Self assembly of ABC triblock copolymer thin films on a brush-coated substrate

Abstract

Self assemblies of ABC triblock copolymer thin films on a densely brush-coated substrate were investigated by using the self-consistent field theory. The middle block B and the coated polymer form one phase and the alternating phase A and phase C occur when the film is very thin either for the neutral or selective hard surface (which is opposite to the brush-coated substrate). The lamellar phase is stable on the hard surface when it is neutral and interestingly, the short block tends to stay on this hard surface. The rippled structure forms when the cylindrical phase exists near the surface between grafted polymers and ABC block copolymers. Due to the existence of the hydrophilic brush-coated surface serving as a soft surface of the film, the energy fluctuation existing in the film confined by two hard surfaces disappears. The results are helpful for designing the nanopattern of the film and realizing the functional thin film, such as adding the functional short block A to the BC diblock copolymer.

Full text

Chinese Journal of Polymer Science Vol. 27, No. 4, (2009), 583
−
592 Chinese Journal of
Polymer Science
©2009 World Scientific
SELF ASSEMBLY OF ABC TRIBLOCK COPOLYMER THIN FILMS ON A BRUSH-
COATED SUBSTRATE*
Zhi-bin Jiang, Rong Wang** and Gi Xue**
Department of Polymer Science and Engineering, State Key Laboratory of Coordination Chemistry, Nanjing National
Laboratory of Microstructures, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, China
Abstract Self assemblies of ABC triblock copolymer thin films on a densely brush-coated substrate were investigated by
using the self-consistent field theory. The middle block B and the coated polymer form one phase and the alternating phase
A and phase C occur when the film is very thin either for the neutral or selective hard surface (which is opposite to the brush-
coated substrate). The lamellar phase is stable on the hard surface when it is neutral and interestingly, the short block tends to
stay on this hard surface. The rippled structure forms when the cylindrical phase exists near the surface between grafted
polymers and ABC block copolymers. Due to the existence of the hydrophilic brush-coated surface serving as a soft surface
of the film, the energy fluctuation existing in the film confined by two hard surfaces disappears. The results are helpful for
designing the nanopattern of the film and realizing the functional thin film, such as adding the functional short block A to the
BC diblock copolymer.
Keywords: Functional self-assembly; Thin film; Simulation; Self-consistent field theory; ABC triblock copolymer.
INTRODUCTION
Block copolymers can microphase separate to form a variety of ordered nanoscale morphologies[1, 2]. Self
assembly and phase separation in diblock copolymers have been well studied and characterized both
theoretically and experimentally in the last few decades[3−10]. Recently, there has been a great interest in studying
the thin film of block copolymers experimentally and theoretically. The function of the thin film is very
important for its application besides the perfect nanopattern of the film. In thin films, incompatibility between
different polymer components and the thin film thickness creates frustration, the effect of which can be probed
by surface-induced effect. The presence of a surface or interface can strongly influence the microdomain
morphologies and the kinetics of microdomain ordering. In general, phase separation is accompanied by a
minimization of the interfacial area of contact between dissimilar components, resulting in a reduction of the
enthalpy. This is accompanied by a reduction of the conformational entropy of the polymer chains. The complex
and rich phase behaviors depend not only on molecular parameters such as the interaction energies between
distinct blocks and the architectures of block copolymers, but also on external variables such as electric
fields[11, 12], temperature gradients[13], chemically patterned substrates[14−21] and interfacial interactions[22−25].
The phase behavior of diblock copolymer melts confined in a parallel slit or in a thin film has been
extensively studied[3, 26−29]. Comparing with two-component systems (i.e. AB diblock copolymers), the phase
behavior of ABC triblock terpolymers is much more complex, and a much larger number of simulation
* This work was supported by the National Natural Science Foundations of China (Nos. 20504013, 20674035, 20874046 and
50533020), the National Basic Research Program of China (No. 2007CB825101), the Nanjing University Talent
Development Foundation (No. 0205004107), and the Natural Science Foundation of Nanjing University (No. 0205005216).
** Corresponding author: Rong Wang (汪蓉), E-mail: rong_wang73@hotmail.com
Gi Xue (薛奇), E-mail: xuegi@nju.edu.cn
Received September 8, 2008; Revised October 27, 2008; Accepted November 11, 2008

