Cornucopian Cylindrical Aggregate Morphologies from Self-Assembly of Amphiphilic
Triblock Copolymer in Selective Media
Ying Jiang,†,‡Jintao Zhu,§Wei Jiang,*,§and Haojun Liang*,†,‡,§
Hefei National Laboratory for Physical Sciences at Microscale, UniVersity of Science & Technology of China,
Hefei, Anhui, 230026, People’s Republic of China, Department of Polymer Science and Engineering, UniVersity
of Science & Technology of China, Hefei, Anhui, 230026, People’s Republic of China, State Key Laboratory of
Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences,
Changchun 130022, and Graduate School of the Chinese Academy of Sciences, People’s Republic of China
ReceiVed: May 10, 2005; In Final Form: July 18, 2005
We have investigated, both experimentally and theoretically, the aggregation of ABA amphiphilic triblock
copolymers in dilute solution. We observed a number of complex architectures having toroidal and network
structures, including some novel ones. The computational analyses of these systems offer some insight into
the origins of the self-assembly of these amphiphiles. The results we obtained using real-space self-consistent
field theory reveal that the formation of network and toroidal structures from the block copolymers occurs as
the result of the breaking of “inhomogeneous vesicles”; the observed polymorphism results from the existence
of multiple metastable states.
Nanoscale aggregation through the self-assembly of block
copolymers in selective solvents is the subject of an extensive
number of investigations because of their industrial potential
for applications in many fields, including drug delivery,
cosmetics, catalysis, separations, microelectronics, and ma-
terials.1-9Amphiphilic block copolymers have been demon-
strated to possess the ability to self-assemble in solution into
various complex ordered microstructures, such as spherical
micelles, rodlike micelles, large compound micelles, vesicles,
large compound vesicles, hexagonally packed hollow hoop
structures (“HHH” structures), and tube-, onion-, and bowl-
shaped structures.10-16Among these complex microstructures,
the branched, network, and toroidal micelles have attracted the
most attention.17-19Bates and co-workers demonstrated that the
diblock copolymer poly(1,2-butadiene-b-ethylene oxide) (PB-
PEO) can self-assemble into Y-junctions and three-dimensional
networks, which formed through the re-assembly of the Y-
junctions.17Very recently, Pochan and co-workers found that
almost all of the microstructures assembled from poly(acrylic
acid-b-methyl acrylate-b-styrene) (PAA99-PMA73-PS66) triblock
copolymers are ringlike or toroidal micelles.19If we attribute
toroid formation to the re-assembly of Y-junctions, we should
find Y-junctions in the equilibrium structures, as did Bates and
co-workers in their system, but Y-junctions are rarely found
(cf. the images in refs 18 and 19). Therefore, these experimental
results verified that the toroidal aggregates might not form
through an end-to-end connection process, which implies the
existence of other mechanisms for the formation of the micro-
structures in dilute solution. In addition, another feature shared
by the assembly of block copolymers in dilute solution is the
coexistence of disparate morphologies, i.e., very different
patterns coexist in solution.6,7The reason for the coexistence
of those disparate morphologies, i.e., polymorphism, remains
an open problem. With these problems in mind, we studied the
aggregation morphologies of the P4VP-b-PS-b-P4VP triblock
copolymer in dilute solution and then used self-consistent field
theory (SCFT) under similar conditions to those used experi-
mentally in an effort to provide some new insight into the
2. Experimental Section
2.1. Sample Preparation. The copolymer used in this study
was the triblock copolymer P4VP43-b-PS260-b-P4VP43 (the
subscripts indicate the block lengths; PDI ) 1.09), which was
purchased from Polymer Source Inc., Canada. The indirect
method was used to prepare sample 1. The triblock copolymer
was first dissolved in dioxane (initial concentration ranged from
0.5 to 4 wt %), which is a good solvent for both the PS and
P4VP blocks, and then deionized water was added, at a rate of
0.2 wt %/min to the copolymer solution up to 25 wt %, with
stirring to induce the self-assembly of the block copolymer. The
resulting solution was then stirred for 1 day. Subsequently, the
solution was sealed and kept for 15 days without stirring.
