Polystyrene-poly(2-vinyl pyridine) [PS_6 P2VP_6] heteroarm star copolymer melts are studied experimentally (using transmission electron microscopy) and theoretically in the strong segregation regime. We found a pronounced difference in the behavior of heteroarm star copolymers from conventional diblock copolymers. For heteroarm star copolymers there is a systematic deviation in the long period of lamellar structures from the N^2/3 law obeyed by diblock copolymers. Our theoretical analysis provides a modification of the N^2/3 dependence by considering the extra stretching (compared to diblock copolymers) of the arms of star block copolymers near the star junction point at the lamellar interface. The predictions of our model are in a good agreement with the available experimental data for symmetric and asymmetric star block copolymers.
[C18.002] Phase behavior of three and four miktoarm star polymers
Francois Drolet (Hyperdigm Research), Glenn H. Fredrickson (University of California, Santa Barbara)
By means of self-consistent mean field theory, we examine
the phase behavior of melts of starblock copolymer molecules
consisting of three or four arms of different composition
joined together at a central core. Constraints peculiar to
the star architecture lead to a unique set of
microstructures in which the star junctions are often
confined to points (or lines in three dimensions) where
domains of different monomer species intersect. The SCF
equations are solved in real space in two and three
dimensional simulation cells with periodic boundary
conditions. Results are presented for melts of star
molecules with varying armlengths and for different sets of
monomer-monomer interaction strengths. The effect of adding
small amounts of homopolymer or solvent molecules to the
melt is also discussed.
[C18.003] Effect of central junction point of AnBn star block copolymers on chain conformation in strong segregated limit
Yuqing Zhu, Samuel P. Gido (Polymer Science & Engineering Department, University of Massachusetts at Amherst, Amherst, MA 01002), Maria Moshakou, Hermis Iatrou, Nikos Hadjichristidis (Department of Chemistry, University of Athens, Panepistimiopolis Zografou 15771, Athens, Greece)
In order to probe the effect of branched chain architecture
on chain conformation and morphology, a series of five AnBn
miktoarm star block copolymers with n = 1, 2, 4, 6 and 16
were investigated. These materials were produced by
synthesizing large batches of identical A and B arms and
linking them together in different numbers. The samples all
had nearly 50/50 volume fractions and formed lamellar
morphologies that were studied via SAXS and TEM. A slight
increase in lamellar spacing with increasing junction point
functionality was found in this series of samples and can be
attributed to molecular crowding near the junction point.
This junction point effect may underlie the experimentally
observed systematic deviation of mikoarm star block
copolymer morphology from the theory of Milner.
[C18.004] Equlibrium Properties of Triblock Copolymers
K. Rasmussen, T. Lookman, A. Saxena (Los Alamos National Laboratory), R.C. Desai (University of Toronto)
We apply self consistent mean field theory to the
Edwards-Doi hamiltonian for triblock copolymers. We study
numerically the phase diagram and obtain the structure
factor. Fluctuations about the disordered and ordered mean
field phases are taken into account in order to determine
the stability properties of the mean field phases. We
compare our results to experiments and to the behaviour of
diblock copolymers.
[C18.005] Morphological Behavior Spanning the Symmetric AB Diblock and ABC Triblock Copolymer States
Travis Bailey, Hoai Pham, Frank Bates (University of Minnesota, Chemical Engineering and Materials Science Department)
A majority of studies involving ABC triblock copolymers have
focused on the unique morphologies that particular molecules
or blends express. However, unlike the phase behavior of AB
diblocks, the progression of these morphologies as a
function of composition is not very well understood. This
work focuses on understanding the progression of
morphologies expressed as molecules change composition from
the symmetric AB diblock to the symmetric ABC triblock
state. This type of transformation was achieved through
systematic addition of PEO to a single symmetric PS-PI
diblock copolymer (MW~18000g/mol), resulting in a series of
10 poly(styrene-b-isoprene-b-ethyleneoxide) triblock
copolymers varying only the amount of PEO added. Final
compositions ranged from 2.9 to 32.9symmetric) PEO by volume, the remaining volume always being
divided equally between the PS and PI segments. The
molecular weight of the parent diblock was chosen such that
resulting triblocks could undergo order-disorder transitions
at experimentally accessible temperatures over much of the
composition range studied. The discussion will concentrate
on the characterization of 6 morphologies observed between
these 2 symmetric states and discuss some of the kinetic and
directional (heating vs. cooling) characteristics of 2
thermally induced order-order transitions also observed.
Finally, the effects of changing the connectivity of the PS
and PI blocks on this morphological progression may also be
considered.
[C18.006] Morphology formation in rod-coil diblock copolymers
Wentao Li, Dilip Gersappe (Dept. of Materials Science and Engg, SUNY Stony Brook)
We have developed a two dimensional mean field model to
study the formation of self-assembled structures in
polymeric materials that have both rigid and flexible
segments. In our model the chain rigidity is controlled by
the energy difference between the gauche and the trans
states. We have used this model to investigate the phase
structures observed in diblock copolymer systems where one
of the block is rigid. We vary the rigidity of the block,
the volume fraction of the blocks and the Flory Huggins
parameter ,\chi , between the blocks.Our model is able to
predict the formation of morphologies ranging from
cylindrical, lamellar and the zigzag lamella structures. The
stability of the different structures will be discussed
based on free energy calculations.