Z.B. Jiang et al.
584
parameters is needed to describe thin films: the film thickness (H), the volume fractions of the components fA, fB
and fC (1 – fA – fB), three mutual interaction parameters between the components
χ
AB,
χ
AC,
χ
BC and interaction
parameters between the interfaces and the three components (
χ
AS,
χ
BS, and
χ
CS, and S representing the surface).
Pickett and Balazs have used the self-consistent field theory to probe the preferential orientation of lamellae
formed by an ABC triblock terpolymer confined between two walls attracting the middle block[30]. They found
that an orientation of the lamellae perpendicular to the plane of the film orientation is highly favored, indicating
that triblock terpolymers possess distinct advantages over diblocks in technological applications. Monte Carlo
simulations by Feng and Ruckenstein for ABC melts in thin films show that the microdomain morphology can
be very complicated and is affected by the composition, the interactions[31] and even the geometry of the
confinement. Chen and Fredrickson have applied the self-consistent field theory and strong segregation limit
studies (SSL) to investigate the films of linear ABC triblock terpolymer melts[32] for the particular case where A
and C blocks are in equal size, the interaction parameters are identical, and both walls have identical chemical
properties. Self-consistent field theory (SCFT)[33] and dynamic density functional field theory[34] are also used to
study symmetric ABC triblock copolymer thin films. The above results show that the morphology of block
copolymer thin films depends on the film thickness, the surface-polymer interaction, and the incompatibility
between different blocks of the copolymer, which is usually characterized by a Flory-Huggins parameter. We
can tailor surface fields, film thicknesses and even the geometry of the confinement to manipulate the
microdomain structure, shape and orientation.
In practice, besides using pure (silicon) substrates, the hydrophobic or hydrophilic substrates are prepared
by chemically grafting self-assembled monolayer onto (silicon) substrate[35], which form the so-called “polymer
brush” to provide a simple way of modifying surface properties, such as adhesion, lubrication and wetting
behavior. Ma and his group members[36, 37] observed the structure transformation of the AB diblock copolymer
thin film by tailoring the grafting density of the coated surface or the concentration of the copolymer. In this
paper, we use a combinatorial screening method based on the real space implementation of the SCFT, originally
proposed by Drolet and Fredrickson for block copolymer melts[38, 39], to search the equilibrium microphases of
ABC linear triblock copolymers with short end block confined between the polymer brush-coated surface and
the flat impenetrable surface in 2D due to a computationally cost task of solving SCF equations in 3D. Polymer
films on brush-coated substrate are mimicked as a polymer melt confined between the brush-coated surface and
a hard surface. The simulations are performed on a square grid Lx × Lz. The walls are presented as lines at z = 0
and Lz . Hence, the film thickness is Lz.
THE MODEL
We assume the ABC triblock copolymer is confined between the polymer-grafted substrate and the flat
impenetrable surface (hard surface) with a distance Lz along the z-axis. There are nc ABC triblock
copolymer chains with polymerization N and ng polymer chains with polymerization P (here, we take P =
N) grafting on the substrate. Each copolymer chain consists of N segments with compositions (average
volume fractions) fA and fB (fC = 1 – fA – fB), respectively. The monomers of the ABC triblock copolymer
and the grafted polymers are assumed to be flexible with a statistical length a and the mixture is
incompressible with each polymer segment occupying a fixed volume 1
0
−
ρ
. The substrate coated by the
polymers is horizontally placed on the xy plane at z = 0 and the hard free surface is placed at z = Lz. The
volume of the system is V = LxLz, where Lx is the lateral length of the substrate and the flat impenetrable
surface along the x-axis and Lz is the film thickness. The grafting density is defined as
σ
= nga/Lx. The
average volume fractions of the grafted chains and copolymers are
ϕ
g = ngN/
ρ
0V and
ϕ
c = ncN/
ρ
0V,
respectively.
In the SCFT one considers the statistics of a single copolymer chain in a set of effective external
fields wi, where i represents block species A, B, C or grafted polymers. These external fields, which
represent the actual interactions between different components, are conjugated to the segment density