Finally, a large amount of deionized water was added to the
solution to quench the resulting aggregates. The resulting
mixture was dialyzed against distilled water to remove dioxane
from the solution.
For sample 2, a direct sample preparation method was used.
The block copolymer was dissolved in a dioxane/water mixture
(initial copolymer concentration in the common solvent was 1
wt %) having a water content of 25 wt %. The solution was
then stirred for different periods of time. Finally, a large amount
water was added, and dialysis was performed. The length of
time between the dissolution of the copolymer into the solvent
mixture and the addition of the large amount water was
* Authors to whom correspondence should be addressed. E-mail:
email@example.com (H.J.L.); firstname.lastname@example.org (W.J.).
†Hefei National Laboratory for Physical Sciences at Microscale,
University of Science and Technology of China.
‡Department of Polymer Science and Engineering, University of Science
and Technology of China.
§State Key Laboratory of Polymer Physics and Chemistry, Changchun
Institute of Applied Chemistry, Graduate School of the Chinese Academy
J. Phys. Chem. B 2005, 109, 21549-21555
10.1021/jp052420m CCC: $30.25© 2005 American Chemical Society
Published on Web 10/20/2005
considered to be the annealing time. During all of the dialysis
processes, the pH of the distilled water was adjusted to 4 to
prevent the colloid solutions from precipitating.7, 18
2.2. Transmission Electron Microscopy. The resulting
aggregate morphologies were visualized using a combination
of a regular transmission electron microscope (TEM) and a
tapping-mode atomic force microscope (AFM). Transmission
electron microscopy was performed using a JEOL JEM-2000FX
TEM operating at an acceleration voltage of 160 kV. The
dialyzed colloidal solutions were diluted by a factor of 10-20
to prepare the TEM samples. A drop of the very dilute solution
was placed onto a copper TEM grid covered with a polymer
support film that had been precoated with thin film of carbon.
After 15 min, the excess of the solution was blotted away using
a strip of filter paper. The samples were left to dry in air and at
room temperature for 1 day before observation.
2.3. Atomic Force Microscopy. An SPA300HV AFM was
operated in the tapping mode using an SPI3800 controller (Seiko
instruments Industry Co., Ltd.). The tip was of a sharpened
tetrahedral type (R < 10 nm; tip height: 14 µm) and the
cantilever fabricated from silicon had a spring constant of 2
N/m and a resonance frequency of 70 kHz. To prepare the
samples for AFM, the very dilute solution (a few drops) obtained
after dialysis was spin-coated onto the freshly cleaved mica
substrates. All of the samples were dried in air at room
temperature for 1 day prior to observation. The AFM experi-
ments were all performed in air and at room temperature.
3. Theoretical Section
In this section, we outline the formulation of self-consistent
field theory (SCFT) for analyzing ABA amphiphilic triblock
copolymers in dilution solution. Amphiphlic triblock copolymers
having hydrophilic segments (A), hydrophobic segments (B),
and solvent molecules (S) are involved in a volume V. The
volume fractions of segments A and B in the system are fAand
fB, respectively. As a result, the volume fractions of the
copolymer and solvent in solution are fP) fA+ fBand fS) 1
- fP, respectively. In real-space SCFT, one considers the
statistics of a single copolymer chain in a set of effective
chemical potential fields ωI, where the subscript I represents a
block species, either A or B. Those chemical potential fields,
which replace the actual interactions between the different
components, are conjugated with the segment density field, φI,
of the block species I. Similarly, the solvent molecules are
considered to be in an effective chemical potential field ωSthat
conjugates with the solvent density field φS. Hence, the free
energy function (in units of kBT) of the system is given as
where N is the length of the copolymer chain, ?ijis the Flory-
Huggins interaction parameter between species i and j, P is the
Lagrange multiplier (as a pressure), QS) ∫ dr exp(-ωS) is the
partition function of the solvent in the effective chemical
potential field ωS, and QP) ∫ drq(r, 1) is the partition function
of a single chain in the effective chemical potential field ωAor
