molecular weight SI diblock copolymers with
a lower molecular weight SIS triblock copolymer were prepared. The four series of
blends are referred to throughout this work on the basis of the molecular weight of the
large block copolymer, that is, SI450, SI700, SI1000, and SI1500. The blend
compositions in weight percent SI were 5%, 10%, 25%, 50%, 75%, 90%, and 95%, for a
total of 28 blend samples. A particular blend sample is identified by the series name (as
46
above) and the composition in weight percent, with that of the diblock copolymer listed
first. For example, SI450 95/5, refers to the blends of the 438 000 g/mol SI diblock
copolymer containing 95 wt % of the diblock and 5 wt % of the SIS triblock.
Additionally, neat films of the SIS triblock and the four SI diblocks were prepared in the
same manner as the blends.
3.1 Results and Discussion
TEM analysis reveals, as expected, that all the neat block copolymers, having near
symmetric composition, form the lamellar structure in the bulk state (Figure 3.1) and is
corroborated by the scattering data. The TEM images of the various blend series are
shown in Figure 3.2 – Figure 3.4. As a general observation, the majority of the blends
exhibit macrophase separation into two distinct morphologies and the presence of the two
kinds of microdomains is also evident in the scattering profiles, shown in Figure 3.5 –
Figure 3.8. Thus the reflections from the diblock occur at lower q values, with multiple
reflections from the triblock appearing at higher q, the strength of these scattering peaks
depending upon blend composition. In the case of the SI450 and SI700 blends (images of
the latter not shown), the behavior is very similar, and all blend samples exhibit solely the
lamellar morphologies of the original block copolymers, with the exception of SI700
5/95, where PS cylinders in a PI matrix, in addition to thin lamellae and thick lamellae,
were observed (Figure 3.2h). In this instance, however, the USAXS data, indicates a
predominantly lamellar-lamellar morphology (Figure 3.6), suggesting that only a small
volume percent of isolated islands of cylinders exist. In the case of the two higher
molecular weight diblock blends (SI1000 and SI1500), the macrophase separation is
47
accompanied by the appearance of non-lamellar morphologies in a wide range of
compositions (see Figure 3.3 and Figure 3.4).
a
b
c
d
300 nm
Figure 3.1. Bright field TEM micrographs of thin OsO4 stained sections of the neat diblock
copolymers, showing all with lamellar morphologies: a) SI450, b) SI700, c) SI1000, d) SI1500.
48
Figure 3.2. Bright field TEM micrographs of thin OsO4 stained sections of blends of SI450 with SIS,
with compositions in weight percent (SI450/SIS): a) 5/95, b) 10/90, c) 25/75, d) 50/50, e) 75/25, f)
90/10, g) 95/5, h) the exceptional SI700 5/95 blend exhibits some cylindrical domains in the minority
SI700 phase in addition to thick and thin lamellar regions. Note that the micrographs were taken
from areas containing both the thin triblock lamellae and thick diblock lamellae, to indicate the
coexistence of the two phases, and are not representative of the actual volume percent of each type of
domain, which varies strongly with blend composition.
49
Figure 3.3. Bright field TEM micrographs of thin OsO4 stained sections of blends of SI1000 with SIS,
with compositions in weight percent (SI1000/SIS): a) 5/95, b) 10/90, c) 25/75, d) 50/50, e) 75/25, f)
90/10, g) 95/5. The 10/90 and 50/50 blends exhibit a disordered morphology with IMDS curvature
towards the PS domains, whereas the 25/75 and 75/25 blends reveal a PS cylindrical morphology.
According to the scattering data, the 10/90 blend appears to be disordered cylinders, whereas the
50/50 blend could be double gyroid, but it is not entirely clear. Nonetheless, micrographs for the
latter blend suggest a bicontinuous morphology.
50
Figure 3.4. Bright field TEM micrographs of thin OsO4 stained sections of blends of SI1500 with SIS,
with compositions in weight percent (SI1500/SIS): a) 5/95, b) 10/90, c) 25/75, d) 50/50, e) 75/25, f)
90/10, g) 95/5. The 5/95, 10/90, and 25/75 blends exhibit a disordered morphology, which once again
appears from the scattering data to be cylinders. The 75/25 blend appears to exhibit a poorly ordered
double-gyroid structure, and a detail of the structure, showing characteristic serpentine features, is
shown in the inset of (e). Note that while the effective volume fraction of the blends remains in the
lamellar region of the phase diagram ( 0.41 < Φ eff
), the IMDS is non-flat, with curvature
PS < 0.44
towards the PS domains.
51
The shift of the first order scattering peak (q1) with increased SIS loading, provides
a means of tracking the change in domain spacing of the high molecular weight diblock
rich phase (Figure 3.9). For all the blends studied, the domain spacing of the diblock rich
phase decreases upon addition of the triblock until a saturation point is reached and
thereafter the domain spacing remains relatively unchanged. This decrease in domain
spacing upon addition of a suitable surfactant-like modifier is well-known and arises as a
result of the localization of the triblock at the inter-material dividing surface (IMDS)
between the two high molecular weight blocks, effectively increasing the interface area
per unit volume and leading to chain relaxation near the interface.4,5 On the other hand,
the domain spacing of the triblock rich phase remains constant throughout, indicating
very little solubility of the large diblocks in the triblock.
Another observation from the scattering data, specifically for the SI450 and SI700
blends, is that the long range order of the diblock rich domains appears to improve with
added triblock, as evidenced by the sharper and more pronounced low q scattering peaks.
Presumably, the added triblock copolymer could be acting as a plasticizer for the diblock
domains, reducing the glass transition temperature, and diluting the entanglement
networks of both the PS and PI domains, thus allowing for enhanced mobility of the
chains.6 Additionally, the shrinking size of the diblock phase regions as their volume
fraction decreases, could be leading to an enhanced effect of the phase boundaries to
“template” the ordering, in analogy to the commensurate ordering of block copolymers in
troughs reported previously by our group.7 It is also noteworthy that the diblock rich
domain spacing begins to plateau at around 25% by weight addition of the triblock,
which is likely a good estimate of the solubility limit of the triblock in the diblock.
52
Figure 3.5. USAXS profiles for the SI450 series of blends. The lamellar reflections from the two
different phases are clearly evident, with the intensities of the SIS triblock reflections increasing with
the weight fraction of the triblock in the blend. A single box outline indicates reflections from the
diblock domains and a double box those of the triblock domains.
53
Figure 3.6. USAXS profiles for the SI700 series of blends, which are qualitatively similar to those of
the SI450 blends. A single box outline indicates reflections from the diblock domains and a double
box those of the triblock domains.
54
Figure 3.7. USAXS profiles for the SI1000 series of blends. The higher order peaks of the large
diblock are weak or absent, indicating poor long range order. A single box outline indicates
reflections from the diblock domains and a double box those of the triblock domains.
55
Figure 3.8. USAXS profiles for the SI1500 series of blends. The change in the scattering profile going
from 25% SIS to 50% SIS is clearly evident, indicating a change in the morphology from double
gyroid-like to cylinders. A single box outline indicates reflections from the diblock domains and a
double box those of the triblock domains.
56
350
Domain Spacing (d ) [nm]
SI450
300
SI700
250
200
150
100
0
10
20
30
40
50
60
70
80
90
100
SIS Weight Percent
350
Domain Spacing (d ) [nm]
SI1000
300
SI1500
250
200
150
100
0
10
20
30
40
50
60
70
80
90
100
SIS Weight Percent
Figure 3.9. Domain spacing ( d = 2π q1 ) as a function of the triblock content for the (a) SI450 and
SI700 blend series, and (b) for the SI1000 and SI1500 blend series, obtained by tracking the position
of the first order reflection in the USAXS data. The domain spacing decreases with increased
triblock content and levels off after around 25% by weight. The error in the measurement was
estimated from the broadening of the first order scattering peak, and reflects the higher uncertainty
at larger spacing (lower q), due to the inverse relation between d and q. For the SI1000 and SI1500
blends with cylindrical morphology, the cylinder radius is directly proportional to the domain
spacing, d, by the relation RCYL = d 2 f
3π , where f is the 2-D area (“volume”) fraction, based on
hexagonal packing.
57
Lamellar/Lamellar
50
45
Cylinder/Lamellar
Gyroid (Bicontinuous)/Lamellar
Lamellar
C-L C-L
C-L
C-L
G-L
HPL-L
L
L-L C-L
C-L
BC-L
C-L
L-L
L
C-L L-L
L-L
L-L
L-L
L-L
L
SI1500
Molecular Weight Ratio (R )
40
35
30
25
SI1000
SI700
20
L-L L-L
15
L-L
L-L
L-L
L-L
L
SI450
10
Flat IMDS
5
Curved IMDS
0
0
10
20
30
40
50
60
70
80
90
100
SI Weight Percent
Figure 3.10. Morphological phase diagram of the binary blends in the parameter space of molecular
weight ratio, R = M ndiblock 12 M ntriblock , and blend composition, in weight percent SI (to facilitate
comparison with previous studies). The data points for each blend series are depicted in a unique
color. The blue shaded area represents the region where the blends exhibit lamellar (flat IMDS)
morphologies (with one exception at 5% of the SI700 blend). In the yellow shaded area,
morphological phase transitions are observed, from lamellar arrangement to structures with IMDS
curvature – cylinders and double gyroid-like, identified by different data point shapes on the graph.
The dotted line indicates where the blends macrophase separate: to the right of the line, the blends
are miscible and exhibit a single microphase separated morphology, whereas to the left the blends
are macrophase separated, with two coexisting microphase separated morphologies.
Based on the microscopy and scattering data, a morphological phase diagram in
the parameter space of molecular weight ratio (R) and composition was constructed and
is shown in Figure 3.10. As mentioned previously, the molecular weight ratio was
computed based on the assumption the triblock copolymer behaves morphologically as a
diblock of half the molecular weight.3 There are two key features of note in the phase
diagram. First, all the blends become multiphased in the weight fraction range of SI, wSI
< 0.9. That is, the blends phase separate into two distinct types of microdomain
58
structures, one of which is always the lamellar structured SIS triblock. This macrophase
separation has been observed before in previous studies,8-12 and was attributed to the
initial onset of microphase separation of the larger block copolymer upon solvent
evaporation.8 Nonetheless, in the present investigation, the miscibility gap is larger than
that reported in the earlier studies, where the block copolymers were found to be
immiscible for a weight fraction range of the large copolymer, wlarge < 0.7.13 This is
undoubtedly linked to the much larger mismatch in the molecular weights of the diblocks
with respect to the triblock in the present study, and implies that the former is virtually
insoluble in the latter. This larger miscibility gap was predicted in a theoretical study of
block copolymer blends by Matsen.14 Matsen’s study presented two phase diagrams, for
R = 10 and 25, and up to χNlarge = 600 (c.f. Figure 2 in reference 14). The phase diagrams
showed that for blends where the interaction parameter and molecular weight ratio are
large, as is the case in the present study (e.g. χNlarge ~ 700 and R ~ 25 for the series of
SI700 blends), the blends become immiscible when wlarge < 0.85, in close agreement with
our experimental results.
The second notable feature is that morphological transitions (i.e. to non-lamellar
morphologies) begin to appear in the SI majority phase at R ~ 30. Compared to the
consolidated phase diagram previously presented by Yamaguchi and Hashimoto,13 where
a two phase region begins at R ~ 7 and is assumed to extend beyond R > 15, here we find
no morphological transitions in the range 10 < R < 30 (with the single exception of the
SI700 5/95 blend). Moreover, though morphological transitions have been reported
previously,9,11,13 these were restricted to the formation of the cylindrical microstructure.15
In the present study, in addition to hexagonally packed PS cylinders (Figure 3.3c&e, and
59
Figure 3.4d), a disordered or worm-like cylindrical (PS) phase (Figure 3.3b&d, and
Figure 3.4a-c), and a bicontinuous phase resembling the double gyroid (Figure 3.4e) are
observed. As a direct result of the very high molecular weights of the diblock
copolymers, the SI1500 and especially the SI1000 blend samples show rather poor long
range order in TEM images and in USAXS, as evidenced by the broad peaks and weak
(or absent) higher order reflections (Figure 3.7 and Figure 3.8). The USAXS data are
largely consistent with the microscopy observations, with characteristic scattering peak
ratios at 1 and
4 present in the SI1500 scattering results (as well as
12 in SI1500
50/50), substantiating the characterization of these samples as having the cylindrical
morphology in the diblock rich phase. For the SI1000 blends (10/90, 25/75, and 75/25),
though the low q scattering data shows essentially one peak, a thorough analysis of many
TEM micrographs and comparison to the SI1500 TEM data, allows for the assignment of
the cylindrical morphology to these samples with a high degree of certainty.
In the blend sample exhibiting the presumed double gyroid morphology, SI1500
75/25, the scattering data shows two distinct peaks, with peak ratios of 1 and
approximately 2.75, which is inconsistent with a cylindrical morphology, but this
scattering peak ratio coincides with the {631} reflection of the double gyroid ( 23 3 ≈
2.77). Furthermore, the disappearance of the peak at
4 , evident in the neighboring
blend sample (SI1500 50/50) which shows the cylindrical morphology, requires the
assignment of another, non-cylinder, morphology to this blend. The TEM micrograph
(Figure 3.4e) of this blend is highly reminiscent of the double gyroid morphology and
extends over large areas (Figure 3.11). The morphology is clearly not very well ordered,
resulting in only a few broad scattering peaks, which do not allow for conclusive
60
assignment of the blend morphology. Nonetheless, taken together, the data suggest that
the observed morphology is likely double gyroid. With respect to the stability of this
phase, the sample was annealed for an extra seven days at 125°C with no change
observed in the scattering indicating that the morphology is likely not kinetically trapped.
