of 5
Rapid self-assembly of brush block
copolymers to photonic crystals
Benjamin R. Sveinbjörnsson
a,1
, Raymond A. Weitekamp
a,b,1
, Garret M. Miyake
a
, Yan Xia
a
,
Harry A. Atwater
b
, and Robert H. Grubbs
a,2
a
Arnold and Mabel Beckman Laboratories for Chemical Synthesis, Division of Chemistry and Chemical Engineering, California Institute of Technology
,
Pasadena, CA 91125; and
b
Thomas J. Watson Laboratories of Applied Physics, California Institute of Technology, Pasadena, CA 91125
Contributed by Robert H. Grubbs, July 30, 2012 (sent for review July 3, 2012)
The reduced chain entanglement of brush polymers over their
linear analogs drastically lowers the energetic barriers to reorgani-
zation. In this report, we demonstrate the rapid self-assembly of
brush block copolymers to nanostructures with photonic bandgaps
spanning the entire visible spectrum, from ultraviolet (UV) to near
infrared (NIR). Linear relationships were observed between the
peak wavelengths of reflection and polymer molecular weights.
This work enables
bottom-up
fabrication of photonic crystals
with application-tailored bandgaps, through synthetic control of
the polymer molecular weight and the method of self-assembly.
These polymers could be developed into NIR-reflective paints, to
combat the
urban heat island effect
due to NIR photon therma-
lization.
T
he rich morphologies afforded by the self-assembly of block
copolymers (BCPs) yield versatile hybrid materials with
diverse applications (1), such as lithographic templates (2), solid
electrolytes (3), and photonic crystals (PCs) (4). When the do-
main periodicities of typical copolymer structures reach hundreds
of nanometers, the effective optical lengths of the domains
approach visible wavelengths. The resulting periodic modulation
of the dielectric function can yield a photonic bandgap near the
visible; within this gap, there are no allowed frequencies at which
light can propagate through the material (5). The one-dimen-
sional case, consisting of a stack of alternating layers, is termed
a dielectric (or Bragg) mirror. This simple architecture forms the
basis for a variety of modern optical elements, including filters,
antireflection coatings, and resonant cavities. Recently, very high
molecular weight block copolymers have enabled chemically and
mechanically tunable PCs at visible frequencies (4, 6
8), provid-
ing a versatile platform for the development of unique nanostruc-
tures with exciting possibilities for functional, moldable, and
paintable PCs.
For many applications, such as dielectric mirrors, broadband re-
flection is a requirement. Typically, this is accomplished by employ-
ing materials with high refractive index contrast (9). Size dispersity
in multilayer structures offers another approach to broadband
reflection. In this way, the inherent dispersity in self-assembled
systems can be employed advantageously. In this report, we de-
monstrate broadband reflection into the NIR with two low-index
materials, with a refractive index contrast of approximately 0.1.
Because self-assembly methods easily provide dozens to hundreds
of layers, a reflection coefficient of unity can, in principle, be
obtained. To realize truly paintable photonic crystals, self-assembly
must occur rapidly, with little or no processing, to yield dry, robust
ordered nanostructures. This future technology has many potential
applications, for example as photonic cladding for telecommunica-
tions fibers and NIR reflective paints. These photonic paints could
be employed as surface coatings to improve energy efficiency in
urban environments, combating the
urban heat island effect
by reflecting infrared radiation that would otherwise thermalize.
Traditionally, PCs have been fabricated using
top-down
tech-
niques such as layer-by-layer stacking (10), electrochemical etch-
ing (11), multibeam holography (12), and phase mask lithography
(13). These techniques offer the advantage of precision but re-
quire complex apparatuses and many processing steps. Colloidal
assembly represents a
bottom-up
approach to PC fabrication
(14, 15), although it is generally limited to face-centered cubic
geometries. While colloidal templating is rapid and inexpensive,
infilling with high refractive index inorganic materials is usually
required to access a full photonic bandgap (14, 15). BCP nano-
structures offer an attractive solution because they can be pre-
pared from commodity chemicals and synthetically tuned to yield
a wide range of geometries and functionalities with unique
chemical, mechanical, and optical properties.