ωB. The end-segment distribution function q(r, s) provides the
probability that a section of a chain, having contour length s
and containing a free chain end, has its “connected end” located
at r. The parametrization is chosen such that the contour variable
s increases continuously from 0 to 1, corresponding from one
end of the chain to the other. With the use of a flexible Gaussian
chain model to describe the single-chain statistics, the function
q(r, s) satisfies the following modified diffusion equation:
where θi(s) is equal to 1 if s belongs to block i; otherwise it is
equal to 0. In eq 2, the lengths are scaled by the (overall) radius
of gyration of an unperturbed chain. The appropriate initial
condition is q(r, 0) ) 1. Here, ωiis ωAwhen 0 < s < f1and
f1+ f2< s < 1 or ωBwhen f1< s < f1+ f2(fiis the volume
fraction of block i). Similarly, the second distribution function
q′(r, s) (containing another chain end) is also satisfied by eq 2
with the initial condition q′(r, 0) ) 1, but in this case, ωiis ωA
when 0 < s < f3and f2+ f3< s < 1 or ωBwhen f3< s < f2
+ f3. The density of each component is obtained by using the
From the equilibrium condition, the minimization of free energy
with respect to density and pressure, δF/δφ ) δF/δP ) 0, we
obtain another four equations:
Here, constant shifts in the potential are introduced into the
Using this method allows the low free-energy solutions of
the equations to be determined within a planar square or box
having a periodic boundary condition. The initial value of ω is
constructed as ωj(r) ) Σi*j?ij(φi(r) - fi), where firepresents the
average volume fraction of the copolymer segments or solvent
and φi(r) - fisatisfies the Gaussian distributions:
Here, ? is defined as the density fluctuation at the initial
temperature. The effective pressure field, P ) C2C3(ωA+ ωB)
+ C1C3(ωB+ ωS) + C1C2(ωA+ ωS)/2(C1C2+ C2C3+ C1C3),
on each grid is obtained upon solving eq 4, where C1) ?SA+
?BS- ?AB, C2) ?SA+ ?AB- ?BS, and C3) ?AB+ ?BS- ?SA.
The density field φI of species I, conjugated with the
chemical potential field ωI, can be evaluated based on eqs 2
and 3. The chemical potential field ωIcan be updated by using
the equation ωI
∑M*I?IM(φM(r) - fM) + P(r) - ωI
force. In our simulation, the time step was ∆t ) 0.3, and we
iterated the above steps until the free energy converged to a
local minimum where the phase structure corresponds to a
metastable state. This iteration scheme constitutes a pseudo-
dynamic process having the steepest descent on the energy
old+ ∆t(δF/δφI)*, where (δF/δφI)* )
oldis the chemical potential
F ) -fSln(QS/V) -fP
?ASφAφS+ ?BSφBφS- ωAφA- ωBφB- ωSφS-
P(1 - φA- φB- φS)] (1)
∂sq(r, s) ) ∇2q(r, s) - Nθi(s)ωiq(r, s)(i ) 1, 2, 3)
1dsq(r, s)q′(r, 1 - s)θi(s)(3)
ωA(r) ) ?AB(φB(r) - fB) + ?SA(φS(r) - fS) + P(r)
ωB(r) ) ?AB(φA(r) - fA) + ?BS(φS(r) - fS) + P(r)
ωS(r) ) ?SA(φA(r) - fA) + ?BS(φB(r) - fB) + P(r)
φA(r) + φB(r) + φS(r) ) 1(4)
〈(φi(r) - fi)〉 ) 0
〈(φi(r) - fi) (φj(r′) - fj)〉 ) ?fifjδijδ(r - r′) (5)
21550 J. Phys. Chem. B, Vol. 109, No. 46, 2005
Jiang et al.
landscape by being nearest to the metastable solution. It is
possible to reach various metastable states, depending on the
We performed the numerical simulation on the three-
dimensional space using a 40 × 40 × 40 cubic lattice having
space L ) 13.333 and grid size ∆x ) 0.3333 in the units of Rg
(unperturbed mean-square radius of gyration of a copolymer
chain). The simulation for each sample was performed until the
phase pattern was stable and invariable with time and ∆F <
10-6. The simulation of the homogeneous block copolymer
solution was reiterated for 10 to ca. 20 times from different
initial random states and using different random numbers to
ensure that the phenomena were not accidental. In the present
simulation, the length of chain N was 68, the length fraction of
the A block was 0.147, and fPwas 0.1 to ensure that the system
reflected a dilute solution. We assumed the interaction param-
eters to be ?ABN ) 25.5, ?BSN ) 27.2, and ?ASN ) -15.3,
respectively; these values ensure that the long middle block (B
block) is hydrophobic and the two end blocks (A blocks) are
hydrophilic, to be consistent with the experimental results. In
particular, we considered ABA triblocks that were symmetric
about their midpoint, i.e., the A blocks are fixed at an equal
length (equal volume fractions f1) f3).