The observation of this double gyroid-like phase, which was not reported in previous
studies on blends of diblock copolymers, is not only appealing from a strictly
morphological perspective, but also lends further evidence as to the stability of the double
gyroid phase in block copolymer melts in general at high segregation strengths.16-18
Figure 3.11. Low magnification wide area TEM image of the SI1500 75/25 blend showing large areas
of a distorted gyroid-like structure.
61
Since the effective volume fraction of the blends remains within the lamellar
region of the phase diagram, Yamaguchi and Hashimoto ascribed the morphological
transitions into curved IMDS morphologies, to the influence of the asymmetric
composition of the lower molecular weight block copolymer, which prefers a
spontaneous non-zero curvature at the IMDS between the dissimilar blocks (Figure 3.12).
They argued that in the neat lower molecular weight copolymer, this small value of
interface curvature would promote large radius domains, inconsistent with chain packing
considerations, and hence the resulting neat morphology is lamellar. However, upon
addition of a second, higher molecular weight block copolymer, the preferred non-flat
curvature of the IMDS can be realized, since the larger block copolymer chains can fill
the extra space required to accommodate the small non-zero spontaneous curvature (c.f.
Figure 14 in reference 13).11,13 It is evident then, that for a small compositional
asymmetry in the lower molecular weight block copolymer, higher values of R (i.e.
longer chains of the large block copolymer) would be required to induce the non-flat
IMDS morphologies by allowing the formation of larger radius structures. This is
precisely what is observed in the present study. As in the prior work, the overall volume
fraction of the blends here would indicate a lamellar morphology in the diblock rich
phase (ΦPS in the range 0.41 – 0.44), nonetheless, as the molecular weight of the diblock
increases, curved IMDS morphologies appear in the blends composed of SI1000 and
SI1500. Also noteworthy is that the size of the cylindrical domains stays relatively
constant in the blends, as evidenced by the roughly constant domain spacing in the blends
with a cylindrical morphology (see Figure 3.9b). Since, the spontaneous curvature is
expected to be determined by the mismatch in size of the respective blocks in the
62
triblock, which is constant, this lends further support to the explanation for the
appearance of cylindrical domains resulting from an expression of a spontaneous
curvature, as outlined above.
Figure 3.12. Schematic representation of chain packing of diblock copolymers with an asymmetric
composition. The schematic illustrates the spontaneous curvature implied by the underlying
asymmetry. In the neat block copolymer, this curvature is not expressed, while the addition of a
larger block copolymer of appropriate size (to fill the extra volume) is capable of stabilizing the
curved IMDS morphology.
Despite experimental observations, prior theoretical studies have not predicted
this morphological transition in nearly symmetric block copolymer blends, with the
exception of the strong segregation limit (SSL) theory of Lyatskaya et al., where a lower
free energy for the cylindrical morphology was found in a certain composition window
63
with wlarge ≤ 0.4 for two lamellar forming diblock copolymers.19 However, the
composition of one of the two diblocks was rather asymmetric (nearly cylinder forming)
and the molecular weight ratio was R ≤ 2. Yamaguchi et al. applied Lyatskaya’s model in
their study and were unable to demonstrate that the cylindrical microstructure is favored
over the lamellar microstructure in their blends.11 The self-consistent field theory (SCFT)
study by Matsen14 focused on selected values of χN and R, and although it demonstrated
the macrophase separation into two coexisting lamellar phases, no cylindrical domains
were reported. Shi and Noolandi utilized the SCFT to map out a phase diagram (a “phase
cube” in the three parameters of, Φ, f1, and f2 – the overall blend composition, and the
compositions of the two block copolymers, respectively) for a pair of diblocks of equal
length (i.e. R = 1) and found interesting changes in the phase diagram, but again their
work did not predict phase transitions to curved IMDS structures when the effective
volume fraction of the blends was near 0.5, unless one of the diblocks was highly
asymmetric (i.e. nearly a homopolymer).20
In another study, Shi and Noolandi investigated the effects of short diblocks
(effectively non-ordering surfactants with χN < 10.5) on the phase behavior of strongly
segregated long diblocks (R = 10),21 and two of their findings are of note in the present
context. First, when their composition was near 0.5, a sizeable proportion (~ 20%) of the
short diblock chains tended to segregate to the interface between the large diblock
domains, acting as surfactants. This is near the estimated value of ~ 25% for the
solubility limit of the triblock in the domains of the large diblock in this study. Second,
the chain end distribution of the long diblock was found to deviate from the analytical
SSL theory of Semenov,22 with the chain end density increasing gradually from the
64
interface to the center of the domain. This hints at the possibility of chain end effects
playing a role in determining the microstructure. In the case of the SSL theory of
Lyatskaya et al., the chains are presumed to be highly stretched and the long diblock
chain ends are explicitly excluded from folding back and mixing with the short diblock
segments near the interface.19 That the long diblock copolymer chains could be folding
back on themselves inside the cylindrical domains is supported by our data, where the
cylinder radius is much smaller than the length of the high molecular weight chains in the
lamellar domains (see Figure 3.9). It seems logical, that in order to best fill the cylindrical
space, the long diblock chains would fold back towards the cylinder IMDS to maintain
constant segmental density and to avoid overcrowding in the center of the cylinder. It
would be of great interest to have SCFT studies in the relevant composition range, which
account for chain segment distribution, in order to compare to the experimental results
and assess if this hypothesis is correct.
The strongly segregating high molecular weight diblock copolymers used in this
study, having very high χN values (470 < χN < 1410), allowed for the exploration of the
phase space that was not accessed in previous studies. Additionally, the higher absolute
molecular weights of the diblocks contributed to an increased miscibility gap and
permitted the extension of the morphological phase diagram for molecular weight ratios
R > 15. It remains to be seen if these factors influenced the morphology of the blends. In
particular, it is of interest to investigate blends where R < 5, but the absolute molecular
weights are large (Mn ~ 1 x 106 g/mol). In previous studies, blends with R < 5 were
miscible at all compositions, but the increased molecular weights and segregation
strength of the two components could lead to phase separation and/or morphological
65
transitions. It is also important to determine whether chain architecture influences the
observed morphology. In the current study, we postulate that the morphology of the neat
triblock is equivalent to that of a diblock of half the molecular weight, as was
demonstrated previously,3 and it is on this basis that the molecular weight ratio, R, is
calculated. Nonetheless, the connectivity of the blocks is a factor for the morphology of
the blends, possibly influencing the nature of the morphological transitions and the
solubility of the block copolymers. For instance, it is clear that bridges are not possible
for the triblock in the large molecular weight diblock, since the PI middle block would
not be able to span the large domain sizes present in the diblock. As such, only mid-block
loops or homogeneous solubility of the triblock in the diblock are possible. It is
interesting to consider the possibility that the connectivity of the triblock (as opposed to
diblock) copolymer could be favoring the formation of 3-D bicontinuous structures with
non-zero mean curvature over the 2-D cylindrical structure.
3.2 Conclusion
A series of blends of high molecular weight diblock copolymers with a lower
molecular weight triblock copolymer were prepared and their morphological
characteristics expressed on a phase diagram in the parameter space of molecular weight
ratio and blend composition. Molecular weight ratios in the range 14 < R < 43 were
accessed, considerably extending the range previously studied. The observed blend
morphologies shared many of the same features previously reported, including miscibility
gaps with macrophase separation into two distinct microphase separated domains, and
morphological transitions from lamellar to cylindrical structures. Additionally, disordered
bicontinuous and double gyroid-like structures were also observed at certain
66
compositions. The change from the flat zero curvature IMDS of the lamellar morphology
to curved IMDS structures was presumed to result from compositional asymmetry of the
block copolymers (ΦPS in the range 0.41 – 0.44) and the preference for a non-zero IMDS
curvature in the SIS triblock. This transition will be the subject of the investigation
presented in the next chapter. The phase diagram showed a narrow region of complete
miscibility, for wSI > 0.9, in line with theoretical studies.14 This study demonstrated the
possibility of accessing a number of different block copolymer morphologies (lamellae,
cylinders, bicontinuous), by blending two block copolymers with only one type of
morphology (lamellae). This approach essentially allows access to a wide range of
morphologies, without the need to resort to sensitive and time-consuming synthetic
chemistry to precisely tailor the block copolymer composition.
67
3.3 References
[1]
G. Hadziioannou, A. Skoulios. "Structural Study of Mixtures of Styrene Isoprene
2-Block and 3-Block Copolymers." Macromolecules, 15(2), 267-271 (1982).
[2]
T. Goldacker, V. Abetz, R. Stadler, I. Erukhimovich, L. Leibler. "Noncentrosymmetric superlattices in block copolymer blends." Nature, 398(6723),
137-139 (1999).
[3]
G. Hadziioannou, A. Skoulios. "Molecular-Weight Dependence of Lamellar
Structure in Styrene Isoprene 2-Block and 3-Block Copolymers."
Macromolecules, 15(2), 258-262 (1982).
[4]
D. Yamaguchi, J. Bodycomb, S. Koizumi, T. Hashimoto. "Ordered structure in
blends of block copolymers. 4. Location of the short diblock." Macromolecules,
32(18), 5884-5894 (1999).
[5]
A. M. Mayes, T. P. Russell, V. R. Deline, S. K. Satija, C. F. Majkrzak. "BlockCopolymer Mixtures as Revealed by Neutron Reflectivity." Macromolecules,
27(25), 7447-7453 (1994).
[6]
D. Mader, M. Bruch, R. D. Maier, F. Stricker, R. Mulhaupt. "Glass transition
temperature depression of elastomers blended with poly(propene)s of different
stereoregularities." Macromolecules, 32(4), 1252-1259 (1999).
[7]
J. Y. Cheng, C. A. Ross, E. L. Thomas, H. I. Smith, G. J. Vancso. "Templated
self-assembly of block copolymers: Effect of substrate topography." Advanced
Materials, 15(19), 1599-+ (2003).
[8]
T. Hashimoto, S. Koizumi, H. Hasegawa. "Ordered Structure in Blends of BlockCopolymers .2. Self-Assembly for Immiscible Lamella-Forming Copolymers."
Macromolecules, 27(6), 1562-1570 (1994).
[9]
T. Hashimoto, K. Yamasaki, S. Koizumi, H. Hasegawa. "Ordered Structure in
Blends of Block Copolymers .1. Miscibility Criterion for Lamellar Block
Copolymers." Macromolecules, 26(11), 2895-2904 (1993).
[10]
S. Koizumi, H. Hasegawa, T. Hashimoto. "Ordered Structure in Blends of BlockCopolymers .3. Self-Assembly in Blends of Sphere-Forming or Cylinder-Forming
Copolymers." Macromolecules, 27(15), 4371-4381 (1994).
[11]
D. Yamaguchi, S. Shiratake, T. Hashimoto. "Ordered structure in blends of block
copolymers. 5. Blends of lamella-forming block copolymers showing both
microphase separation involving unique morphological transitions and
macrophase separation." Macromolecules, 33(22), 8258-8268 (2000).
[12]
C. M. Papadakis, K. Mortensen, D. Posselt. "Phase behavior of binary blends of
symmetric polystyrene-polybutadiene diblock copolymers studied using SANS."
European Physical Journal B, 4(3), 325-332 (1998).
68
[13]
D. Yamaguchi, T. Hashimoto. "A phase diagram for the binary blends of nearly
symmetric diblock copolymers. 1. Parameter space of molecular weight ratio and
blend composition." Macromolecules, 34(18), 6495-6505 (2001).
[14]
M. W. Matsen. "Immiscibility of Large and Small Symmetrical Diblock
Copolymers." Journal of Chemical Physics, 103(8), 3268-3271 (1995).
[15]
Although the statement is made of gyroid (OBDD) structure in the blends in
reference 9, the data presented in that article is in fact more consistent with the
cylindrical morphology. The TEM micrograph for the 50/50 and 80/20 blends
(Fig 4) look rather like cylindrical morphologies. Importantly, however, the
SAXS data reveals the typical scattering peaks of the cylindrical morphology (in
fact, the caption to Fig 9 labels them as "hexagonal" profiles, consistent with
cylinders), indicating that this is the actual (or dominant) morphology. In a
personal communication, the authors of the study confirmed that the majority of
the structure was indeed cylinders, with some isolated areas of gyroid (OBDD).
Furthermore, the composition of these blends varied with casting conditions,
hinting that this is not a stable morphology.
[16]
A. M. Urbas, M. Maldovan, P. DeRege, E. L. Thomas. "Bicontinuous cubic block
copolymer photonic crystals." Advanced Materials, 14(24), 1850-1853 (2002).
[17]
D. A. Davidock, M. A. Hillmyer, T. P. Lodge. "Persistence of the gyroid
morphology at strong segregation in diblock copolymers." Macromolecules,
36(13), 4682-4685 (2003).
[18]
E. W. Cochran, C. J. Garcia-Cervera, G. H. Fredrickson. "Stability of the gyroid
phase in diblock copolymers at strong segregation." Macromolecules, 39(7),
2449-2451 (2006).