[C18.007] Effect of Polydispersity on the Phase Behaviour of Diblock Copolymers
David M. Cooke, An-Chang Shi (McMaster University)
Most polymers are polydisperse. Previous theories of the
mesoscopic structure formed by a diblock copolymer melt have
only considered monodisperse polymers. We examine the effect
of polydispersity in the block lengths on the well-known
phase behaviour of diblock copolymer melts using
self-consistent field theory. The polydispersity effect is
analysed in terms of a perturbation theory, in which the
distribution width (=M_w/M_n-1) is used as a perturbation
parameter. The perturbation results are compared with the
solutions for the monodisperse diblock copolymer melts.
[C18.008] Phase behaviour of blends of AB and AC diblock copolymers
Robert Wickham, An-Chang Shi (Dept. of Physics and Astronomy, McMaster University, Hamilton ON L8S 4M1, Canada)
The phase behaviour of blends of AB and AC diblock
copolymers is examined using self-consistent field theory.
By increasing the repulsion between the B and C blocks,
while keeping the length and composition of the two diblock
species equal, the effects of the repulsion on the
well-known phase behaviour of the pure diblock can be
studied. For weak repulsions, one possible equilibrium phase
is a lamellar phase with mixed (B/C) domains. The stability
of this ...A(B/C)A... lamellar structure relative to the
ABBAACCA structure and to macrophase separation is
investigated. Fluctuations transverse to the lamellar
ordering are examined using the theory of anisotropic
fluctuations. These results are compared to the experiments
of Kimishima et al. [Macromolecules 32, 2585
(1999)] where hydrogenation was used to vary the repulsion
of the B and C blocks.
[C18.009] Nano-confined Polymer Crystallization in Self-assembled Block Copolymers*
S.Z.D. Cheng, L. Zhu, P. Huang, B.H. Calhoun, Q. Ge, R.P. Quirk (Maurice Morton Institute and Department of Polymer Science, The University of Akron, Akron, OH 44325-3909.), E.L. Thomas (Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139), B.S. Hsiao, F. Yeh, L. Liu (Department of Chemistry, The State University of New York at Stony Brook, Stony Brook, New York 11794-3400), B. Lotz (Institute Charles Sadron, 6 Rue Boussingault, Strasbourg 67083, France)
A convenient and effective method to study nano-confined
polymer crystallization is to use self-assembled block
copolymers as templates. Various confined geometries can be
achieved using diblock copolymers on a nanometer length
scale, such as lamellae, cylinders, spheres, double gyroids,
and perforated layers. In this research, nano-confined
polymer crystallization is studied in a poly(ethylene
oxide)-b-polystyrene (PEO-b-PS) diblock copolymer system.
PEO crystal orientations within various confined geometries
have been found to be dependent upon the crystallization
temperatures (Tc). In addition to a lamellar confined
environment, a cylinder-forming PEO-b-PS/PS blend shows that
the PEO crystal c-axis changes from inclined to
perpendicular to the cylinder axis with increasing Tc. In a
hexagonal-perforated-layer (HPL) sample, the orientation of
the PEO crystal c-axis changes from parallel to inclined to
the layers with increasing Tc. At high Tcs in the HPL phase,
the PEO lamellar crystals grow specifically along the (100)
planes of the hexagonal lattice. These specific crystal
orientations have been found in early stages of the PEO
crystal growth.
[C18.010] Quantifying Confined Crystallization within Block Copolymer Microdomains
Y.-L. Loo, R.A. Register (Princeton University), A.J. Ryan (University of Sheffield)
We examined the melt and solid-state structures of a series
of diblock copolymers containing polyethylene as the
minority block, with a rubbery hydrocarbon majority block.
When the interblock segregation strength during
crystallization is sufficiently high (approximately three
times the segregation strength at the order-disorder
transition), crystallization can be effectively confined
within spherical domains formed by microphase separation in
the melt; the resulting crystallization kinetics are
first-order (Avrami n=1). Below this critical interblock
segregation strength, crystallization disrupts the spherical
microdomains, resulting in sigmoidal kinetics (n=2-3).
Cylinder-forming materials are more complex: there exists a
range of intermediate segregation strength where
crystallization is templated but not wholly confined, i.e.,
while the melt morphology is generally retained on cooling,
local distortions and connections between cylinders occur
due to crystallization. The connections between cylinders
result in sigmoidal kinetics (n=3).