The typically slow and complex self-assembly of BCPs inhibits
their ability to assemble to domain sizes large enough to reflect
long wavelengths of visible light. The primary antagonist to self-
assembly is chain entanglement
a defining characteristic of poly-
mers, which significantly impedes high molecular weight (MW)
polymers from achieving large, ordered domains. Reaching do-
main spacings beyond 100 nm is a significant challenge for BCPs
(16
18) because the entanglement of high MW polymers presents
a large kinetic barrier, despite the large thermodynamic driving
force to microphase segregation. As a result, high MW BCPs often
end up in a kinetically trapped state; equilibration is prohibited
at a practical time scale. To overcome the practical limitations to
the domain sizes and refractive indices of typical BCPs, assembled
nanostructures are often swollen with additives, including small
molecules (4, 6, 19), inorganic nanoparticles (20), or other poly-
mers (17) to achieve photonic bandgaps in the visible and NIR.
Additionally, extreme annealing conditions have been used suc-
cessfully to prepare PC films from BCPs (21). The complex anneal-
ing procedures and additives demanded by much of the work to
date on polymer PCs represent a huge barrier to the practical
implementation of BCPs as commercially viable optical elements.
As chain entanglement presents a fundamental energetic barrier
to the reorganization of high MW BCPs into large, ordered nano-
structures, it is a logical focal point for the development of meth-
ods to surmount these limitations. In this report, we employ a
nonlinear macromolecular architecture with significantly reduced
entanglement, the brush copolymer (22, 23), to afford rapid self-
assembly into photonic crystals with tunable reflection across the
entire visible spectrum and into the NIR.
Brush copolymers with high MW, low polydispersity index
(PDI), and complete side chain grafting remain challenging tar-
gets for synthetic polymer chemists. There are many approaches
to these macromolecules, each with their own obstacles (24, 25).
In the
grafting through
or macromonomer (MM) method, the
side chain containing a terminal monomer is synthesized first and
Author contributions: R.A.W., Y.X., and R.H.G. designed research; B.R.S., R.A.W., G.M.M.,
and Y.X. performed research; B.R.S. contributed new reagents/analytic tools; B.R.S., R.A.W.,
G.M.M., Y.X., and H.A.A. analyzed data; and B.R.S., R.A.W., G.M.M., Y.X., H.A.A., and R.H.G.
wrote the paper.
The authors declare no conflict of interest.
1
B.R.S. and R.A.W. contributed equally to this work.
2
To whom correspondence should be addressed, E-mail: rhg@caltech.edu.
This article contains supporting information online at
www.pnas.org/lookup/suppl/
doi:10.1073/pnas.1213055109/-/DCSupplemental
.
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PNAS
September 4, 2012
vol. 109
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www.pnas.org/cgi/doi/10.1073/pnas.1213055109
subsequently polymerized to yield the resulting brush polymer
(24, 26). This approach ensures complete grafting of a well-
defined side chain on every backbone monomer unit; however,
it requires an extremely robust polymerization mechanism to
achieve high MW while maintaining control of the PDI (25). Our
group has recently utilized ruthenium (Ru) mediated ring-
opening metathesis polymerization (ROMP) as an efficient
means to convert MMs to well-defined high MW brush polymers
(22, 27
30). Brush BCPs prepared by this route were observed
to spontaneously assemble into large ordered nanostructures
(
>
100
nm) (28), which piqued our interest in applying this
approach to photonic crystals.
Results and Discussion
The lactide (L) and styrene (S) based MMs employed in this
study were synthesized from
exo
-norbornene functionalized in-
itiators, suited for the ring opening polymerization of racemic L
and the controlled radical polymerization of S. The MMs had
similar MWs and narrow molecular weight distributions (MWDs)
(L-MM:
M
n
¼
6
.