[19]
J. V. Lyatskaya, E. B. Zhulina, T. M. Birshtein. "Theory of Supermolecular
Structures in Polydisperse Block Copolymers .4. Cylindrical Domains in BinaryMixtures of Diblock Copolymers and Cylinder Lamellae Transition." Polymer,
33(2), 343-351 (1992).
[20]
A. C. Shi, J. Noolandi. "Binary-Mixtures of Diblock Copolymers - PhaseDiagrams with a New Twist." Macromolecules, 28(9), 3103-3109 (1995).
[21]
A. C. Shi, J. Noolandi. "Effects of Short Diblocks at Interfaces of Strongly
Segregated Long Diblocks." Macromolecules, 27(11), 2936-2944 (1994).
[22]
A. N. Semenov. "Contribution to the Theory of Microphase Layering in BlockCopolymer Melts." Soviet Physics JETP, 88(4), 1242-1256 (1985).
69
Chapter 4
Influence of Short Block Copolymers on
the Morphology of Binary Block
Copolymer Blends: A Modeling Study
In this chapter the blend systems investigated experimentally in Chapter 3 are
modeled using an analytical strong segregation limit theory, in order to gain a better
understanding of their behavior. The systems were investigated using the strong
segregation theory model of binary blends of diblock copolymers developed by
Lyatskaya et al,1, 2 hereafter referred to as the “BZL” theory or model (after the names of
the authors; Birshtein, Zhulina, and Lyatskaya). Our main interest is in elucidating the
properties of the transition from flat IMDS lamellar microstructures to curved IMDS
microstructures, such as cylindrical and bicontinuous. In the original BZL model, only
the length of one of the blocks in the block copolymer was allowed to vary, the other
block length being the same for both block copolymers. In order to be applicable to the
blends investigated in Chapter 3, the version of the BZL model modified by Yamaguchi
et al.3 to allow for both block lengths to be variable, was used in the present context. This
model was then further adapted to the current study parameters in order to model the
triblock copolymer as a diblock copolymer of half the molecular weight.
4.1 Results and Discussion
In a series of articles, Lyatskaya et al., developed a model for the equilibrium
microstructures of mixtures of block copolymers.1,
70
2, 4-6
The model relies on the block
copolymers to be in the strong segregation regime, where the individual block domains
are well defined with little intermixing, and thus having a narrow interphase region. The
A-B diblock copolymers are modeled as brushes on a common interface, with the A
chains on one side of the interface and the B chains on the other. Furthermore, each
individual domain has one other “surface”, with the boundary of this surface being the
height of the brush of the shorter copolymer, as depicted schematically in Figure 4.1. As
such, each domain has two “brush” regions; one region is composed of segments of both
the long and short diblock chains, and the other is comprised solely of segments of the
long diblock copolymer chain.
Figure 4.1. Schematic representation of a binary mixture of two block copolymers of different
lengths for (a) lamellar morphology, and (b) cylinder morphology. It is important to note that one
triblock copolymer chain has been modeled as two diblock copolymer chains of half the degree of
polymerization of the triblock. For the cylinder morphology (b), the radius of the cylinder is given by
rcyl = HAs + HAl.
To determine the stable morphology at a given composition, an expression for the
free energy per chain, Fx, is derived for both the lamellar and cylinder morphologies (x =
C for cylinder morphology or L for lamellar morphology). The free energy model does
71
not include the entropy of mixing, which is expected to make only a small contribution to
the overall free energy of the blend system, because of the very high molecular weights.1
In units of kT, the free energy per chain is given by Fx = FS + FA + FB, where FS is the
surface free energy at the IMDS, and FA and FB are the conformational free energies of
the A and B block chains, respectively.1 These conformational free energies were derived
with the aid of the formalism developed by Milner, Witten, and Cates in their studies on
grafted polymer brushes.7-9 The BZL model further makes use of two parameters that
characterize the block copolymers used in the blends, namely n, the number (mole)
fraction of one of the components, and α, which describes the relative difference in the
length of the blocks in the copolymer. The modeling is performed with respect to the
number of long diblock chains in the blend, nl, or n =
nl
, with ns being the number
nl + ns
N il − N is
of short chains. The parameter α is defined as α i =
, where N i j is the degree of
s
Ni
polymerization of the i (i = A or B) block chain of the long copolymer (j = l) or short
copolymer (j = s). It is important to note that in order to apply the BZL model to our
experimental system, the degree of polymerization used in the modeling for the short
copolymer chains is half of the actual triblock copolymer used in the blends, i.e.
N is =
1
2
N itriblock . As a result, in the interpretation of the data, the actual number fraction of
the diblock in the experimental blends is related to the number fraction used in the model
by the expression nblend =
2n
. Finally, the block copolymers are modeled as
1+ n
incompressible Gaussian chains, and an expression for the total free energy per chain is
obtained with respect to the structural parameters described in Figure 4.1. This expression
72
is subsequently minimized with respect to the average interface area per block copolymer
molecule. The detailed expressions for the free energy and its derivation are outlined in
the Appendix and the values for the parameters characterizing the block copolymers are
shown in Table 4.1.
Polymer
NPS
NPI
αPS
αPI
ΦPS
SI450
2332
2905
14.7
11.9
0.47
SI700
3861
4679
25.0
19.8
0.49
SI1000
4873
6440
31.8
27.6
0.44
SI1500
6745
9062
44.4
39.3
0.43
SIS
149
225
-
-
0.41
Table 4.1. Polymer characteristics used in the model calculations.
The results of the model are shown in Figure 4.2 and Figure 4.3, where the reduced
free energy (F/Φ, with Φ being the surface free energy at the interface), in units of kT, is
plotted against the number fraction of the large copolymer (diblock) in the blend. All
blends show a narrow window of composition where the cylinder morphology has a
lower free energy over that of the lamellar morphology, and hence is expected to be the
stable and observed microstructure. It is satisfying to note that the model predicts the
cylinder morphology even though the overall volume fraction of the PS domains in the
blend remains in the lamellar composition range (0.41 – 0.45). Furthermore, this is the
first time that this behavior has been predicted in this composition range using this
model. The main reason is undoubtedly due to the fact that the polymers being modeled
have a very high degree of polymerization and the asymmetry of the triblock is relatively
large (ΦPS = 0.41). Since the radius of the inherent curvature decreases with increasing
73
copolymer asymmetry, the necessary volume to be filled is smaller, thereby requiring
relatively shorter chains in order to effectively fill the empty volume created by the
inherent curvature of the asymmetric copolymer. As was mentioned in Chapter 3, in
previous studies by Lyatskaya et al., the stability of the cylinder morphology was only
observed when the block copolymers had complementary asymmetric compositions (Φ1A
= 0.33, Φ2A = 0.69).1 Additionally, in their original model, only the length of one of the
blocks in the block copolymer was allowed to vary, the other block length being the same
for both block copolymers. Yamaguchi et al., adapted the model to allow for both block
lengths to be variable, yet their modeling did not predict the cylinder morphology using
the BZL theory, even though they did observe cylinder morphology in their experimental
blends.3
The interesting aspect of the theoretical data is that it predicts all of the blends to
exhibit a cylindrical morphology in some composition range, yet only the highest
molecular weight SI1000 and SI1500 blends have experimentally been shown to exhibit
these curved IMDS morphologies. To investigate this phenomenon, it is instructive to
look at the range of composition where the cylinder morphology is predicted to be more
stable than the lamellar, i.e. where ∆FCL = FCYL − FLAM < 0 . The dependence of ∆FCL on n
in this composition range is shown in Figure 4.1, and the range of stability for the
cylinder morphology for each of the blends is summarized in Table 4.2.
74
SI450 Blends
60
(a)
20
55
19
50
18
45
17
0
0.1
0.2
F/Φ
40
35
30
25
Cylinder
Lamellar
20
15
0
0.1
0.2
0.3
0.4
0.5
n
0.6
0.7
0.8
0.9
1
SI700 Blends
60
(b)
20
55
19
50
18
45
17
0
0.1
0.2
F/Φ
40
35
30
25
Cylinder
Lamellar
20
15
0
0.1
0.2
0.3
0.4
0.5
n
0.6
0.7
0.8
0.9
1
Figure 4.2. Reduced free energy plots for the diblock/triblock (SI/SIS) blends investigated in Chapter
3: (a) SI450 blends, and (b) SI700 blends. The two lines, blue and red, correspond to the free energy
of the lamellar morphology and cylinder morphology, respectively.
75
SI1000 Blends
70
(a)
65
20
60
19
55
18
F/ Φ
50
17
45
0
0.1
0.2
40
35
30
25
Cylinder
Lamellar
20
15
0
0.1
0.2
0.3
0.4
0.5
n
0.6
0.7
0.8
0.9
1
SI1500 Blends
70
(b)
65
20
60
19
55
18
F/ Φ
50
17
45
0
0.1
0.2
40
35
30
25
Cylinder
Lamellar
20
15
0
0.1
0.2
0.3
0.4
0.5
n
0.6
0.7
0.8
0.9
1
Figure 4.3. Reduced free energy plots for the diblock/triblock (SI/SIS) blends investigated in Chapter
3: (a) SI1000 blends, and (b) SI1500 blends. The two lines, blue and red, correspond to the free
energy of the lamellar morphology and cylinder morphology, respectively.
76
0.5
0.4
0.3
0.2
∆ FCL
0.1
0
-0.1
-0.2
SI450 Blends
SI700 Blends
SI1000 Blends
SI1500 Blends
-0.3
-0.4
-0.5
0
0.02
0.04
0.06
0.08
0.1
n
0.12
0.14
0.16
0.18
0.2
Figure 4.4. Free energy difference between cylinder and lamellar morphology.
Blend Series
nCYL
wCYL
SI450
0.093 – 0.257
0.42 – 0.71
SI700
0.077 – 0.223
0.49 – 0.77
SI1000
0.074 – 0.211
0.55 – 0.80
SI1500
0.073 – 0.193
0.62 – 0.84
Table 4.2. Composition ranges for the stability of the cylinder morphology in the blends. nCYL is the
number fraction of the large diblock in the blends ( nCYL = 2n (1 + n ) ), and wCYL is the corresponding
weight fraction, based on the molecular parameters of the experimental diblock/triblock blends.
There are a number of features worthy of consideration in Figure 4.4. First, the
composition range for stability of the cylinder morphology shifts toward lower values of
n with increasing molecular weight of the diblock, which means that a smaller number of
77
chains of the longer copolymer are required to stabilize the morphology at a given
molecular weight ratio. This implies that the morphology is largely dictated by the
smaller triblock copolymer, since the diblock chains are effectively “filling the space”
created by the expression of the inherent curvature present in the asymmetry of the
triblock. It is also confirmed by the observation of the relatively constant size of the
cylindrical domains in the blends of SI1000 and SI1500 (Chapter 3, Figure 3.9).
Essentially, the triblock copolymer has a preferred radius for the cylinder morphology
resulting from its compositional asymmetry, and the addition of the long diblock
copolymer stabilizes this morphology. Since this radius is “fixed” by the composition,
implying a “fixed” volume for the cylinder, the longer the added diblock copolymer
chains are, the smaller the number of chains that are required to fill the volume. This
behavior, where the shorter copolymer effectively controls the microstructure has been
observed previously by Court and Hashimoto for the lamellar microstructure.10 In their
study, they blended short, symmetric, lamellar-forming diblock copolymers with a longer
asymmetric, sphere-forming diblock copolymer, and investigated the effect on the
interfacial area per chain at the IMDS. They found that the addition of the longer diblock
does not significantly modify the organization of chains at the interface, and the average
interfacial area per chain remained constant and equal to that of the pure symmetric
diblock.
The second intriguing feature of Figure 4.4, is the existence of a stability region for
the cylinder morphology in all the blends, which is not present in the experimental
results. It should be mentioned at the outset, that the BZL model cannot completely
model the behavior of blends under investigation, since it does not take into consideration
78
the possibility of macrophase separation in the blends. Nevertheless, it is precisely the
fact that the blends macrophase separate that leads to the apparent discrepancy between
the model and experimental results. In Chapter 3, it was estimated that the “solubility
limit” of the triblock in the blends was roughly 25% by weight, based on the observation
that the spacing of the lamellar or cylindrical domains in the blends reached a plateau at
this concentration (Chapter 3, Figure 3.9). Table 4.2 lists the stability range of the
cylinder domains in the blends and it indicates that there is a threshold concentration
required. For the two lower molecular weight diblocks, SI450 and SI700, the threshold
values are 29% and 23% by weight of the triblock respectively. For the SI450 blends, the
threshold value is above the “solubility limit”, and hence these macrophase separated
blends would not be expected to exhibit a cylindrical morphology, as confirmed by the
experimental results. In the case of the SI700 blends, the threshold composition is 23%
by weight of the triblock, very close to the estimated 25% value. In effect, since cylinder
morphologies are not observed in the SI700 blends, and no blend compositions were
investigated in the region between 10% - 25% by weight triblock, it is safe to assert that
the “solubility limit” is closer to 23%, based on the model data. The fact that this
macrophase separated blend series is near the boundary of the cylinder stability region is
reinforced by the observation of cylindrical domains in the SI700 5/95 blend (Chapter 3,
Figure 3.2(h)), which has a very high content of SIS triblock. In the case of the two
higher molecular weight diblocks, SI1000 and SI1500, the threshold composition values
are 20% and 16% by weight triblock respectively. Both of these values are below the
“solubility limit” of the triblock and as a result, these series of blends exhibit the
cylindrical morphology, along with other morphologies with IMDS curvature.