4. Results and Discussion
Figure 1 displays the results of using the indirect method
(sample 1) to determine the three-dimensional branched ag-
gregates of 4 wt % P4VP43-b-PS260-b-P4VP43(abbreviated as
ABA) in a dioxane/water mixture containing 25 wt % water.
The branches are unambiguously distinguishable from the
overlaps through measurement of the optical densities at the
junctions, i.e., the overlaps appear darker than other parts of
the micelles, while the optical densities are uniform throughout
the branches. The branched cylinders can also be clearly
observed from the AFM height images (in Figure 2 the arrows
point at the branches). We found that the aggregate morphol-
ogies were sensitive to the initial copolymer concentration in
dioxane. The aggregates comprised stretched (or individual) rods
and only occasionally did we observe branches when the
copolymer concentration was 1 wt % in dioxane. The experi-
mental results indicate that branch formation was favored at a
higher copolymer concentration. From the TEM and AFM
images (Figures 1 and 2), we can readily identify many 3-fold
interconnecting cylindrical micelles (Y-junctions terminated by
enlarged spherical caps), resulting in a network. Moreover, the
occasional looped structure can be observed in the structure,
and the enlarged end-caps can also be seen clearly at the ends
of the stretched rodlike microstructures. Therefore, both branched
linear wormlike micelles and Y-junctions terminated by enlarged
spherical caps characterize this representative image. Similarly,
Kindt and Tlusty et al. predicted theoretically that, under
appropriate conditions, Y-junctions would appear in cylinder-
forming three-component (surfactant/oil/water) microemulsions,
leading to network formation and phase separation.21-23Rods
interconnected in three dimensions are also observed occasion-
ally through experiment. The diameters of the rods are mono-
disperse, and the origin of the branched points is the same as
that of the bicontinuous morphology observed in the bulk. The
Eisenberg group reported a similar result that they observed
from polystyrene-b-poly(acrylic acid)/DMF/water systems.24-26
It has been proposed that the formation of the interconnected
rods must occur mainly as a result of adhesive collisions and
fusion of the micelles.
Figure 3 displays the results of using the direct method, a
typical TEM micrograph, of the aggregate morphologies of 1
wt % triblock copolymer in a dioxane/water mixture containing
25 wt % water. In addition, we also observe complex looped
micelles in the AFM height images presented in Figure 4 (see
the arrows). The micrograph is characterized by a mixture of
looped micelles and network-like compound micelles. Very few
Y-junctions were terminated by enlarged spherical caps relative
to those found in Figures 1 and 2 and ref 17. The difference
between Figures 1 and 3 suggests that the micellar morphologies
are critically dependent on the choice of manufacturing process.
It can be understood that the structures in dilute solution, which
should correspond to a set of metastable states, closely relate
to the initial states and the manufacturing conditions.
At present, there are only a few theoretical reports on studies
of the formation of these types of complex microstructures.21-23
On the basis of the results published by Kindt21and Tlusty et
Figure 1. TEM micrograph of a sample prepared using the indirect
method, displaying part of the network formed from 4 wt % P4VP(43)-
b-PS(260)-b-P4VP(43) in a dioxane/water mixture having a water
content of 25 wt %.