1
×
10
3
g
mol, PDI
¼
1
.
20
; S-MM:
M
n
¼
5
.
7
×
10
3
g
mol, PDI
¼
1
.
02
). More importantly, the advanta-
geous characteristics (i.e., livingness, stability, functional group
and steric tolerance) of Ru-mediated ROMP enable the sequen-
tial polymerization of the MMs to brush BCPs in high yields
with controlled MWs and narrow MWDs (Fig. 1). The MW of the
brush BCPs were controlled by the MM to Ru ratio, and ranged
from
1
.
08
×
10
6
to
6
.
64
×
10
6
g
mol, while maintaining relatively
narrow MWDs (PDI
¼
1
.
07
1
.
58
) considering the ultra-high
MWs, highlighting the robustness of ROMP. For this study, we
targeted blocks with near equal weight ratios with the goal of
achieving lamellar nanostructures (see
SI Appendix
for details).
After preparing a series of well-defined brush BCPs with a
broad range of MWs, we investigated a number of simple self-
assembly methods to yield thin, solid films. Our annealing meth-
ods included controlled evaporation from dichloromethane
(DCM) and tetrahydrofuran (THF) solutions, before and after
thermal annealing, as well as direct thermal annealing of the solid
polymer powder under compression between two glass substrates.
The drastic effect of the assembly method on the resulting nano-
structures is most starkly visualized by a single brush BCP
(
M
n
¼
2
.
94
×
10
6
g
mol), which appeared blue when cast from
DCM, green when cast from THF, and red after thermally anneal-
ing the green film cast from THF (Fig. 1
C
). Quantitative reflec-
tion measurements were performed on a spectrophotometer
equipped with an
integrating sphere
diffuse reflectance acces-
sory (see
SI Appendix
). The reflection spectra confirm the large
differences between samples prepared by different annealing
procedures (Fig. 2
A
). For the sample shown in Fig. 2, the first
(longest wavelength) peak of reflection shifts by hundreds of
nanometers, depending on the method of film preparation.
The difference in color is not due to residual solvent; the films
are completely dry, and we did not observe any color change upon
placing a sample in high vacuum for more than 50 hours.
Scanning electron micrograph (SEM) cross-sections were used
to directly image the film morphologies to further investigate
causes of the observed reflection spectra. Although the thermally
annealed samples must be composed of larger domains than the
films prepared via controlled evaporation (as suggested by the
greater
λ
max
), we were curious as to why the film cast from
DCM provided the markedly altered reflection spectra. SEM
images provided insight into the self-assembly of the films from
different techniques, clearly visualizing the polymer morpholo-
gies and domain sizes (Fig. 2
B
E
). For this polymer, all of the
films, except those prepared from DCM, showed the expected
stacked lamellar morphology for symmetric BCPs. In the case of
the film cast from DCM, a disordered morphology is observed in
the SEM image. The evaporative self-assembly process is dictated
by a number of factors, including the kinetics of evaporation,
quality of solvent, S/L interaction parameters, as well as the
energetics of the glass/polymer interface. For many samples, the
degree of lamellar order decreased as a function of distance from
the glass interface (see
SI Appendix
). For BCPs with approxi-
mately equal volume fractions, the lamellar morphology is the
most thermodynamically stable, as it minimizes the interfacial
surface energy between the two constituent polymers. THF
afforded larger and better ordered domains than DCM, which
we attribute to the fact that it is a good solvent for this copolymer
system (31). In addition, its decreased volatility affords improved
chain mobility: rearrangement occurs during evaporation, before
the chains enter the glassy state once all solvent is removed. After
thermal annealing, these samples become more ordered, with
larger domain sizes, as observed in the SEMs and evidenced by
the reflection spectra. Films that were directly thermally an-
nealed from dry polymer powder also formed well-ordered lamel-
lae with long wavelength reflection. The improved reflection
coefficient is a consequence of film thickness.