79
Furthermore, as predicted by the model, the SI1000 90/10 blend exhibits only the
lamellar morphology, 10% by weight triblock being below the calculated threshold value
of 20%, whereas the SI1500 90/10 blend, being close in composition to the 16%
threshold, is beginning to exhibit curved morphologies, as evidenced by the hexagonally
perforated lamellae observed in this blend. Taken together, it is clear that the model
results are consistent with the observed morphologies in the blend, and the calculated
values of the stability region of the cylinder domains corresponds well with the
experimentally determined compositions.
Lastly, Figure 4.4 shows that the minimum of the free energy difference between
the cylinder and lamellar morphologies initially decreases with increasing diblock
copolymer molecular weight, and then slightly decreases. This indicates that as the larger
copolymer chains get longer, they eventually become too long to favorably stabilize the
cylindrical microstructure, and the lamellar microstructure would be recovered. It is
interesting to note that this kind of reentrant phase behavior was demonstrated previously
by Yamaguchi et al.11 In their phase diagram, single phase lamellar morphologies were
observed at molecular weight ratios less than 5. Upon increasing the molecular weight
ratio, in the range 5 < R < 7, macrophase separated blends with cylindrical morphology
were observed, but for values of R > 7, once again only lamellar morphologies were seen.
This lends further support to the interpretation that the smaller copolymer, in the present
case the triblock, is dictating the evolution of the microstructure. The minimum of the
free energy of the system is achieved by the expression of the preferred radius of
curvature implied in the inherent asymmetry of the block copolymer. When there is too
little or too much of the larger diblock, or it is too long or too short, at a given molecular
80
weight ratio and composition, the microstructure reverts back to the standard lamellar
morphology predicted by the classical block copolymer phase diagram in this
composition range.
The experimental observations presented in Chapter 3 and the model calculations
of this chapter serve to explain the rich nature of the binary block copolymer blend phase
diagram. Taken together with other studies,10,
12-14
the data presented show that the
interesting morphologies observed are due to the smaller triblock copolymers and larger
diblock copolymer junctions segregating to a common interface. This phenomenon,
dubbed the “cosurfactant effect” by Court and Hashimoto,12 influences the morphology
by effectively lowering the segregation strength of the blend and thereby stabilizing
“non-standard” microstructures in a given composition range. The exact morphologies
observed depend on the characteristics of the two block copolymers, and the key
parameters are the block copolymer compositions, block copolymer molecular weight
ratio, and blend composition. It is important to note that the blend morphology cannot be
simply explained by the overall composition of the A and B blocks in the blend, as is the
case for the classical single block copolymer phase diagram. In effect, the new
parameters mentioned provide an extra level of control for the tuning of the classical
single block copolymer phase diagram, beyond simply volume fraction of one of the
components.
4.2 Conclusion
In this chapter, a model based on strong segregation theory was employed to aid in
the understanding of the experimentally observed morphologies in binary blends of block
copolymers. Though the model did not allow for the possibility of macrophase separation
81
in the blends, and explicitly accounted only for the cylindrical or lamellar morphologies,
the resulting calculations were able to shed light on the experimental observations. The
model showed that for all the lamellar-lamellar blends studied, there is a composition
window where the cylindrical morphology is favored over the lamellar morphology. The
composition limits for the stability of the cylindrical morphology obtained from the
model matched closely with the experimentally observed composition limits of the
curved IMDS morphologies, even though these were not confined solely to cylindrical
morphologies, and included bicontinuous and gyroid-like microstructures. The lack of
experimentally observed cylindrical morpholgies in the SI450 and SI700 blends was
determined to result from the macrophase separation evident in the blends, which
precluded enough low molecular weight triblock being present in the high molecular
weight diblock-rich domains to achieve a cylindrical morphology. Furthermore, the
observations were consistent with, and reinforced, prior studies on binary block
copolymer blends, indicating that the segregation of the block copolymer domains on a
common interface leads to the perturbation of the classical block copolymer phase
diagram boundaries.
82
4.3 References
[1]
J. V. Lyatskaya, E. B. Zhulina, T. M. Birshtein. "Theory of Supermolecular
Structures in Polydisperse Block Copolymers .4. Cylindrical Domains in BinaryMixtures of Diblock Copolymers and Cylinder Lamellae Transition." Polymer,
33(2), 343-351 (1992).
[2]
E. B. Zhulina, Y. V. Lyatskaya, T. M. Birshtein. "Theory of Supermolecular
Structures in Polydisperse Block Copolymers .3. Cylindrical Layers of Bidisperse
Chains." Polymer, 33(2), 332-342 (1992).
[3]
D. Yamaguchi, S. Shiratake, T. Hashimoto. "Ordered structure in blends of block
copolymers. 5. Blends of lamella-forming block copolymers showing both
microphase separation involving unique morphological transitions and
macrophase separation." Macromolecules, 33(22), 8258-8268 (2000).
[4]
T. M. Birshtein, Y. V. Liatskaya, E. B. Zhulina. "Theory of Supermolecular
Structures of Polydisperse Block Copolymers .1. Planar Layers of Grafted
Chains." Polymer, 31(11), 2185-2196 (1990).
[5]
E. B. Zhulina, T. M. Birshtein. "Theory of Supermolecular Structures in
Polydisperse Block Copolymers .2. Lamellar Superstructure Consisting of 2Block Copolymers." Polymer, 32(7), 1299-1308 (1991).
[6]
T. M. Birshtein, Y. V. Lyatskaya, E. B. Zhulina. "Theory of Supermolecular
Structures in Polydisperse Block Copolymers .5. New Double Cylindrical
Structure in Binary Mixture of Cylinder-Forming Diblock Copolymers." Polymer,
33(13), 2750-2756 (1992).
[7]
R. C. Ball, J. F. Marko, S. T. Milner, T. A. Witten. "Polymers Grafted to a
Convex Surface." Macromolecules, 24(3), 693-703 (1991).
[8]
S. T. Milner, T. A. Witten, M. E. Cates. "A Parabolic Density Profile for Grafted
Polymers." Europhysics Letters, 5(5), 413-418 (1988).
[9]
S. T. Milner, T. A. Witten, M. E. Cates. "Theory of the Grafted Polymer Brush."
Macromolecules, 21(8), 2610-2619 (1988).
[10]
F. Court, T. Hashimoto. "Morphological studies of binary mixtures of block
copolymers. 2. Chain organization of long and short blocks in lamellar
microdomains and its effect on domain size and stability." Macromolecules,
35(7), 2566-2575 (2002).
[11]
D. Yamaguchi, T. Hashimoto. "A phase diagram for the binary blends of nearly
symmetric diblock copolymers. 1. Parameter space of molecular weight ratio and
blend composition." Macromolecules, 34(18), 6495-6505 (2001).
[12]
F. Court, T. Hashimoto. "Morphological studies of binary mixtures of block
copolymers. 1. Cosurfactant effects and composition dependence of morphology."
Macromolecules, 34(8), 2536-2545 (2001).
83
[13]
F. Court, D. Yamaguchi, T. Hashimoto. "Morphological studies of binary
mixtures of block copolymers: Temperature dependence of cosurfactant effects."
Macromolecules, 39(7), 2596-2605 (2006).
[14]
F. Court, D. Yamaguchi, T. Hashimoto. "Morphological and scattering studies of
binary mixtures of block copolymers: Cosurfactant effects observed in the
parameter space of temperature, blend composition, and molecular weight ratio."
Macromolecules, 41(13), 4828-4837 (2008).
84
Chapter 5
Liquid Crystalline Side Chain Block
Copolymer Nanocomposites
This chapter explores the behavior of composites prepared by blending gold
nanoparticles with a liquid crystalline side chain block copolymer (LCBCP). This work
was done in cooperation with Eric Verploegen from the labs of Prof. Paula Hammond at
MIT, who synthesized and characterized the neat LCBCP used in the experiments
described here. Previous studies on block copolymer nanocomposites have demonstrated
the ability to control the spatial distribution of nanoparticles in the block copolymer
matrix by an appropriate choice of nanoparticle size and chemical functionality with
respect to that of the block copolymer chemistry and domain spacing.1-11 Specifically,
nanoparticles could be preferentially sequestered in one of the microphase separated
domains of the block copolymer by stabilizing the nanoparticles with a ligand having
favorable enthalpic interactions with the selected domain. Furthermore, the nanoparticles
could be targeted to a specific location within the block copolymer domain depending on
the size, in addition to the chemistry, of the nanoparticle. That is, the nanoparticles could
be homogeneously distributed in the domain, segregate to the IMDS between the
domains, or lie in the center of the targeted domain, as was described in detail in the
Chapter 1 (Section 1.5). Beyond the initial control of the nanoparticle spatial distribution
within the nanocomposite, to our knowledge, the changing of particle location in situ has
not currently been reported, and is the motivation behind the work reported in this
chapter.
85
The main aim in this chapter was to investigate the effects on nanocomposite
morphology of blending nanoparticles with a microphase separated block copolymer,
where one of the domains has the potential to itself undergo an internal reorganization. In
this case, the internal reorganization results from the ordering of the liquid crystalline
(LC) side chain into smectic layers below the transition temperature, Tiso = 89°C. We
hypothesize that this sets up the possibility to change the nanoparticle spatial distribution
in the nanocomposite by taking the LCBCP through the LC phase transition, from
smectic to isotropic and vice versa, as depicted schematically in Figure 5.1. To this end, a
series of composites were prepared of a LCBCP with gold nanoparticles, which were
stabilized using various thiol-terminated ligands, and characterized by TEM. In addition
to studying the morphology of the as cast blends, the nanocomposites were processed in
such a way as to elucidate the effect of the order-disorder transition of the LC side chain
on the localization of the nanoparticles. That is, the blends were annealed above the
smectic to isotropic transition temperature (Tiso = 89°C), and then were either quenched
or allowed to cool slowly (< 1°C /min) through the transition temperature, to allow the
onset of the LC side chain ordering to influence the spatial location of the nanoparticles.
Figure 5.1. Schematic demonstrating the hypothesis of using a liquid crystal phase transition to drive
nanoparticle location in a block copolymer nanocomposite.
86
5.1 Results and Discussion
The LCBCP used, poly(styrene-b-vinylmethylsiloxane) (PS-PVMS), described in
detail in Chapter 2 (Section 2.1.2), has a morphology of poorly hexagonally packed,
worm-like PS cylinders, with a diameter d ~ 45 nm, in a PVMS matrix, shown in Figure
5.2. The PVMS domains contain the LC side chains, which form interdigitated smectic
layers with average layer spacing of 3.4 nm, as determined by small-angle x-ray
scattering (SAXS).12 A series of blends of varying composition were prepared using gold
nanoparticles stabilized with mercaptopropyltrimethoxysilane (MPS), butanethiol
(ButSH), hexanethiol (HexSH), and dodecanethiol (DodSH) ligands. The chemical
structures of the ligands are shown in Figure 5.3. The nanoparticles had an average core
diameter of approximately 3 nm, as determined by TEM (Figure 5.4 – Figure 5.7), and
the nanoparticle details are listed in Table 5.1. Films with nanoparticle loadings of both ~
5% ± 0.5% and ~ 15% ± 1.5% by weight (0.3% ± 0.2% and 1% ± 0.8% by volume,
respectively) were prepared for each of the different surface ligand nanoparticles.
Figure 5.2. Bright field TEM micrograph of the neat, as cast LCBCP showing a poorly hexagonally
packed, worm-like cylindrical morphology of PS cylinders (light domains) in a PVMS matrix (dark
domains). The image is unstained, with the contrast arising from the more electron dense siloxane
groups in the PVMS.
87
Figure 5.3. Chemical structures of the stabilizing ligands used to synthesize the gold nanoparticles.
Figure 5.4. ButSH stabilized gold nanoparticles: TEM micrograph and size distribution histogram.
Figure 5.5. HexSH stabilized gold nanoparticles: TEM micrograph and size distribution histogram.
88
Figure 5.6. DodSH stabilized gold nanoparticles: TEM micrograph and size distribution histogram.
Figure 5.7. MPS stabilized gold nanoparticles: TEM micrograph and size distribution histogram.
Ligand
dcore [nm] a
tcorona [nm] b
deffective [nm] c
MPS
3.62 ± 0.95
0.74
5.10 ± 0.95
ButSH
3.31 ± 0.79
0.52
4.35 ± 0.79
HexSH
3.04 ± 0.86
0.77
4.58 ± 0.86
DodSH
3.30 ± 0.74
1.52
6.34 ± 0.74
Table 5.1. Size characteristics of the nanoparticles. a dcore is the average value of more than 200
measured nanoparticles and the error is the standard deviation. b tcorona is the value reported for the
ligand length drawn in the Chem3D Pro software from CambridgeSoft. c deffective = dcore + 2tcorona.