Figure 2. AFM height images of the branched cylindrical aggregate
formed from the copolymer/dioxane/water mixture presented in Figure
Self-Assembly of Amphiphilic Triblock Copolymer
J. Phys. Chem. B, Vol. 109, No. 46, 2005 21551
al.,22,23a possible mechanism for the formation of the toroid or
network in Figure 3 might be that initially wormlike micelles
having Y-junctions terminated with enlarged spherical caps are
generated and then these micelles convert into toroidal micelles
through intrafusion of the ends of the worms; finally, these
toroidal and wormlike micelles fuse together and rearrange into
network compound micelles. If this mechanism is correct, the
Y-junctions should be favored over the toroidal micelles so that
it would be reasonable to expect that the wormlike micelles
and Y-junctions terminated with enlarged spherical caps should
be visible among the final microstructures, as was observed by
the Eisenberg group in their system.24-26The Y-junctions
terminated with enlarged spherical caps that were observed in
ref 17 and in Figures 1 and 2 are, however, rarely observed in
our Figure 3. The dominating microstructures in Figure 3 are
the compound toroidal and individual toroidal micelles. These
differences might imply a different mechanism for the formation
of these microstructures, i.e., other mechanisms may exist
besides the one suggested by Kindt and Tlusty et al. To clarify
the matter, we applied the self-consistent field theory (SCFT)
to this system.
SCFT is a mesoscopic simulation technique proposed by
Edwards in the 1960s; in subsequent decades, it was adapted
explicitly by Helfand and others to treat the self-assembly of
block copolymers in melt.27-31To circumvent the flaw in the
Matsen-Schick approach,32,33which requires an initial guess
of the relevant morphologies, Drolet and Fredrickson suggested
the implementation of a real-space SCFT where low free-energy
morphologies are obtained upon relaxation from random
potential fields.34-36Recently, Liang and co-workers applied
the method to the investigation of the mesophases (e.g., sphere-
and wormlike micelles or vesicles) of amphiphilic diblock
copolymers in dilute solution.37Herein, we use this approach
to study the toroid and network formation that occurs upon the
self-assembly of the triblock copolymers in dilute solution.
Figure 5 displays the network, looped, wormlike, and
spherical micelles obtained through both simulation and experi-
ment. It is clear that some of the typical microstructures observed
experimentally were reproduced in the simulations. The initial
component density in the simulations satisfies the Gaussian
distribution expressed as
where φi(r) represents the respective component density at r, fi
is the average density of the different components, and ? is
defined as the initial density fluctuation amplitude. An observa-
tion of the toroid formation process depicted in Figure 5D
reveals that the triblock copolymers initially aggregated into
an “inhomogeneous vesicle,” a micelle whose water and
hydrophilic components are distributed inhomogeneously within
its center. Upon growing to a critical size, this inhomogeneous
vesicle breaks at a certain place on the surface; this process
leads to the redistribution of the block copolymers as a result
of the balance of the internal free energy. As a result, a toroidal
structure is produced (Figure 5D). A detailed description of the
evolution of this process is described in a following section.
Figure 6a displays the evolution of a single loop. From the
results of the simulation, we find that the early stages of this
microstructure’s formation are quite similar to that observed
the case of the vesicle. During the first 50 steps [Figure 6a (I)],
the solvent in the irregular micelle is absolutely dominant
[Figure 6b (I-S)] and the hydrophilic segment A [Figure 6b (I-
A)] and hydrophobic block B [Figure 6b (I-B)] are dispersed
homogeneously in the micelle. After 100 steps [Figure 6a (II)
and (III)], the density of the hydrophilic block A in the central
area of the irregular micelle increases gradually [Figure 6b (II-
A), (III-A)] as a result of the attractive force of the solvent.
Simultaneously, Figure 6b (II-B) and (III-B) indicates that the
density of the hydrophobic block B increases around the central
area of the hydrophilic block A. The existence of hydrophobic
segment B leads to a decrease in the solvent density in that
region because of repulsion between the hydrophobic segment
and the solvent. Because of the inhomogeneous distribution of
the hydrophobic block B around the central area of the
hydrophilic block A, the polymeric shell comprised of block B
begins to break [Figure 6b (III-B)]. Subsequently, a connection
Figure 3. TEM micrographs of a sample prepared using the direct
method, displaying the aggregates formed from 1 wt % P4VP(43)-b-
PS(260)-b-P4VP(43) in a dioxane/water mixture, having a water content
of 25 wt %, after annealing for 6 days.