We observed the first order peak of reflection to be a linear
function of MW, for all of the self-assembly techniques employed.
This is in contrast to a corresponding linear copolymer system,
where the domain spacing is proportional to MW
0
.
81
(32).
Because the peak wavelength and domain spacing are directly
related by the equation
λ
max
¼
2
ð
n
1
x
1
þ
n
2
x
2
Þ
(18), our results
suggest that the brush BCPs studied yield a larger increase in
domain spacing per monomer incorporated than a corresponding
linear system. Given the high persistence lengths of these brush
polymers (22), we rationalize this observation in terms of the
Fig. 1.
(
A
) S- and L-based MMs were sequentially polymerized by ROMP to brush BCPs. (
B
) A schematic representation depicts the brush BCPs and their
assembly into ordered lamellar nanostructures. (
C
) Different annealing techniques render unique PCs for the same polymer, as shown in this photograph.
Sveinbjörnsson et al.
PNAS
September 4, 2012
vol. 109
no. 36
14333
CHEMISTRY
degree of backbone extension enforced by the steric congestion of
the brushes. Thus, the brush polymer architecture enables both a
large equilibrium scaling for self-assembled structures as well as
a very fast equilibration rate, due to the significantly reduced
chain entanglement (even at ultra-high MW).
Direct thermal annealing of the polymer powders under com-
pression proved to be the most successful assembly technique, in
that it enabled ultra-high MW polymers to reach ordered nano-
structures with PC characteristics at NIR wavelengths (Fig. 3
E
and
F
). By contrast, in the case of controlled evaporation, most of
the high molecular weight polymers (
M
n
>
3
×
10
6
g
mol) did
not assemble into films with distinct Bragg reflection peaks. The
unmatched structural order achieved through thermal annealing
is highlighted by the fact that the ultra-high MW polymers
possessed photonic bandgaps well into the NIR (up to
λ
max
¼
1311
nm), an unprecedented wavelength regime for unswelled
BCP photonic crystals. Furthermore, the low energetic barriers
to reorganization enable the application of any BCP self-assem-
bly technique to our system, to achieve improved lamellar order
and optical performance. As NIR dielectric mirrors, these robust
solid state PCs enable a host of exciting applications for BCPs to
telecommunications and thermal radiation management.
To justify the proposed mechanism of the observed reflection
spectra, transfer matrix simulations (9) were employed to model
the reflection spectra of the polymer photonic crystals. The
complex refractive indices of each block were measured for the
corresponding brush homopolymers by ellipsometry. The inputs
to our script are: the frequency-dependent refractive indices,
measured first order peak of maximum reflectance, number of
layers approximated by SEM, and the weight fractions of each
block measured by NMR (see
SI Appendix
). An initial guess of
the size of each block domain was made using the first order peak
of reflection, using the equation
λ
max
¼
2
ð
n
1
x
1
þ
n
2
x
2
Þ
, assuming
equal polymer densities. To account for the increased bandwidth
of the reflection peaks due to size dispersity and disorder in the
nanostructure, two free parameters were introduced: coefficients
of variation (CVs) for layer thickness and phase decoherence.
Introducing partial phase decoherence in transfer matrix simula-
tions has been previously demonstrated as a means of approxi-
mating interfacial roughness (33). A normal distribution of
thickness and phase perturbation was used, averaged over 1000
simulations and smoothed to remove noise (see
SI Appendix
for
modeling details).
The angle dependent reflection spectra of a well-ordered sam-
ple were measured and compared with one-dimensional transfer
Fig. 2.
(
A
) Reflection spectra are plotted for the brush BCP (
M
n
¼
2
.