89
In general, the TEM analysis reveals that in most of the nanocomposites the
nanoparticles aggregate and macrophase separate from the block copolymer matrix, with
the exception being the composites with the ButSH ligand (Figure 5.8 – Figure 5.11). It
should be noted here, however, that nanoparticles with core sizes less than ~ 2 nm could
not be resolved in the TEM images of the nanocomposites at the magnifications depicted
in the figures. At higher magnifications, loss of contrast does not allow for the distinction
of small nanoparticles from speckles arising from phase variations in the TEM image.13
Nonetheless, large clusters of the visible nanoparticles (core size > 2 nm) randomly
distributed throughout the block copolymer matrix indicate that the incorporation of these
nanoparticles is entropically and/or enthalpically unfavorable in the case of nanoparticles
stabilized with MPS, HexSH, or DodSH. Furthermore, there is no apparent effect of the
thermal processing history on the morphology of the composites. A representative
comparison
of
the
variously
processed
composites
containing
ButSH-coated
nanoparticles indicates that these nanoparticles always reside in the PS domains (Figure
5.12), regardless of whether the films were simply solvent cast at room temperature,
annealed at 140°C and quenched, or annealed at 140°C and cooled slowly (< 1°C/min)
through Tiso. The only noticeable difference in the images being the size of the
nanoparticles in the annealed films, apparently as a result of coarsening at the elevated
temperature (140°C) used during the anneal, and is supported by a comparison of the
particle size distribution of the as cast ButSH-containing LCBCP nanocomposites with
the quenched and slow cooled nanocomposite films (Figure 5.13 and Table 5.2). The fact
that the observed morphology remains unchanged as a result of the thermal treatment
suggests that the final morphology is largely determined at the time of solvent casting,
90
with the nanoparticles being sequestered in the PS domains, since the annealing
temperature is above the glass transition temperature of both blocks of the LCBCP, as
well as above the LC side chain smectic-isotropic transition.
Figure 5.8. Bright field TEM micrographs of LCBCP composites as cast from toluene with 15% wt
MPS-functionalized gold nanoparticles. The nanoparticles have aggregated, creating a poorly
dispersed composite. The two images are of the same sample at different magnifications.
91
Figure 5.9. Bright field TEM micrographs of annealed and slow cooled LCBCP composites cast from
toluene with 15% wt DodSH-functionalized gold nanoparticles. The nanoparticles are again
aggregated, creating a poorly dispersed composite. The two images are of the same sample at
different magnifications.
92
Figure 5.10. Bright field TEM micrographs of LCBCP composites as cast from chloroform with 5%
wt HexSH-functionalized gold nanoparticles. The nanoparticles are mainly aggregated, but the
higher magnification image on the right appears to show that the nanoparticles tend to reside near
the interfaces of the two domains. The two images are of the same sample at different magnifications.
93
Figure 5.11. Bright field TEM micrographs of annealed and quenched LCBCP composites with 5%
wt ButSH-functionalized gold nanoparticles. In these films, the nanoparticles are found to be well
dispersed in the PS domain: (a) cast from toluene, (b) cast from THF.
94
Figure 5.12. Bright field TEM micrographs of the LCBCP composites containing 5% wt gold
nanoparticles initially cast from toluene: (a) as cast film, (b) annealed and quenched film, (c)
annealed and slow cooled film. All films show the nanoparticles preferentially sequestered in the PS
(light) domains. The two annealed films, (b) and (c), appear to show coarsening of the gold
nanoparticles.
95
(a)
Normalized Frequency
1
0.9
5% ButSH - As Cast
0.8
5% ButSH - Quench
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
Diameter [nm]
(b)
Normalized Frequency
1
0.9
5% ButSH - As Cast
0.8
5% ButSH - Slow Cool
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
Diameter [nm]
Figure 5.13. Nanoparticle size distribution comparison for LCBCP nanocomposites originally cast
from THF and containing 5% ButSH functionalized gold nanoparticles: (a) comparison of the as cast
composite with the annealed and quenched composite, (b) comparison of the as cast composite with
the annealed and slow cooled composite. The nanoparticle size distributions were determined from
TEM micrographs using the ImageJ image analysis software with a grayscale threshold level of 100125. As mentioned in the text, nanoparticles with diameters less than 2 nm could not be resolved in
the TEM images, and as a result the histogram is truncated at this level. Even so, “false particles” are
evidently counted even in the 2.5 nm bin. Nevertheless, an increase in particle size is clear from the
histogram, and reflected in the calculated average nanoparticle diameter (Table 5.2).
96
Composite
Nanoparticle Diameter
p Value
5% ButSH – As Cast
2.56 ± 0.84
–
5% ButSH – Anneal/Quench
3.06 ± 1.47
< 0.01
5% ButSH – Anneal/Slow Cool
3.17 ± 1.49
< 0.01
Table 5.2. Average nanoparticle diameter comparison between the three differently processed
LCBCP nanocomposites originally cast from THF with 5% ButSH stabilized gold nanoparticles. The
p value was determined from a student t test on the distributions.
Initially, it might be assumed that the MPS ligand would provide a favorable
interaction with the LC domain of the LCBCP, as it would present siloxane groups on the
surface of the nanoparticles. These in turn would have a neutral or favorable interaction
with the siloxane backbone of the PVMS domain. The actual TEM images of the
nanocomposites, however, tell a different story, and it is evident that the nanoparticles are
incompatible with the LC domain. On closer examination of the chemistry of the block
copolymer, and in particular the chemistry of the LC mesogen, it is clear that the
chemical functionality accessible to the nanoparticle is not the siloxane backbone of the
PVMS, since it is 100% functionalized with the LC mesogens. In fact, it is the butane end
groups that interact with the nanoparticle (Figure 5.14).
Figure 5.14. Schematic showing the chemical architecture of the PS-PVMS LCBCP, indicating that
the PVMS polymer backbone is "screened" by the LC side chains. The ligands on the nanoparticles
interact with the alkane terminus of the LC side chain.
97
The block copolymer nanocomposites containing the two longer chain ligands,
DodSH (Figure 5.9) and HexSH (Figure 5.10), show behavior similar to those containing
the MPS ligand (Figure 5.8), with mainly large macrophase separated clusters of
nanoparticles in the film. It should be noted, that in the case of the HexSH-coated
nanoparticles, there are regions where these nanoparticles appear to localize near the
interfaces between the PS and PVMS domains. This suggests that the size and chemistry
of these nanoparticles puts them in an intermediate state of the phase behavior in this
particular composite system. That is, the nanoparticles are incompatible with both
domains of the block copolymer, but the enthalpic and entropic interactions are such that
not all the nanoparticles macrophase separate.
On the other hand, the nanocomposites prepared with the ButSH nanoparticles
show a miscible morphology with well dispersed nanoparticles. Intriguingly, however,
the nanoparticles are homogeneously distributed in the PS domain, and excluded from the
PVMS domain, opposite to the originally hypothesis (Figure 5.11). The interesting nature
of this behavior is further enhanced when films of the SI450 diblock copolymer are
prepared using the ButSH nanoparticles. In this case, the nanoparticles segregate into the
PI domain, as expected, and not into the PS domain as is the case in the LCBCP
nanocomposite (Figure 5.15). Although the affinity of the nanoparticles to a particular
domain of a block copolymer matrix is determined by the relative interaction of the
particles with the respective block copolymer domains (i.e. χAP vs. χBP), the curious
exclusion of the ButSH nanoparticles from the LC domain into an “unfavorable” domain
appears to hint at a contribution from an entropic effect. Although it is possible that the
PS/ButSH enthalpic interaction is more favorable than the PVMS/ButSH interaction, this
98
seems unlikely in light of the chemistry of the LC mesogen, which possesses an alkane
tail end, and the fact that the ButSH nanoparticles, having similar chemistry to the PI
backbone, do indeed sequester in this domain in the presence of a PS domain. More
likely is the possibility that the ButSH ligand density on the nanoparticle is low and part
of the gold surface is exposed, which can have a favorable interaction with the PS chains.
However, the fact that in the presence of PI the ButSH nanoparticles sequester
preferentially in the PI domain rather than the PS domain, indicates that the gold-PS
interaction is secondary to the ButSH-PS interaction.
Figure 5.15. Bright field TEM micrograph of a SI450 composite as cast from toluene with 5% wt
ButSH-stabilized gold nanoparticles. The nanoparticles are seen to be preferentially dispersed in the
PI domains (dark) in this OsO4-stained image. The light PS domains are free of nanoparticles.
99
Since it was indicated earlier that the morphology of the nanocomposite was
largely determined at the time of solvent casting, the issue of whether use of a
preferential solvent was causing the segregation of the ButSH NPs to the PS domains was
evaluated. Though the films were originally cast from toluene, which is a good solvent
for PS, a subsequent study with other solvents of varying selectivity was carried out. The
quality of a solvent for a particular polymer can be determined from a comparison of the
solubility parameters, δ, of the solvent and polymer. The enthalpy of mixing, ∆Hm, can be
expressed in terms of the solubility parameters as
∆H m
2
= (δ1 − δ 2 ) ϕ1ϕ 2 .14 In general, for
V
the free energy of mixing to be less than zero, the difference in solubility parameters
needs to be as small as possible. Therefore, the smaller the difference in solubility
parameter between the polymer and the solvent, the more selective the solvent toward the
polymer, or alternatively, the more soluble the polymer is in the solvent. The solubility
parameter “map” of the various components of the block copolymer is shown in (Figure
5.16). The values of the solubility parameter for PS and PDMS were obtained from
reference 14, and references 15 and 16, respectively. The solubility parameter of the LC
side-chain PVMS domain was computed using the group contribution method of van
Krevelen17 (see Appendix). From this chart, it is obvious that toluene is a selective
solvent for the PS domain, and hence could potentially be responsible for the observed
morphology. Nonetheless, films cast from chloroform and dichloromethane, a neutral and
PVMS-selective solvent, respectively, exhibit an equivalent morphology to the films cast
from toluene and THF (Figure 5.17). It is clear then, that solvent selectivity can be ruled
out as a driving force for this morphology.
100
LC-PDMS
20 Dichloromethane (19.8)
19 Chloroform (19.0)
Polymer
δ
(MPa1/2)
Tetrahydrofuran (18.6)
PS
PDMS
15.3
PS
18.4
LC(PDMS)
20.1*
18
17
Toluene (18.2)
Cyclohexane (16.8)
* Calculated from group contribution theory
16
PDMS
Heptane (15.1)
15 Triethylamine (15.1)
Figure 5.16. Solubility parameter values for the LCBCP and solvents used in composite preparation.
A likely explanation is that the smectic LC structure in the PVMS domain is the
determining factor in the localization of the nanoparticles, because the free energy
penalty for accommodating large defects in the layering of the LC side-chain mesogens is
high (Figure 5.18). In other words, the bending energy of the LC smectic domain upon
introduction of the nanoparticles, is much higher than the initial unfavorable interactions
between the ButSH ligands and the PS chains. The strong exclusion of the nanoparticles
from the LC domain is further aided by the interdigitated arrangement of the mesogens.12
Not only would the nanoparticles cause large bending energies if included within the
smectic layers, but pushing the interdigitated mesogens apart likely incurs an enthalpic
penalty from the favorable interactions resulting from expected pi-stacking of the
mesogens. In effect, the LC ordering is very highly favored, and resists any inclusions
which would disrupt the smectic layering.
101
Figure 5.17. Bright field TEM micrographs of LCBCP composites as cast with 5% wt ButSHfunctionalized gold nanoparticles. In these films, the nanoparticles are again found to be well
dispersed in the PS (light) domains: (a) cast from chloroform, (b) cast from dichloromethane.
102
Figure 5.18. Schematic showing the disruption of the LC side chain smectic layering as a result of
introducing a nanoparticle of comparable size into the ordered domains.
The introduction of defects into LC ordering by colloidal particles is well known,
and the mutual interaction of the defects can lead to organization of the colloidal
particles.18-20 In these cases however, the difference in size between the colloidal particles
and the LC mesogen was larger (at least an order of magnitude), which is different from
the present case, where the nanoparticles are of the same size as the LC mesogen and
smectic layer spacing. Only a few studies have reported on similar systems, where the
nanoparticle size is on the order of the LC domain size, and the reported results were not
very conclusive. Martinez-Miranda et al. mixed magnetic nanoparticles with a smectic-A
LC, and found subtle differences in phase behavior under a magnetic field, depending on
the surface coating of the nanoparticles.21 Nevertheless, a detailed morphology was not
proposed and it remains unclear what kind of structural effects were present. Shandryuk
et al. blended trioctylphosphine-coated CdSe quantum dots with a smectic-CA LC sidechain polymer and proposed a layered structure of the resulting composite. Although
103
their microscopy data did not show a long range, stacked morphology, local alignment of
the LC polymer could be possible and was suggested by the scattering data.22
Here, taken together, the data indicate the following proposed mechanism for the
formation of the nanocomposite morphology. During the casting process, as the solvent
evaporates, in the initially homogeneous LCBCP/nanoparticle blend, at some critical
solvent concentration, the LC side chains will begin to order into the smectic phase.