Figure 4. AFM height images of the ramification (see the arrow)
formed from 1 wt % P4VP(43)-b-PS(260)-b-P4VP(43) in a dioxane/
water mixture, having a water content of 25 wt %, after annealing for
6 days (i.e., the sample presented in Figure 3).
〈(φi(r) - fi)〉 ) 0
〈(φi(r) - fi)(φj(r′) - fj)〉 ) ?fifjδijδ(r - r′)
(i, j runs all of the components)
21552 J. Phys. Chem. B, Vol. 109, No. 46, 2005
Jiang et al.
is formed between the solvent molecules within and outside
the irregular micelle [Figure 6b (IV-S)]. As noted upon
processing from I to III, the volumes for those three micelles
are nearly the same [Figure 6a (I), (II), and (III)]. We presume
that the triblock copolymer chains diffuse outside into the early-
formed irregular micelle, which helps the assembly of the
micelle. Next, the connectivity between the solvents inside and
outside the micelle leads to the redistribution of components A
and B. As noted in Figure 6b IV, the density of the hydrophobic
component in the central area decreases in this area, while that
of the hydrophilic component increases. In particular, we note
that the hydrophilic component became homogeneously dis-
tributed in the central area during the following evolution
process, as indicated in Figure 6b (V-A). It is the hydrophilic
component in the central area that attracts the solvent into this
region. Finally, upon further evolution, the solvent dissolved a
circular hole to form a single cylindrical loop (Figure 6a VI) in
which the solvent occupies the center completely (Figure 6b
The double loops or network microstructures in the three other
groups depicted in Figure 5A-C are formed through similar
processes, but they broke in more than one place on the surface.
Figures 7 and 8 display some of the typical subpatterns that
appeared in the numerous samples prepared using the direct
method. A striking feature shared by all of the micelles presented
in these figures is their mirror symmetry, which reflects the
Figure 5. Ordered microphases of the amphiphilic triblock copolymer in dilute solution obtained at different values of the initial density fluctuation
? and relative free energy F (∆F < 10-6in our calculations) and using the interaction parameters ?ABN ) 25.5, ?BSN ) 27.2, and ?ASN ) -15.3;
(A) ? ) 1.0 × 10-6, F ) 0.8203; (B) ? ) 2.5 × 10-5, F ) 0.8182; (C) ? ) 2.5 × 10-3, F ) 0.8245; (D) ? ) 0.01, F ) 0.8374. For the sake of
comparison, TEM micrographs of the samples prepared experimentally using the direct method are presented in the right-hand column.
Self-Assembly of Amphiphilic Triblock Copolymer
J. Phys. Chem. B, Vol. 109, No. 46, 2005 21553
tendency to balance the internal free energy through the
redistribution, by fragmentation, of the block copolymer mol-
ecules after micelle formation.17Herein, we provide a mecha-
nism that is different from the one suggested by Kindt and Tlusty
et al. The aggregation of the triblock copolymer in dilute solution
is a complex process, and thus, it is reasonable that more than
one mechanism may exist to govern the process.
Another remarkable feature disclosed by the TEM images
(cf. Figure 3) of the polymeric aggregates is the coexistence of
disparate morphologies, i.e., the network and the multiple,
double, and single loops possessing tails all coexist in Figures
3, 7, and 8. This polymorphism is generally found in other
polymeric aggregate systems in dilute solution.20,38It has been
proposed that the polydispersity inherent in macromolecular
samples is one factor that, at least partially, contributes to this
coexistence,36but such polymorphism is far from understood.
It is a worthwhile task to perform further theoretical studies.
As stated above, the aggregate structures of the block copolymer
chains in dilute solution are dependent on the initial density
fluctuation amplitude ?. In fact, a solution that is homogeneous
on the macroscale can be inhomogeneous on the microscale.