Self Assembly of ABC Triblock Copolymer Thin Films on a Brush-Coated Substrate 585
fields,
φ
i, of different species i. Hence, the free energy (in unit of kBT) of the system is given by
]
2
1
[d/
)]([d/)/ln()/ln(
s
,S
gggccc
∑∑
∫
∫
∑
∑
≠
+
+−+−−−=
jii
iijiij
ii
iii
NNV
wVVQVQF
rr
r
r
δφχφφχ
φξφϕϕϕϕ
1
11
(1)
where
χ
ij is the Flory-Huggins interaction parameter between species i and j,
ξ
is the Lagrange multiplier
(as a pressure),
χ
iS is the interaction parameter between the species i and the free hard surface S. rs is the
position of the free hard surface. ),(d cc 1rrqQ ∫
= is the partition function of a single copolymer chain in
the effective external fields wA, wB and wC, and ),(d gg 1rrqQ ∫
= is the partition function of a grafted
polymer chain in the external field wg. The fundamental quantity to be calculated in mean-field studies is
the polymer segment probability distribution function, q(r, s), representing the probability of finding
segment s at position r. It satisfies a modified diffusion equation using a flexible Gaussian chain model
),(),(
6
),( 2
2swqsq
Na
sq
srrr −∇=
∂
∂ (2)
where w is wA when 0 < s < fA, wB when fA < s < fA + fB, wC when fA + fB < s < 1 for ABC triblock
copolymer and wg for the grafted polymer. The initial condition of Eq. (2) satisfies qc(r, 0) = 1 for ABC
triblock copolymer. Because the two ends of the block copolymer are different, a second distribution
function ),(
csq r
+ is needed which satisfies Eq. (2) but with the right-hand side multiplied by −1 and the
initial condition 1)1,(
c=
+rq. The initial condition of qg(r, s) for grafted polymer is qg(r = rz, 0) = 1 and
qg(r ≠ rz, 0) = 0, where rz presents the position of the substrate at z = 0, and that of ),(
gsq r
+
is 1)1,(
c=
+rq. The periodic boundary condition is used for qc(r, s), ),( sqcr
+, qg(r, s), and ),(
gsq r
+ along
x-direction when ],0[ z
Lz ∈. qc(r, s), ),( sqcr
+, qg(r, s), and ),( sqgr
+ are equal to zero when z < 0 or
z > Lz.
Minimization of the free energy with respect to density, pressure, and fields, δF/δ
φ
= δF/δ
ξ
=
δF/δw
= 0, leads to the following equations.
∑
≠
++=
A
,ASAA s
)()()(
i
ii NNw rr
rrr
δχξφχ
(3)
∑
≠
++=
B
,BSBB s
)()()(
i
ii NNw rr
rrr
δχξφχ
(4)
∑
≠
++=
C
,CSCC s
)()()(
i
ii NNw rr
rrr
δχξφχ
(5)
∑
≠
++=
g
,gSgg s
)()()(
i
ii NNw rr
rrr
δχξφχ
(6)
φ
Α(r) +
φ
Β(r) +
φ
C(r) +
φ
g(r) = 1 (7)
∫+
=A
0cc
c
c
A),(),(d)( fsqssq
Q
Vrrr
ϕ
φ
(8)