Whether this occurs before or after the critical solvent concentration for block copolymer
microphase separation is reached is not important, as long as the distribution of the
nanoparticles remains homogeneous and their mobility is unhindered. Presumably, the
LC phase would begin to form after microphase separation of the block copolymer, as
this prior phase transition would increase the local concentration of LC side chains. As
the LC phase begins to form, the free energy penalty of accepting large distortions in the
smectic layering due to the presence of the nanoparticles becomes too large, and the
nanoparticles are excluded from the LC domains. At this point, the nanoparticles can
either be incorporated into the PS domains, be restricted to the interface between the PS
and PVMS domains, or macrophase separate. In the case of the ButSH-coated
nanoparticles, the suspected small favorable enthalpic interaction between the gold
surface and the PS chains, outweighs the unfavorable ButSH/PS interaction and the
entropic penalty of confining the nanoparticles to the interface. As a result, the ButSHstabilized nanoparticles are homogeneously distributed in the PS domains. In the case of
the HexSH-coated nanoparticles, it is assumed the gold surface is inaccessible to the PS
chains, hence the unfavorable HexSH/PS interactions prevent the nanoparticles from
sequestering in the PS domains. The particles are small enough that some are able to
104
localize at the IMDS, although many are found to macrophase separate in clusters. Both
the DodSH and MPS nanoparticles macrophase separate, the former being incompatible
with the PS chains and too big for the interface, while the latter are simply incompatible
with both blocks of the LCBCP.
Although the mechanism proposed above is a plausible explanation for the
observed nanocomposite morphologies, it should be noted that the morphology
development in this system is a complex process and sensitive not only to the individual
interactions between the components, but also the processing conditions. As mentioned
previously, the affinity of the nanoparticles to a particular domain of the block copolymer
matrix is determined by the relative interaction of the particles with the respective block
copolymer domains, and this enthalpic interaction could be influencing the localization of
the nanoparticles, in addition to the LC ordering. Which of these mechanisms is dominant
in determining the final morphology is an interesting topic for future study. Furthermore,
it has been mentioned that the morphology is largely determined during solvent casting,
indicating that the processing conditions are key factors influencing the microstructure
formation and worthy of additional investigation. In fact, a qualitative observation of
nanoparticles in a nematic LC matrix demonstrated that the macroscopic structure of the
resulting films was markedly different. Solvent cast films showed a macrophase
separated morphology with large beads of nanoparticles evident, whereas films that had
been subsequently heated above the nematic-isotropic transition temperature and allowed
to cool to room temperature showed evidence of homogeneously dispersed nanoparticles.
105
5.2 Conclusion
A series of blends of a LCBCP with gold nanoparticles were studied to
understand the nature of microphase formation in such composites and to evaluate the
possibility of modifying the morphology by inducing a temperature-dependent phase
transition. The results indicated that the LC ordering of the PVMS side chains was the
driving force behind the observed morphologies, whereby the nanoparticles were
excluded from the smectic domains. This was presumed to arise due to the high free
energy penalty associated with the disruption of the mesogen packing and the smectic
layering in the LC side chain PVMS domain. The localization of the nanoparticles
outside the PVMS domains depended on the nature of the nanoparticle size and surface
chemistry. Smaller nanoparticles with weak favorable interactions were found in the PS
domains. The larger the nanoparticle, and the more incompatible the surface coating, the
more strongly the nanoparticle was excluded from the PS domain, resulting eventually in
a macrophase separated morphology. This demonstrates the various levels of control over
the morphology of block copolymer naocomposites. Although both the size and the
chemistry of the nanoparticles with respect to the block copolymer are important in
determining the entropic and enthalpic interaction in the composite, just as important is
the nature of the interactions within the block copolymer domains, as well as the
processing conditions used for the nanocomposite preparation. In the system described
here, the internal interactions arose from the LC side chains, but other interactions, for
example electrostatic or hydrogen bonding, could potentially be used as another set of
tools to tailor and tune the morphology of block copolymer nanocomposites.
106
5.3 References
[1]
J. Huh, V. V. Ginzburg, A. C. Balazs. "Thermodynamic behavior of
particle/diblock copolymer mixtures: Simulation and theory." Macromolecules,
33(21), 8085-8096 (2000).
[2]
R. B. Thompson, V. V. Ginzburg, M. W. Matsen, A. C. Balazs. "Predicting the
mesophases of copolymer-nanoparticle composites." Science, 292(5526), 24692472 (2001).
[3]
J. Y. Lee, R. B. Thompson, D. Jasnow, A. C. Balazs. "Effect of nanoscopic
particles on the mesophase structure of diblock copolymers." Macromolecules,
35(13), 4855-4858 (2002).
[4]
G. A. Buxton, J. Y. Lee, A. C. Balazs. "Computer simulation of morphologies and
optical properties of filled diblock copolymers." Macromolecules, 36(25), 96319637 (2003).
[5]
S. W. Sides, B. J. Kim, E. J. Kramer, G. H. Fredrickson. "Hybrid particle-field
simulations of polymer nanocomposites." Physical Review Letters, 96(25)(2006).
[6]
J. J. Chiu, B. J. Kim, E. J. Kramer, D. J. Pine. "Control of nanoparticle location in
block copolymers." Journal of the American Chemical Society, 127(14), 50365037 (2005).
[7]
B. J. Kim, J. Bang, C. J. Hawker, J. J. Chiu, D. J. Pine, S. G. Jang, S. M. Yang, E.
J. Kramer. "Creating surfactant nanoparticles for block copolymer composites
through surface chemistry." Langmuir, 23(25), 12693-12703 (2007).
[8]
B. J. Kim, J. Bang, C. J. Hawker, E. J. Kramer. "Effect of areal chain density on
the location of polymer-modified gold nanoparticles in a block copolymer
template." Macromolecules, 39(12), 4108-4114 (2006).
[9]
B. J. Kim, G. H. Fredrickson, E. J. Kramer. "Effect of polymer ligand molecular
weight on polymer-coated nanoparticle location in block copolymers."
Macromolecules, 41(2), 436-447 (2008).
[10]
M. Bockstaller, R. Kolb, E. L. Thomas. "Metallodielectric photonic crystals based
on diblock copolymers." Advanced Materials, 13(23), 1783-1786 (2001).
[11]
M. R. Bockstaller, Y. Lapetnikov, S. Margel, E. L. Thomas. "Size-selective
organization of enthalpic compatibilized nanocrystals in ternary block
copolymer/particle mixtures." Journal of the American Chemical Society,
125(18), 5276-5277 (2003).
[12]
E. Verploegen, T. Zhang, N. Murlo, P. T. Hammond. "Influence of variations in
liquid-crystalline content upon the self-assembly behavior of siloxane-based block
copolymers." Soft Matter, 4(6), 1279-1287 (2008).
[13]
E. J. Roche, E. L. Thomas. "Defocus electron microscopy of multiphase
polymers: use and misuse." Polymer, 22(3), 333-341 (1981).
107
[14]
J. Brandrup, E. H. Immergut, eds., Polymer Handbook, 3rd ed. (Wiley
Interscience, New York, 1989).
[15]
E. E. Hamurcu, B. M. Baysal. "Solubility Parameter of a Poly(Dimethylsiloxane)
Network." Journal of Polymer Science Part B-Polymer Physics, 32(3), 591-594
(1994).
[16]
M. Roth. "Solubility Parameter of Poly(Dimethyl Siloxane) as a Function of
Temperature and Chain-Length." Journal of Polymer Science Part B-Polymer
Physics, 28(13), 2715-2719 (1990).
[17]
D. W. van Krevelen. "Chapter 7: Cohesive Properties and Solubility," in
Properties of Polymers: Their Estimation and Correlation with Chemical
Structure, 2nd ed. (Elsevier Scientific Publishing Company, New York, 1976),
pp. 129-159.
[18]
T. Hegmann, H. Qi, V. M. Marx. "Nanoparticles in liquid crystals: Synthesis,
self-assembly, defect formation and potential applications." Journal of Inorganic
and Organometallic Polymers and Materials, 17(3), 483-508 (2007).
[19]
P. Poulin. "Novel phases and colloidal assemblies in liquid crystals." Current
Opinion in Colloid & Interface Science, 4(1), 66-71 (1999).
[20]
M. Adams, Z. Dogic, S. L. Keller, S. Fraden. "Entropically driven microphase
transitions in mixtures of colloidal rods and spheres." Nature, 393(6683), 349-352
(1998).
[21]
L. J. Martinez-Miranda, K. McCarthy, L. K. Kurihara, J. J. Harry, A. Noel.
"Effect of the surface coating on the magnetic nanoparticle smectic-A liquid
crystal interaction." Applied Physics Letters, 89(16)(2006).
[22]
G. A. Shandryuk, E. V. Matukhina, R. B. Vasil'ev, A. Rebrov, G. N. Bondarenko,
A. S. Merekalov, A. M. Gas'kov, R. V. Talroze. "Effect of H-bonded liquid
crystal polymers on CdSe quantum dot alignment within nanocomposite."
Macromolecules, 41(6), 2178-2185 (2008).
108
Chapter 6
Directions for Future Study
This chapter will outline several suggested research directions that would extend
and build upon the results reported in the present work. A number of interesting questions
and ideas worthy of further investigation arose naturally out of the work reported in this
thesis. The suggested studies described in this chapter represent novel applications
inspired by the current work, as well interesting unanswered questions posed by the
obtained results, which could lead to deeper insights into the nature of the systems
described. In particular, all of the work contained in this thesis was concerned with bulk
systems, in order to exclude the effects of surfaces and confinement, on the interpretation
of the observed morphological behavior. It would, however, be very interesting to study
the influence of surfaces and confinement on the behavior of the systems reported here
and this is described in Section 6.1. In the following section, variations on block
copolymer nanocomposites are explored. Section 6.2.1 deals with using non-traditional
biological nanoparticles to prepare block copolymer nanocomposites. The nanoparticles
are rod-like tobacco mosaic virus, which can be easily functionalized with metal
nanoparticles to potentially create composite materials with interesting properties. In
section 6.2.2, on the other hand, we propose to use recently developed block copolymer
gels in conjunction with gold nanoparticles in an attempt to create tunable plasmonic
devices.
109
6.1 Block Copolymer Blends in Confined Geometry
As has been outlined in this thesis, numerous studies have addressed the question
of the behavior of binary blends of block copolymers in the bulk state, of which this work
is one contribution.1-17 On the other hand, very few studies have been dedicated to block
copolymer blends in thin films, or other confined geometries such as fibers.18-22 Out of
these studies, none have looked at binary block copolymer blends where the molecular
weight ratio, R, was greater than 5, i.e. where macrophase separation is expected to occur.
The main idea behind the study of these systems in confined geometries arises
from the unique behavior of block copolymers under confinement. Russell et al.23, 24 and
Ma et al.,25 have shown that block copolymers confined to cylindrical geometries, where
the radius of the cylinder is on the order of a few repeat units of the underlying neat block
copolymer morphology, exhibit novel morphologies that are influenced by the
confinement. In addition, the “bulk” behavior as well as the microstructure of block
copolymer thin films is influenced by the ratio of the underlying block copolymer domain
spacing to the thickness of the film.26 The former behavior manifests itself in terracing
and islands on the surface of films when the native domain spacing of the block
copolymer is incommensurate with the thickness of the film. The latter behavior is
displayed in preferential alignment of the block copolymer microdomains, as well as
changes in the crystallographic packing of the morphology (i.e. from FCC to BCC),
arising from entropic confinement effects and surface energy effects due to the substrate
and free surfaces. As such, the behavior of the bulk systems described in this thesis,
specifically the morphologies observed, could be vastly different in a thin film or fiber
geometry.
110
It is known, that polymer blends in thin films can undergo confinement-induced
miscibility.27, 28 This hints at the possibility of obtaining a single microphase separated
morphology with the blends utilized in this thesis. Whereas in the bulk, nearly all the
blends investigated here showed macrophase separation, it is conceivable that in a thin
film geometry, these same blend compositions could exhibit a single microphase
separated morphology induced by confinement and surface effects. That this is attainable
is suggested by some self-consistent mean field theory (SCFT) modeling performed on
the blends used in this system. The blends were modeled using the SCFT formulation of
Fredrickson,29 on a two dimensional, 128 x 128 lattice, and discretized such that each
side is equivalent to 6 times the radius of gyration (Rg) of the long diblock copolymer.
Since in the formulation of the model, the evaluation of the fields and densities was done
with respect to the size of the longer diblock copolymer, high χN value (250 < χN < 745,
depending on the degree of polymerization of the diblock) were used in order to ensure
that the triblock copolymer would phase separate (i.e. (χN)triblock > 10.5). These and other
modeling parameters are outlined in Table 6.1. The density distribution plots of the block
copolymer chains are shown in Figure 6.1 - Figure 6.5 (further details of the model and
the code utilized can be found in the Appendix).
Simulated
Blend
SI450
Ndiblock
Ntriblock
fdiblock
ftriblock
1/R
χN
ntriblock
287
41
0.469
0.400
0.1399
250
0.50
SI700
463
41
0.489
0.400
0.0866
405
0.50
SI1000
601
41
0.440
0.400
0.0667
525
0.50
SI1500
853
41
0.430
0.400
0.0469
745
0.50
Table 6.1. Modeling parameters used in the SCFT simulation, describing the characteristics of the
polymers. The values were chosen to be comparable to the molecular characteristics of the polymers
used in the blend experiments described in Chapter 3.
111
dbk
tbk
1
1
0.5
0.5
0
0
dbk A
tbk A
1
1
0.5
0.5
0
0
Figure 6.1. Density distribution plots for the SI450 blends simulation – dbk refers to the density of the
diblock and tbk refers to the density of the triblock. “A” refers to the density distribution of the A
block of the block copolymer, which in these simulations corresponds to the PS domains.
dbk
tbk
1
1
0.5
0.5
0
0
dbk A
tbk A
1
1
0.5
0.5
0
0
Figure 6.2. Density distribution plots for the SI700 blend simulation – dbk refers to the density of the
diblock and tbk refers to the density of the triblock. “A” refers to the density distribution of the A
block of the block copolymer, which in these simulations corresponds to the PS domains.