For instance, the local density of polymer chains will be different
from region to region. Thus, once phase separation occurs, those
pre-aggregated chains arising from density fluctuation should
act as “nuclei” from which the phase growth begins. Because
of the ? dependence of the final microstructures, fluctuations
having a smaller or larger amplitude will lead to a variety of
diverse morphologies. Certainly, in applications of real-space
SCFT to concentrated solutions and melts, ? dependence of the
microstructures was not found because the initial density
fluctuation amplitude was very small relative to the original
density, i.e., its influence was negligible (note that the coexist-
Figure 6. (a) Ordered microphases (from Figure 5D) of the amphiphilic triblock copolymer in dilute solution at different times during its
evolution: (I) t ) 15; (II) t ) 30; (III) t ) 150; (IV) t ) 300; (V) t ) 375; (VI) equilibrium state. (b) Isodense density distributions (φ) of A, B,
and S along the cross-section of the diameter of the terminally formed loop presented in Figure 5D, but perpendicular to the plate on which the loop
resides, calculated at different times during its evolution. Black indicates high density; gray, low density.
Figure 7. Typical TEM micrographs of a sample prepared using the
direct method, depicting the complex looped structures most often
observed from 1 wt % P4VP(43)-b-PS(260)-b-P4VP(43) in a dioxane/
water mixture after annealing for different periods of time (bar length:
Figure 8. Typical TEM micrographs of a sample prepared using the
direct method, depicting the looped ramification most often observed
from 1 wt % P4VP(43)-b-PS(260)-b-P4VP(43) in a dioxane/water
mixture after annealing for different periods of time (bar length: 100
21554 J. Phys. Chem. B, Vol. 109, No. 46, 2005
Jiang et al.
ence of diverse morphologies is seldom observed in melts). In Download full-text
the cases when using dilute solutions, however, the initial density
fluctuation amplitude was comparable to its original density,
and its influence could no longer be ignored. The values of ?
and the free energies obtained from the simulations in Figure 5
are (A) ? ) 1.0 × 10-6, F ) 0.8203; (B) ? ) 2.5 × 105, F )
0.8182; (C) ? ) 2.5 × 10-3, F ) 0.8245; and (D) ? ) 0.01, F
) 0.8374, respectively. Obviously, each system does not possess
the lowest free energy, but rather is trapped in higher free-energy
states, i.e., in a set of metastable states. Again, from these data,
we observe that the structures depend so sensitively on the ?
values that a tiny change in ? may result in quite different
morphologies. We believe that inhomogeneity in solution can
definitely lead to the coexistence of these disparate morphol-
ogies. This concept explains, at least partially, why the diverse
micromorphologies for a given block copolymer in dilute
solution can be produced experimentally through different
manipulation procedures. Thus, we attribute the polymorphism
of this system largely to its metastability, in addition to the
polydispersity of the triblock copolymer. Our results are similar
to those observed in vesicle systems formed through the self-
assembly of P4VP43-b-PS366-b-P4VP43in dilute solution.39The
preparation of these metastable states depends strongly on which
path the system travels on the free-energy landscapes; these
routes are governed by the initial conditions, such as the local
We have obtained cornucopian aggregates, including some
novel structures, from an ABA amphiphilic triblock copolymer
in selective media. These complex morphologies enrich our
knowledge of the potential products obtained from the self-
assembly of block copolymers in selective media, and they offer
us some insight into the self-assembly process. The results of
simulations performed using the SCFT reveal that the formation
of network and looped structures from the block copolymers is
due to the breaking of “inhomogeneous vesicles.” A main reason
for the coexistence of the diverse morphologies in dilute solution
is that the systems exist in a set of metastable states that correlate
well with the initial density fluctuation (?). Filtration of these
branched and looped cylindrical aggregates should yield highly
porous layers that we believe could have significant practical
interest. Porous solids of this type might be attractive as supports
for immobilized enzymes (or other catalysts) and for applications
such as chromatography or sewage separation, where stability,
a large hydrophilic surface area, and easy accessibility to liquids
are all necessary properties.40Moreover, these branched and
network structures may offer new opportunities for designing
advanced materials having defined properties.
Acknowledgment. We are grateful for the financial support
provided by the General (203074050, 90403022) and Major
(20490220) Programs of the National Natural Science Founda-
tion of China (NSFC), the Chinese Academy of Sciences
(project KJCX2-SW-H07), the 973 Program of MOST (nos.
2005CB623807, 2003CB615600), and the Fund for Distin-
guished Youth of Jilin Province, China.
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Self-Assembly of Amphiphilic Triblock Copolymer
J. Phys. Chem. B, Vol. 109, No. 46, 2005 21555