Z.B. Jiang et al.
586
∫++
=BA
A
),(),(d)( cc
c
c
B
ff
fsqssq
Q
Vrrr
ϕ
φ
(9)
∫+
+
=1
BA
),(),(d)( cc
c
c
Cff sqssq
Q
Vrrr
ϕ
φ
(10)
∫+
=1
0gg
g
g
g),(),(d)( sqssq
Q
Vrrr
ϕ
φ
(11)
Here, we solve Eqs. (3)−(11) directly in real space by using a combinatorial screening algorithm proposed
by Drolet and Fredrickson[38, 39]. The algorithm consists of randomly generating the initial values of the fields
wi(r). By using a Crank-Nicholson scheme and an alternating-direct implicit (ADI) method[40], the diffusion
equations are then integrated to obtain q and q+, for 0 < s < 1. Next, the right-hand sides of Eqs. (8)−(11) are
evaluated to obtain new values for the volume fractions of blocks A, B, C, and grafted polymers.
The simulations are performed on a two-dimensional square grid Lx × Lz. The walls are presented as lines at
z = 0 (substrate) and Lz (hard surface) and Lx = 100 (in unit of a) along x-direction in all simulations. The
film thickness is Lz. And we can vary Lz to change the thickness of the thin film. The simulation is carried
out until the phase patterns are stable and the free energy difference between two iterations is smaller than 10−5,
i.e., ΔF < 10−5. It should be noted that the resulting microphases largely depend on the initial conditions.
Therefore, all the simulations are repeated at least 10 times using different random states to guarantee the
structure is not occasionally observed. We only address the thin films of ABC triblock copolymer on the
densely polymer-grafted substrate and the grafted polymers are assumed to be identical with the middle block
B. The grafting density of the grafted chains is set to
σ
= 0.2 to insure that the polymer brush is in the
dry brush regime (
σ
N1/2 > 1) and the pattern of the ABC triblock copolymer film is perfect. The
polymerization of ABC triblock copolymer is N = 100 and that of the grafted chains is same with the
copolymers, i.e., P = N = 100. The lamellar phase with compositions fA = 0.18, fB = 0.39 and fC = 0.43 in
melts[41] is studied, which is similar with the composition in experiments[35]. The interaction parameters
between different components are
χ
ijN = 35. In this work, we focus on two cases: the hard surface (opposite
to the substrate) is (1) neutral and (2) good for the middle block B.
RESULTS AND DISCUSSION
Morphology of the ABC Triblock Copolymer
Figure 1 presents the morphologies of the ABC block copolymer by increasing the film thickness with the
neutral hard surface. The morphology of the coated polymer is shown with the black color under the
morphology of ABC triblock copolymer. The microphase patterns, displayed in the form of density, are the gray,
white and black, assigned to A, B and C, respectively. Due to the higher grafting density of the coated polymer,
the brush height is h =
σ
Pa[42], therefore, the effective thickness of the ABC block copolymer is only about
hLL zz −=
eff . When the film thickness is very small, such as )22.1(25 g
eff RLL zz == , the end blocks A and C
form the alternating cylinders in the phase consisting of the middle block B and the coated polymer B. The
vertical lamellar phase occurs when the film thickness is )18.3(33 g
eff RLL zz == . With the film thickness
increasing to )67.3(35 g
eff RLL zz == in Fig. 1(c), the short end block A stays at the upper hard interface, so,
the lamellar phase forms near the hard surface. The block B forms lamellae on the coated surface due to the
thinner film thickness. At the time, the block A which is adjacent to block B cannot separate from the block
copolymer, so they form one phase. Then only the lamellar phase occurs in this case. With further increasing the
film thickness to )16.4(37 g
eff RLL zz == as shown in Fig. 1(d), the short block A also forms lamellae parallel

Self Assembly of ABC Triblock Copolymer Thin Films on a Brush-Coated Substrate 587
to the hard surface. But at the polymer coated surface, the dispersed A cylindrical phase occurs owing to the
coated polymer and the block B forming the majority. The domain size of the A cylinder phase near the coated
surface becomes large with the film thickness increasing until the lamellar phase near the coated surface occurs,
such as from Lz = 37 to 48. Another period will form when further increasing the film thickness, for example, Lz
= 50 to 60 (not shown). The lamellar phase will always form near the hard surface but the size of the cylinder
phase A near the coated surface enlarges as the film thickness increases.
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 1 Morphologies of the ABC triblock copolymer confined between the polymer coated surface and the
neutral free hard surface for fA = 0.18, fB = 0.39, fC = 0.43 at
χ
ABN =
χ
ACN =
χ
BCN = 35,
χ
ASN =
χ
BSN =
χ
CSN = 0 with different film thicknesses
a) )22.1(25 g
eff RLL zz == ; b) )18.3(33 g
eff RLL zz == ; c) )67.3(35 g
eff RLL zz == ;
d) )16.4(37 g
eff RLL zz == ; e) )9.4(40 g
eff RLL zz == ; f) )86.6(48 g
eff RLL zz == ;
Gray, white and black phases correspond to blocks A, B and C, respectively; The morphology of the
polymer coated substrate is shown in black under the morphology of the ABC triblock copolymer.
When the upper surface is good for B, such as
χ
BSN = 0 and
χ
ASN =
χ
CSN = 20, the self assembly of the
ABC triblock copolymer changes a lot although the two surfaces (one is the polymer coated surface, the other is
the free hard surface) are good for the block B. Figure 2 shows the morphologies of the ABC block copolymer
with different film thicknesses. The morphology of the coated polymer is shown with the black color under the
morphology of ABC triblock copolymer. The morphologies are more complex and show much difference
compared with the ABC block copolymer thin films in a slit[30], where the perpendicular lamellar phase easily
forms. The block B of the copolymers and the coated polymers B form one phase when the film thickness is
x
z