112
dbk
tbk
1
1
0.5
0.5
0
0
dbk A
tbk A
1
1
0.5
0.5
0
0
Figure 6.3. Density distribution plots for the SI1000 blends simulation – dbk refers to the density of
the diblock and tbk refers to the density of the triblock. “A” refers to the density distribution of the A
block of the block copolymer, which in these simulations corresponds to the PS domains.
dbk
tbk
1
1
0.5
0.5
0
0
dbk A
tbk A
1
1
0.5
0.5
0
0
Figure 6.4. Density distribution plots for the SI1500 blend simulation – dbk refers to the density of
the diblock and tbk refers to the density of the triblock. “A” refers to the density distribution of the A
block of the block copolymer, which in these simulations corresponds to the PS domains.
113
dbk
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Density line profile
Density line profile
1
1
dbk-A
dbk-B
tbk -A
tbk -B
dbk-A
dbk-B
0.9
0.9
tbk-A
0.8
0.8
tbk-B
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
16
32
48
64
80
96
112
0
128
0
16
32
48
64
80
96
112
128
Figure 6.5. Density distribution plot with line profiles for the SI450 blends simulation. The image at
top displays the density distribution profile of the diblock and the lines indicate the profile locations.
The line profiles indicate that the triblock preferentially segregates to the IMDS and that the large
“pool” of triblock is not microphase separated.
The similar appearance of the phase separated density distribution arises from the
identical initial conditions used (the random number generator was not independently
seeded for each of the runs), but is not expected to have an effect on the type of
equilibrium morphology obtained (e.g. cylinders or lamellae). Two things are evident
from the density distribution profiles: (1) all the blends investigated show non-lamellar
morphologies, and (2) there is only a very small region of macrophase separated triblock
copolymer, which itself is not microphase separated. The appearance of non-lamellar
morphologies in all the blends can be interpreted in the context of the BZL strong
segregation theory modeling of Chapter 4. There, it was shown that all the blends, if they
were molecularly mixed, would exhibit the cylinder morphology in a narrow composition
114
range. Although the composition used in the SCFT does not correspond to the
composition window deduced from the BZL model, in the latter macrophase separation
was not allowed, whereas in the former some macrophase separation is observed, which
could explain the appearance of the cylindrical domain in a different composition
window. Additionally, the SCFT modeling makes use of an actual triblock copolymer
description, where the mid-block cannot “separate” and must form bridges or loops,
rather than modeling the triblock as a diblock of half the molecular weight.
The existence of the small macrophase separated region, which does not
microphase separate, is surmised to arise from the small simulation size, with the
simulation “box” being just 6Rg of the large diblock in length and width. The resulting
boundary conditions create a situation where the native equilibrium block copolymer
domain spacing cannot be accommodated without large entropic penalties and so the
block copolymer remains in a homogeneously mixed state. This suggests that
confinement of the block copolymer blends in a geometry that is less than 6Rg in linear
dimension, such as in an ultra-thin film or a microscale electrospun fiber, could induce
miscibility. As a result, the blends investigated here in bulk, with large molecular weight
ratios, R > 15, may be able to form single microphase separated morphologies in thin
films. The benefit of this observation is that in this manner it is possible to overcome two
competing effects. Namely, that curved IMDS morphologies are observed at higher R
values, but at the same time higher R values lead to macrophase separation. In thin films,
it should be possible to achieve high R values, with the concomitant curved IMDS
morphologies, in a miscible blend.
115
There are several applications that could benefit from thin film morphologies with
curved IMDS morphologies, in particular, morphologies that are bicontinuous. Block
copolymer blend thin films with bicontinuous morphology could be used to make
filtration or separation membranes. They could be used in such applications as water
purification and/or desalination, fuel cells, or battery technology. Furthermore,
bicontinuous thin films, of appropriately chosen chemistry, could be used in photovoltaic
cells, providing intimate high surface area contacts between hole and electron
transporting domains.
6.2 Block Copolymer Gel and Nanoparticle Composites
Recently developed highly swellable gels, based on poly(styrene-b-2vinylpyridine) PS-P2VP block copolymers,30 are an attractive platform for the
incorporation of nanoscale particles to augment their properties and usefulness. The gels
respond to a wide range of stimuli, including humidity, ionic strength, pH, and
temperature. The defining characteristic of the gels, is that it is possible to swell one of
the domains (poly(2-vinylpyridine) (P2VP)) without swelling the other (poly(styrene)
(PS)), either by chemical modification of the P2VP domain or judicious selection of
solvent, thereby constraining the gel to swell only in one direction. This leads to large
uniaxial swelling of more than 1000%. The gels were developed in the context of optical
devices, and the uniaxial swelling along with appropriate selection of molecular
characteristics of the block copolymer and stimuli, allowed for the tuning of the
reflectivity of the gels in the entire visible range of the spectrum. This tunability and
flexibility in using various external stimuli serves as an invitation to enhancing the
properties of these gels by incorporating nanoparticles. Two different ideas were initially
116
explored: (1) addition of biological nanoparticles, in this case tobacco mosaic virus
(TMV), to the gels, used as “carriers” of functional materials, and (2) addition of
standard, oligomer-stabilized, gold nanoparticles in an effort to make tunable plasmonic
devices.
6.2.1
Block Copolymer Gel and TMV Composites
The main motivation behind this research direction, is the unique properties of
TMV and the fact that the gels can be used in an aqueous environment. TMV is a high
aspect ratio, rod-like, cylindrical virus, approximately 300 nm in length and 18 nm in
diameter, it is monodisperse in both its shape and size, and possesses numerous
functional groups on its exterior and interior, offering many opportunities for precise
control and tailoring of the nanoparticle properties (Figure 6.6).31 The drawback of using
a biological nanoparticle, however, is the limitation of working in an aqueous
environment, which is why the use of the amphiphilic PS-P2VP swellable gels is
essential.
Figure 6.6. Tobacco mosaic virus: (a) TEM micrograph of a single virus particle, reproduced from
reference 32, (b) schematic of TMV structure reproduced from reference 31.
117
As a result of its monodisperse size and shape, along with its large aspect ratio,
TMV forms large well-ordered liquid crystalline arrays when cast from solution (Figure
6.7).33 This property has been harnessed in an attempt to make highly ordered arrays of
the TMV rods using a convective assembly approach.34 The ability to make well-aligned
arrays of molecules would be useful in a wide range of applications, and permits the
engineering of materials with anisotropic properties. Furthermore, the aforementioned
wealth of functional groups on the TMV surfaces, allows for the decoration of the virus
with, for example, metal nanoparticles (Figure 6.8). Using simple reduction chemistry,
not only can the exterior of the TMV be metalized, but also the interior of the cylindrical
channel, which could be exploited to make nanowires of precise geometry.35, 36 As such,
the TMV could be used as a “carrier” to deliver and assemble monodisperse, high aspect
ratio, metal nanoparticles at a specific location in a block copolymer.
Figure 6.7. Liquid crystalline arrangement of TMV on a carbon coated grid. The TMV was cast onto
the grid from a 10% wt aqueous suspension and allowed to dry. The image is unstained.
118
Figure 6.8. TMV decorated with nickel nanoparticles. The nanoparticles were deposited on the
surface of the TMV using a simple reduction reaction of a nickel salt described in reference 36.
In preliminary studies on the feasibility of this approach, unmodified TMV
particles were selectively delivered to the P2VP domains of a symmetric, lammelarforming PS-P2VP block copolymer gel, the characteristics of which are listed in Table
6.2, and whose chemical structure is depicted in Figure 6.9. The block copolymer was
spin cast from a 5% wt/wt solution in PGMEA onto a glass slide (pre-treated with a
silane adhesion promoter), and annealed under chloroform vapor at ~ 40°C overnight.
The film was subsequently exposed to the vapor of a 10% by volume solution of
bromoethane in hexane, at room temperature overnight, in order to quaternize the
pyridine units on the P2VP pendant side groups. This quaternization adds positive
charges along the P2VP chain (shown schematically in Figure 6.10) and makes the P2VP
domain swell in water. These films were then immersed in 10% by weight suspension of
119
TMV in water and left to stand overnight. The aqueous TMV suspension was able to
swell the gel, as evidenced by an observed iridescent red color.
Polymer
PS-P2VP
M nPS
102,000
M nP 2VP
97,000
PDI
1.12
Table 6.2. Molecular characteristics of the block polymer used to make the PS-P2VP/TMV
composites.
Figure 6.9. Chemical structure of PS-P2VP block copolymer.
Figure 6.10. Quaternization of the P2VP block using bromoethane vapor.
TEM analysis of cross-sections of the dried films demonstrates that the swollen
gel allows for the penetration of the TMV rods into the P2VP domains (Figure 6.11). The
cross-sections of the TMV infiltrated gels were obtained using a focused ion beam (FIB)
and were taken in close proximity to (~ 1 µm), and parallel, to the film edge. The thin
sections were then exposed to iodine vapor to preferentially stain the P2VP domains,
which show up dark in the micrographs. Figure 6.11 shows rounded shape particles
inside the P2VP domains, which are apparently TMV rods that have penetrated the
120
domains with the axis of the rod perpendicular to the film edge, as would be anticipated.
TMV rods aligned parallel to the film edge would not be expected to penetrate into the
domains, since they would be blocked, like in a sieve, on the P2VP polymer chains, as
shown schematically in Figure 6.12.
Figure 6.11. TEM micrograph of TMV particles in a dried PS-P2VP block copolymer. The TMV
particles are preferentially localized in the P2VP domains, which appear slightly darker due to
staining with iodine vapor.
Figure 6.12. Modes of infiltration of TMV into swollen P2VP domains. In (a) the TMV axis is
oriented perpendicular to the film edge, allowing the virus to penetrate the “forest” of P2VP chains.
In (b) the TMV axis is oriented parallel to the film edge, and the virus would be “caught” by the
chains thus not allowing for its penetration into the film.
121
It is interesting to note, however, that no evidence of TMV rods was found deeper
into the film. TEM micrographs of film sections taken ~ 1 mm from the film edge were
devoid of the type of particles seen in Figure 6.11. Furthermore, it is presumed that the
TMV can only penetrate the gel film from the edges, and not from the top free surface,
since the PS domains do not swell in water. The reason for the limited penetration of the
TMV into the block copolymer gel could be due to an electrostatic interaction between
the virus and the quaternized P2VP. As a result of quaternization, the P2VP chains have a
series of positive charges along the chain. The TMV, on the other hand, is known to have
a net negative charge in its surface.37 It is conceivable then, that as the TMV penetrates
into the P2VP domains, the electrostatic interactions between the negatively charged
virus and the P2VP chains bind and trap the TMV, preventing the penetration of the virus
particles deeper into the domain. This sort of trapping behavior due to favorable
interactions has been reported in theoretical studies on the exfoliation of clay sheets by
polymers. Balazs et al., showed that when the interaction between a clay sheet surface
and the intercalating polymer is highly attractive, exfoliation is not possible since the
polymer begins to act as a glue holding the individual clay sheets together.38, 39
This initial study demonstrated the feasibility of using a virus nanoparticle as an
additive to a swellable block copolymer gel. Several follow-up investigations could be
carried out to elucidate the nature of the diffusion of the TMV in the gel. To determine
whether electrostatic interactions are the reason for the limited penetration of the TMV,
diffusion studies using various ionic strength solutions or appropriately modified virus
could be done. The possibility of using external fields to aid the infiltration of the virus
into the gel could be investigated. Finally, since the well-defined TMV particles and
122
block copolymer gel are nearly a model system, a systematic study of diffusion times,
could lead to new insights on the diffusion of anisotropic particles in a polymer matrix.
6.2.2
Block Copolymer Gel and Gold Nanoparticle Composites
The idea behind this research is to utilize the tunability of the block copolymer gel
in order to control the optical response of the gold nanoparticles. The general mechanism
is depicted schematically in Figure 6.13, whereby the swelling of the gel changes the
spacing between individual nanoparticles inside the swollen domain. Two requirements
need to be satisfied at the outset; first, the nanoparticles need to be big enough and
adequately monodisperse so as to give a sharp and well-defined plasmon peak, and
second, the surfaces of the nanoparticles need to be appropriately tailored so that they can
be dispersed in one of the block copolymer domains.
Figure 6.13. Schematic of a suggested implementation of a “tunable plasmonic gel”. Gold
nanoparticles are preferentially localized in the swellable domain of a block copolymer gel. The
swelling of the domain leads to a change in the average spacing between nanoparticles and possibly a
shift in the plasmon resonance.
A batch of gold nanoparticles stabilized by a P2VP oligomer was synthesized
using the one-phase reduction method described in Chapter 2. The P2VP ligand had a
123
number average molecular weight of 1300 g/mol, a PDI of 1.08, and was endfunctionalized with a thiol group. The gold nanoparticles had an average core size of
approximately 5 nm and a fairly well-defined surface plasmon in THF at 516 nm (Figure
6.14). These nanoparticles were then used to make nanocomposites with a PS-P2VP
block copolymer, whose molecular parameters are listed in Table 6.3. The films were
prepared by spin casting from a 5% wt/wt solution of the block copolymer in PGMEA,
which contained the appropriate amount of P2VP-stabilized gold nanoparticles to create a
dry composite film having 15% ± 1.5% by weight gold nanoparticles (1% ± 0.8% by
volume). The spin cast composite films were then annealed overnight in chloroform
vapor at ~ 40°C.