[C18.011] Microdomain-Tailored Crystallization Kinetics of Block Copolymers
Hsin-Lung Chen (Department of Chemical Engineering, National Tsing Hua University, Hsin-Chu, 30013 Taiwan, R.O.C.), Tsang-Lang Lin (Department of Engineering and System Science, National Tsing Hua University, Hsin-Chu, 30013 Taiwan, R.O.C.), Takeji Hashimoto (Department of Polymer Chemistry, Kyoto University, Kyoto 606, Japan)
Microphase-separated block copolymers offer a convenient
template for studying the phase transformation of chain
molecules in nano-scaled space. In this study, we
demonstrate the implement of microdomain (MD) transformation
to manipulate the kinetics of crystallization in a diblock
copolymer, poly(ethylene oxide)-block-poly(1,4-butadiene)
(PEO-b-PB). A symmetric PEO-b-PB was blended with a low
molecular weight PB homopolymer to generate the block
copolymer blends containing lamellar, cylindrical, and
spherical PEO MDs dispersed in the PB matrix. The
crystallization kinetics of the PEO blocks was found to
display a parallel transition with the transformation of MD
morphology owing to the highly frustrated crystal growth in
the microphase-separated melt. In this case, homogeneous
nucleation became the rate determining process for
crystallization. The direct proportionality between the
nucleation rate and MD volume rendered the basis for the
distinct correlation between crystallization kinetics and MD
morphology.
[C18.012] Self-consistent field theory of twist grain boundaries in block copolymers
Daniel Duque, Michael Schick (Department of Physics, University of Washington, Seattle WA 98195-1560)
We apply self consistent field theory to twist grain
boundaries of block copolymer melts. The distribution of
monomers throughout the grain boundary is obtained as well
as the grain boundary free energy per unit area as a
function of twist angle. This free energy is found to be
small relative to those of tilt grain boundaries. We define
an intermaterial dividing surface in order to compare it
with minimal surfaces which have been proposed. Our
calculation shows that the dividing surface is not a minimal
one, but the linear stack of dislocations seems to be a
better representation of it for most angles than is Scherk's
first surface.
[C18.013] T-Junction Grain Boundaries in Block Copolymer - Homopolymer Blends
Samuel Gido, Engin Burgaz (University of Massachusetts Amherst)
T-junction grain boundaries were studied in a blend of
polyisoprene homopolymer and a single graft block copolymer
I2S with two equal length blocks of polyisoprene and one arm
of polystyrene linked at a common junction point. The
overall polyisoprene volume fraction in the blend was 0.52
and its equilibrium morphology was lamellar. While
T-junctions were previously observed to be quite rare
compared to other tilt grain boundary morphologies such as
chevrons and omegas, they were found in abundance in the
blend. T-junctions in the blend show a number of distinctive
characteristics including enlarged semicylindrical end-caps
terminating polystyrene lamella, and an increase in the
spacing of the lamella as they near their termination at the
T-junction. Calculations show that the homopolymer present
in the blend stabilizes the cylindrical curvature of the
end-caps, rendering the T-junction morphology more stable in
blends than in neat block copolymers.
[C18.014] Time-Iteration in Mesoscale Polymer Morphology Modeling
Hans Fraaije (University of Leiden)
Mesoscale (1-1000 nm) morphologies in complex polymer
mixtures and solutions have at least three very good things
to offer: nice pictures, tough theory and a niche in
computer simulations. For the last five years I have been
involved in several EU simulation projects (CAESAR and
MesoDyn). These projects were based on a simple numerical
method for dynamical mesoscale formation (J. Fraaije,
J.Chem. Physics, 9202-9212, 99, 1993), within the framework
of the standard mean–field path-integral model for polymers.
According to the theory, morphologies develop in time as a
result of weak potential gradients, similar, but not
identical to TDGL. I will discuss in detail some on the
algorithmic issues concerning the time-iteration of the
mesoscale morphologies. Either one has a “minimizer” view
and regards the time-development as a Jacobi or Picard type
iteration, where the objective is simply to find a stable
point in the iteration map. Or one tries to mimic real
dynamic behaviour by careful selection of kinetic operators.
It is not too difficult to find a unifying framework in
which both views co-exist. As an example of a practical
“dynamical” mesoscale application, I present the latest
results on 3D morphology formation in confined polymer
surfactants solutions. The “minimizer” view concerns rapid
screening of 3D morphologies of thee-colour copolymers in
periodic systems.
[C18.015] Micelle Disordering Transition in Strongly Asymmetric Diblock Copolymer Melts
Elena E. Dormidontova (Department of Chemical Engineering and Materials Science, University of Minnesota, MN 55455), Timothy P. Lodge (Department of Chemistry, Department of Chemical Engineering and Materials Science, University of Minnesota, MN 55455)
The order-disorder transition (ODT) from a well-ordered micelle state (i.e. bcc or fcc phase) into the disordered micelle state (with liquid-like order) is studied analytically in strong segregation limit. The comparison of the free energies (including the intermicelle interaction free energy) of an ordered and disordered phase allows us to define the order-disorder transition temperature as well as to estimate the width of the temperature range where the disordered micelle phase is stable. The preference for the disordered micelle phase is caused mainly by the additional degree of freedom for translational motion. Composition dependence of the ODT temperature is analyzed. A comparison with available experimental data for PS-PI diblock and triblock copolymers demonstrates the capability of our model to predict the ODT values with a reasonable accuracy. Predictions concerning the properties of the polymer system (aggregation number, free unimers fraction, intermicellar distance) at the ODT are also made.