Z.B. Jiang et al.
588
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Fig. 2 Morphologies of the ABC triblock copolymer confined between the polymer coated surface and the selective
free hard surface for fA = 0.18, fB = 0.39, fC = 0.43 at
χ
ABN =
χ
ACN =
χ
BCN = 35,
χ
BSN = 0,
χ
ASN =
χ
CSN = 20 with
different film thicknesses
a) )96.1(28 g
eff RLL zz == ; b) )45.2(30 g
eff RLL zz == ; c) )18.3(33 g
eff RLL zz == ;
d) )67.3(35 g
eff RLL zz == ; e) )41.4(38 g
eff RLL zz == ; f) )86.6(48 g
eff RLL zz == ;
g) ).( g
eff RLL zz 35750 == ; h) )08.8(53 g
eff RLL zz == ; i) )80.9(60 g
eff RLL zz == ;
Gray, white and black phases correspond to blocks A, B and C, respectively; The morphology of the polymer coated
substrate is shown in black under the morphology of the ABC triblock copolymer.

Self Assembly of ABC Triblock Copolymer Thin Films on a Brush-Coated Substrate 589
small )96.1(28 g
eff RLL zz == as shown in Fig. 2(a). The end blocks A and C form alternating phases along the
film, which is consistent with the experimental results[35]. With the film thickness increasing to
)45.2(30 g
eff RLL zz == in Fig. 2(b), the short block A will dissolve into the adjacent block B, and the lamellar
phase forms. When )18.3(33 g
eff RLL zz == in Fig. 2(c), the block B stays on the free surface and the block A
forms the cylinder phase immersed in the B phase near the free surface. The block B in the copolymers and the
coated polymers B form one phase on the other brush coated surface. So the cylindrical phase A forms between
the two surfaces and distributes on the lamellar phase C. With the film thickness further increasing, the
cylindrical phase A on the upper hard surface forms and the domain size of the cylindrical phase A increases a
little, but the domain of the phase A on the other brush coated surface clearly increases, which is shown in
Figs. 2(d) and 2(e). When the film thickness comes to )86.6(48 g
eff RLL zz == , another period begins, see
Figs. 2(f)−2(i). The cylindrical phase A on the hard surface and on the polymer coated surface enlarges with the
film thickness increasing. We can vary the film thickness of the film to obtain the different domain size of the
cylindrical A phase on the two sides of the film. Although the two surfaces (one is the hard surface and the other
is the polymer brush coated surface) of the film is good for the middle block B of the ABC triblock copolymer,
the vertical lamellae phase is not always stable compared with the ABC triblock copolymer film confined
between the two hard surfaces which are good for the middle block B[30].
In general, the vertical lamellar phase is stable when the effective thickness is very small for the case of the
neutral hard surface; the short end block will accumulate near the neutral hard surface when the effective film
thickness is greater than (3−4)Rg. But the middle block B accumulates on the selective surface for block B,
which leads to the block A forming the cylindrical phase immersed in the B phase near the free hard surface.
The phase A forms the cylinder at the polymer coated surface, and the domain size will vary with the film
thickness. The lamellar phase parallel to the film always forms in the middle. The number of the periods
increases with the film thickness increasing.
When the cylinder phase A near the brush coated surface occurs, we can note the rippled structure of ABC
block copolymer near the polymer grafted surface due to the soft surface of grafted polymer, see Figs. 1(d), 1(e),
2(d), 2(e) and 2(h). The corresponding structure of the grafted polymer is also rippled. In order to clearly see the
rippled distribution of the grafted polymers, we give the distribution sum of the grafted polymers along the z-
direction as a function of x, which is shown in Fig. 3. From the figure, we can see that the distribution of the
grafted polymers will change a lot near the interface between the block copolymers and the grafted polymers to
Fig. 3 Density sum of the grafted polymers along z-direction as a function of x for fA = 0.18,
fB = 0.39 and fC = 0.43 at
χ
ABN =
χ
ACN =
χ
BCN = 35
a) Neutral free hard surface,
χ
ASN =
χ
BSN =
χ
CSN = 0; b) Good for block B,
χ
BSN = 0,
χ
ASN =
χ
CSN = 20; The density sum is the integral in the z-direction of the volume fraction of the
polymer brush for a fixed x.