Figure 6.14. Characteristics of P2VP-stabilized gold nanoparticles: (a) UV-Vis absorbance spectrum
in THF, (b) TEM micrograph.
Polymer
PS-P2VP
M nPS
57,000
M nP 2VP
57,000
PDI
1.08
Table 6.3. Molecular characteristics of the polymer used to make the P2VP/Au nanoparticle
composites.
124
The optical behavior of the films under swelling with methanol was investigated
through absorbance measurements. The results are shown in Figure 6.15, and indicate
that under the conditions investigated, the effect of the swelling is small. The main effect
appears to be the dilution of the nanoparticles, and the resulting decrease and broadening
in the surface plasmon response, as seen in the diffuse, lower intensity absorbance. It
seems that at this concentration, the nanoparticles are too dilute to show a pronounced
optical effect upon swelling/de-swelling. In addition, TEM reveals that the morphology
of the dried blends is not conducive to the kind of behavior envisioned, since the
nanoparticles align along the interfaces between the PS and P2VP domains (Figure 6.16).
As a result, the spacing between individual nanoparticles is not changing greatly, only the
distance between lines of nanoparticles is changing. However, the initial distance
between the lines is large enough, that the subsequent increase has no effect on the
plasmon response. It should be noted, that these micrographs are taken from films that
have been “actuated”, that is films that have been swollen and de-swollen. Since, the
evaporation of the solvent from the film is fast (< 1 s), it is possible that the nanoparticles
are not moving far from the interface upon swelling with methanol or ethanol. Even if the
nanoparticles did disperse uniformly in the swollen domains, at the concentration used in
this experiment, the average spacing between nanoparticles in the swollen state would
still be on the order of the spacing between the IMDS-segregated lines of nanoparticles in
the dried state, and no effect on the plasmon would be expected.
125
0.1
Dry Film
Swollen (Methanol)
Absorbance
0.08
0.06
0.04
0.02
0
300
400
500
600
700
800
900
Wavelength [nm]
Figure 6.15. UV-Vis absorbance spectrum of the PS-P2VP block copolymer gel with 15% wt gold
nanoparticles.
Figure 6.16. TEM micrograph of a PS-P2VP block copolymer containing 15% wt gold nanoparticles.
The slightly darker regions are P2VP domains preferentially stained with iodine vapor. The
nanoparticles are found to localize at the interface between the PS and P2VP domains.
126
These initial studies indicate the broad range of parameters that need to be
systematically investigated to appropriately design a tunable plasmonic device. It is clear,
that in order to achieve a homogeneous distribution of nanoparticles in one of the
domains, either the particles need to be smaller, or the domains need to be larger. In the
former case, as the nanoparticles get smaller, the characteristic surface plasmon peak
becomes poorly defined and eventually disappears. As such, it is preferable to increase
the size of the block copolymer domains by using polymers of higher molecular weight.
The drawback to using higher molecular weight block copolymers is the difficulty in
obtaining well-ordered lamellar films, which are necessary for good swelling properties.
A much narrower nanoparticle size distribution would also be beneficial in enhancing the
plasmon response of the nanoparticles. Furthermore, a series of concentration studies
would be beneficial to elucidate what is the optimal nanoparticle concentration in the
domains to achieve a noticeable effect in plasmon shift or disappearance. Finally, in this
first investigation, the nanoparticles were targeted to the swellable P2VP domains.
Another interesting study would look at PS-stabilized nanoparticles, targeted to the nonswelling, PS domains of the block copolymer gel.
6.3 Conclusion
The field of block copolymer based nanocomposites provides fertile ground for
numerous studies of fundamental scientific or applied interest. The ability to combine
nanoscale particles that possess unique physical characteristics with a structure directing
block copolymer matrix opens up opportunities for preparing materials with precisely
tailored and optimized physical properties. The work outlined in this thesis has
127
demonstrated the use of blends of block copolymers and block copolymers with liquid
crystal side chains to direct and tune the morphology of the resulting composite materials.
The current chapter suggested several extensions of this work in order to take advantage
of the possibilities presented by the results reported here, which is sure to lead to many
more interesting research directions in the future.
128
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132
Chapter 7
Appendix
7.1 Group Contribution Calculation
The solubility parameter, δ, for the LC side chain containing PVMS domain was
computed using the group contribution method of van Krevelen.1 The solubility
parameter is related to the cohesive energy density by the relation δ 2 =
Ecoh
, where V is
V
the molar volume. According to van Krevelen, the solubility parameter of a given
compound can be estimated by summing the contributions to Ecoh and V of the
component chemical groups making up the compound, i.e. δ 2 =
∑E
∑V
coh
i
. The solubility
i
parameter for the LC-PVMS domain was determined on the basis of the groups and
tabulated values shown below.
Group
Number of Groups
Ecoh [cm3/mol]
V [cm3/mol]
-Si-
3
3390
0
-O-
4
3350
3.8
-CH3
7
4710
33.5
-CH-
1
3430
-1.0
-COO-
2
18000
18.0
-CH2-
8
4940
16.1
phenylene
3
31940
52.4
133
7.2 BZL Strong Segregation Theory Model
The equations listed below are reproduced from the version of the BZL model2-6
modified by Yamaguchi et al.7 The details of the derivation may be found in the articles
cited above. The modified BZL model applies to a binary mixture of AB diblock
copolymers, with N i j being the degree of polymerization of the i (i = A or B) block chain
of the long copolymer (j = l) or short copolymer (j = s). The chain segment unit length is
a, and the polymer stiffness is characterized by the parameter p = A/a, where A is the
Kuhn segment length. The model further makes use of two parameters, namely n and α,
to characterize the composition of the blends and the individual block copolymers,
respectively. The blend composition is given by the number (mole) fraction of the long
diblock, n =
nl
, where nl and ns are the number of long and short chains,
nl + ns
N il − N is
respectively. The composition of the block copolymers is given by α i =
, which
N is
describes the relative difference in the length of the blocks in the copolymer (i = A or B).
In units of kT, the free energy per chain is given by Fx = FS + FA + FB, where FS is the
surface free energy at the inter-material dividing surface (IMDS), and FA and FB are the
conformational free energies of the A and B block chains, respectively. The free energy
per chain, Fx, is derived for both the lamellar and cylinder morphologies (x = C for
cylinder morphology or L for lamellar morphology), and the resulting expressions, after
minimizing with respect to the average interfacial area per chain (i.e. dFx/dσ), are given
below:
Fx =
( ) (PQ )
3
Φ N Bs
2
1
3
1
(1)
3
x
134
P = π 2 4Φ p B
QC (n) =
(2)
p N s 2(4 + 3hAs r )
r2
G (α B , n) + B As
+
2
p A N B (2 + 3hAs r )3
 r
p B N As
α A n 3 
s
pA N B
 r + hAs
 2[4 + 3hAl (r + hAs )]

3
 [2 + hAl (r + hAs )]
QL ( n) = 1 + α B n 3 +
p B N As
1 + α An3
s
pA N B
3
(
)
(3)
(4)
r = 2(1 + α B n)
(5)
hAs
Ns  1 

= −1 + 1 + As 
r
N B  1 + α B n 
(6)
hAl
N As  1 + α A n 
N As  1 



= 1+ s 
− 1 + s 
r
N B  1 + α B n 
N B  1 + α B n 
(7)
 2 2 6u 2 (1 + α B ) + 0.5l 2u (1 − 5α B − 10α B2 ) − 
 u −l 
+ 
2
3
2
0.5l (1 + α B ) − u (6 − α B − 5α B
 

2
G (α B , n) = (1 + α B n )
 − 3l α B n
4
2 2
2
− 0.5l α B (1 + 5α B ) + 0.5l u (−10 + 3α B + 15α B ) − 


2
2
4
2
 
5u (u − l )(1 + α B ) + u (6 − α B − 5α B )
(8)
135
The values of l ≡ H Bs R (see Figure 7.1) and u were determined numerically in Matlab
using the equations:


1 − l 2 (1 − α B2 ) − α B
l (1 − α B )
2


l
=
−
ln
1 + α Bn
1 − α B2
1 − 1 − l 2 (1 − α B2 ) 
(9)
1 − α B 1 − l 2 (1 − α B2 )
u=
1 − α B2
(10)
n
To be applicable to the block copolymer systems studied experimentally in this thesis, A
refers to the PI domains and B refers to the PS domains. The values of the polymer
stiffness, were taken from reference 7, and are pPS = 1.16 and pPI = 1.26, while
ΦpB = 0.5 was chosen for convenience (Equation 2).7 As in reference 7, the simulations
here made use of modified values of the degree of polymerization, that took into account
the asymmetry in segmental volume, i.e. N ij = (v j v0 )N ij where v0 = (v PS v PI ) 2 and j =
1
PS or PI, and the values are vPS = 107.2 cm3/mol and vPI = 81.9 cm3/mol.7
Figure 7.1. Schematic showing the organization of polymer chains in a cylindrical domain of a binary
blend of diblock copolymers.
136
7.3 Self Consistent Field Theory
The code used for the self consistent field theory (SCFT) simulation was
originally written by Dr. Alfredo Alexander-Katz in Fortran-90. It is an implementation
of the SCFT formulated by Fredrickson.8 In its original form, it was used to model the
blends of a diblock copolymer with a homopolymer. This code was modified in order to
be able to model blends of a diblock copolymer with a triblock copolymer. Two key
modifications were made. The first was the addition of a function to compute the density
along the midblock of the triblock copolymer. The second was the expansion of the main
code to compute the propagator, chemical potential, and density of the triblock
copolymer. Other changes included the random seeding of the random number generator
and adding the necessary variables and structures to store the values of the fields and
molecular parameters of the triblock copolymer.
137
7.4 List of Abbreviations
BCP
ButSH
BZL
CNT
DFT
DodSH
FDTD
FIB
HexSH
IMDS
LC
LCBCP
MO
MPS
NMR
P2VP
PDI
PDMS
PEP
PGMEA
PI
PS
PVMS
SAXS
SCFT
SEC
SI
SIS
SSL
TEM
THF
TMV
USAXS
UV-Vis
block copolymer
butanethiol
Birshtein, Zhulina, Lyatskaya
carbon nanotube
density functional theory
dodecanethiol
finite difference time domain
focused ion beam
hexanethiol
inter-material dividing surface
liquid crystal
liquid crystalline side chain block copolymer
membrane osmometry
mercaptopropyltrimethoxysilane
nuclear magnetic resonance
poly(2-vinylpyridine)
polydispersity index
poly(dimethylsiloxane)
poly(ethylene propylene)
propylene glycol monomethyl ether acetate
poly(isoprene)
poly(styrene)
poly(vinylmethylsiloxane)
small-angle x-ray scattering
self-consistent field theory
size exclusion chromatography
styrene-b-isoprene
styrene-b-isoprene-b-styrene
strong segregation limit
transmission electron microscope
tetrahydrofuran
tobacco mosaic virus
ultra-small-angle x-ray scattering
ultra-violet visible
138
7.5 References
[1]
D. W. van Krevelen. "Chapter 7: Cohesive Properties and Solubility," in
Properties of Polymers: Their Estimation and Correlation with Chemical
Structure, 2nd ed. (Elsevier Scientific Publishing Company, New York, 1976),
pp. 129-159.
[2]
T. M. Birshtein, Y. V. Liatskaya, E. B. Zhulina. "Theory of Supermolecular
Structures of Polydisperse Block Copolymers .1. Planar Layers of Grafted
Chains." Polymer, 31(11), 2185-2196 (1990).
[3]
E. B. Zhulina, T. M. Birshtein. "Theory of Supermolecular Structures in
Polydisperse Block Copolymers .2. Lamellar Superstructure Consisting of 2Block Copolymers." Polymer, 32(7), 1299-1308 (1991).
[4]
J. V. Lyatskaya, E. B. Zhulina, T. M. Birshtein. "Theory of Supermolecular
Structures in Polydisperse Block Copolymers .4. Cylindrical Domains in BinaryMixtures of Diblock Copolymers and Cylinder Lamellae Transition." Polymer,
33(2), 343-351 (1992).
[5]
T. M. Birshtein, Y. V. Lyatskaya, E. B. Zhulina. "Theory of Supermolecular
Structures in Polydisperse Block Copolymers .5. New Double Cylindrical
Structure in Binary Mixture of Cylinder-Forming Diblock Copolymers." Polymer,
33(13), 2750-2756 (1992).
[6]
E. B. Zhulina, Y. V. Lyatskaya, T. M. Birshtein. "Theory of Supermolecular
Structures in Polydisperse Block Copolymers .3. Cylindrical Layers of Bidisperse
Chains." Polymer, 33(2), 332-342 (1992).
[7]
D. Yamaguchi, S. Shiratake, T. Hashimoto. "Ordered structure in blends of block
copolymers. 5. Blends of lamella-forming block copolymers showing both
microphase separation involving unique morphological transitions and
macrophase separation." Macromolecules, 33(22), 8258-8268 (2000).
[8]
G. H. Fredrickson, V. Ganesan, F. Drolet. "Field-theoretic computer simulation
methods for polymers and complex fluids." Macromolecules, 35(1), 16-39 (2002).
139