94
×
10
6
g
mol) films prepared from the controlled evaporation from DCM (blue), or THF,
before (green) and after (red) thermal treatment, as well as via thermal annealing under compression (orange). (
B
) SEM cross-sections reveal the morphology of
the middle of the brush BCP films prepared from the controlled evaporation from DCM (
B
), THF before (
C
) and after (
D
) thermal annealing, as well as by direct
thermal annealing under compression (
E
). The insets are photographs of the samples.
Fig. 3.
(
A
) Reflectance is plotted as a function of wavelength for the films prepared from the controlled evaporation from THF for several different
MW polymers. (
B
)
λ
max
is plotted against MW for films prepared from the controlled evaporation of THF. SEM cross-sections are shown for the middle of
BCP films with
M
n
¼
1
.
53
×
10
6
g
mol. Linear fit
R
2
¼
0
.
997
.(
C
) and
M
n
¼
1
.
99
×
10
6
g
mol (
D
) prepared from the controlled evaporation of THF. (
E
) Reflec-
tance is plotted as a function of wavelength for the films prepared by thermal annealing under compression for several different MW polymers. (
F
)
λ
max
is
plotted against MW for films prepared by thermal annealing under compression. SEM cross-sections are shown for the middle of BCP films with
M
n
¼
1
.
99
×
10
6
g
mol. Linear fit
R
2
¼
0
.
984
.(
G
) and
M
n
¼
4
.
21
×
10
6
g
mol (
H
) prepared by thermal annealing under compression.
14334
www.pnas.org/cgi/doi/10.1073/pnas.1213055109
Sveinbjörnsson et al.
matrix simulations. The angular frequency response shows good
agreement between experiment and simulation (Fig. 4
A
). We
attribute the difference in amplitude to the angular variation due
to the curvature of the lamellae and the differences between the
fitted and actual complex refractive indices. Additionally, simula-
tions were run for three samples formed by three different assem-
bly procedures, with different MWs representative of the full
range of the series studied (Fig. 4
B
D
). For our simulations, the
CV for the layer thicknesses was chosen to be 10%, which we
found to be large enough to demonstrate the effect of size dis-
tribution on the line widths of the optical spectra, while small
enough to clearly resolve the higher order peaks. Partial phase
decoherence further contributes to peak broadening, and is well
rationalized considering the roughness observed by SEM (33).
The qualitative features of the measured spectra are well repre-
sented in the simulations (Fig. 4). Our modeling strongly suggests
that the observed lamellar nanostructures consist of alternating
polymer layers, which represent pseudo-1D photonic crystals.
Despite the moderate to poor lamellar alignment observed in
the SEM cross-sections, our 1D transfer matrix simulations can
qualitatively predict reflection spectra, enabling the design of
optical components using this platform.
In conclusion, we have demonstrated rapid self-assembly of
high molecular weight brush polymers as a facile method for
generating ordered nanostructures with large domain sizes,
specifically pseudo-1D photonic crystals. The reduced chain
entanglement of brush BCPs enables assembly of large nanos-
tructures that reflect long wavelength light without the use of any
additives. The linear trend of
λ
max
as a function of MW enables
one to synthetically
dial-in
dielectric mirrors with first order
peaks spanning from the UV to NIR. We envision that materials
produced through this approach have potential as NIR-reflecting
building materials, to inhibit the thermalization of NIR radiation
in urban environments. Moreover, the functional flexibility of our
approach enables a host of new directions for functional, compli-
ant and stimuli-responsive photonic elements.
ACKNOWLEDGMENTS.
This work was supported by the NSF (CHE-1048404).
R.A.W. was supported in part by the DOE
Light-Material Interactions in
Energy Conversion
Energy Frontier Research Center (DE-SC0001293). R.A.W.
thanks the Resnick Institute for a graduate fellowship. Reflection measure-
ments were collected at the Molecular Materials Research Center of the Beck-
man Institute of the California Institute of Technology. We thank Zhen-Gang
Wang for helpful discussions and Bryce Sadtler for assistance with the reflec-
tion measurements.
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M
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M
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53
×
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C
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94
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PNAS
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