Z.B. Jiang et al.
590
minimize the interfacial energy. The structure of the grafted polymers can be tailored with the film thickness
varying. It can be the flat or rippled structure. The rippled structure in the brush forms when the cylindrical
phase A is near the interface between the block copolymers and the grafted polymers, which is also observed in
the AB diblock copolymer confined between the polymer brush-coated surfaces[36, 37]. The results show that the
grafted polymers serve as a soft surface for self assembly of the ABC triblock copolymer. The frustration that
occurs at the non-tailored surface disappears or decreases in this case.
Free Energy Analysis
In the following, we provide insight into the entropic and the enthalpic free energies of the system. Figure 4
shows the entropic free energy −TS (spheres), the enthalpic free energy U (squares) and the total free energy F
(triangles) (F = U
−
TS) of the system as a function of the reduced film thickness g
eff /RLz. With the film
thickness decreasing, the entropic free energy and the enthalpic free energy increase. But there are shallow
sharps when one period transfers to another period, such as g
eff )32( RLz−≈ , 7.5Rg, 11Rg for the neutral free
surface and g
eff RLz2≈, 6Rg, 10Rg for the selective free surface for the middle block B. Due to the grafted
polymer serving as a hydrophilic part (identical with the block B) of the block copolymer, the large energy
fluctuation is suppressed in our system as compared with the block copolymer confined in the film only by hard
surfaces.
But if the free hard surface is selective for the end block A or C, the lamellar phase forms on the hard
surface. The cylindrical phase A is still stable on the brush-coated surface.
Fig. 4 Enthalpic free energy U (squares), entropic free energy −TS (spheres), and total free energy F
(triangles) of the system for fA = 0.18, fB = 0.39 and fC = 0.43 at
χ
ABN =
χ
ACN =
χ
BCN = 35
a)
χ
ASN =
χ
BSN =
χ
CSN = 0; b)
χ
BSN = 0,
χ
ASN =
χ
CSN = 20
CONCLUSIONS
The self assemblies of ABC triblock copolymer thin films on a densely brush-coated substrate were investigated
by using the self-consistent field theory. The coated polymers are identical with the middle block B of the ABC
triblock copolymer. The middle block B and the coated polymer form one phase together and the alternating
phase A and phase C occur when the film is very thin either for the neutral or selective upper hard surface. The
lamellar phase parallel to the surfaces is stable on the neutral hard surface. Interestingly, the short block (A in
the paper) always stays on the free hard surface when the effective film thickness larger than (3−4)Rg. But when
the hard surface is good for the middle block B, the phase A forms cylinders staying on the interface between
the phase B and phase C near the free surface. The cylindrical phase A easily forms on the polymer coated
surface for either neutral or selective hard surfaces. The cylindrical phase can be controlled, and the domain size
can be tailored by varying the width of the slit. The rippled structure forms when the cylindrical phase exists

Self Assembly of ABC Triblock Copolymer Thin Films on a Brush-Coated Substrate 591
near the interface between grafted polymers and block copolymers. Due to the existence of the hydrophilic
polymer coated surface, the large energy fluctuation existing in the film confined by two hard surfaces
disappears. These observations demonstrate that enthalpic interactions, in addition to entropic considerations,
can play a major role in forming the above complex morphologies.
The results are helpful for designing the functional nanopattern of the film. For example, the short
functional block A can be added to the diblock BC block copolymer, and the functional surface of the short
block A on the film can easily forms in the case for the neutral hard surface. When the hard surface is good for
the middle block B, the functional beads coming from the short block A occur on the surfaces and their size can
be controlled by tailoring the film thickness. Therefore, it is very useful for designing and realizing the
functional thin films besides the structural ones by adding the functional short block A to the BC diblock
copolymer.
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