J Polym Res (2012) 19:9910
DOI 10.1007/s10965-012-9910-9
ORIGINAL PAPER
MesoDyn simulation study on the phase morphologies
of miktoarm PEO-b-PMMA copolymer induced
by surfaces
Dan Mu · Jian-Quan Li · Song Wang
Received: 16 November 2011 / Accepted: 11 June 2012 / Published online: 30 June 2012
© Springer Science+Business Media B.V. 2012
Abstract The compatibility of six groups 12 mik-
toarm poly(ethylene oxide)-block-poly(methyl methacry-
late) (PEO-b-PMMA) copolymers is studied at 400 K via
mesoscopic modeling. The values of the order parameters
depend on the architectures of the block copolymers deeply,
compared with their chain length. Furthermore, the values
of order parameters of the copolymer in the same group are
the same. A study of plain copolymers induced by 18 neutral
surfaces shows that the microscopic phase is influenced by
not only the peculiarities of the inducing surface, but also the
architecture of copolymers. The degree of surface roughness
plays the most significant role on changing phase separation,
the rougher the surface, the higher ordered the microscopic
phase. However, the 23141 and 23241-type copolymers
which are both PEO-rich composition, presents microscopic
phase separation as peculiar lamallae phase morphologies
induced by every surfaces, included their plain copolymers.
Keywords Miktoarm PEO-b-PMMA copolymer ·Lamallae phase morphologies · Inducing surface
D. Mu (B)
College of Chemistry Chemical Engineering and Material
Science, Zaozhuang University, Shandong 277160, China
e-mail: [email protected]
J.-Q. Li
Opto-Electronic Engineering College, Zaozhuang University,
Shandong 277160, China
S. Wang
Institute of Theoretical Chemistry, State Key Laboratory of
Theoretical and Computational Chemistry, Jilin University,
Changchun 130023, China
Introduction
Because of the inherent beauty and potential technological
applications, applied the molecular self-assembly of block
copolymers to form the nanostructured materials is an ac-
tive area of research. Thin films of self-organizing diblock
copolymers may be suitable for semiconductor applica-
tions since they enable patterning of ordered domains with
dimensions below photolithographic resolution over wafer-
scale areas [1]. Block copolymers are known to gener-
ate nanoscale microdomains by microphase separation, if
they are annealed at a temperature lower than their order-
disorder transition temperatures [2]. Recently, thin films
formed by block copolymer with well defined nanostruc-
tures have received considerable attention for their potential
nano-fabrication applications [3–11]. In these applications,
controlling the morphology of the block copolymer thin
film via adjusting the influencing factors to obtain ordered
phase-separated microdomain, has significant and potential
meaning.
PEO and PMMA are both important polymers for syn-
thesis and applications in a variety of engineering and
biomedical areas [12–14]. The study of PEO/PMMA blends
is of interest because of the semicrystalline nature of PEO,
the weak interactions between these two polymers, and
their large difference in the glass transition temperature
(Tg), which make such blends a complex system. Our
former paper clarified the conflicting conclusions drawn
from different laboratories and from different techniques
successfully from theoretical view, we found that the blends
tend to undergo phase separation at higher temperature,
such as 400 K, on the contrary, the PEO/PMMA blends are
miscible at lower temperatures [15].
The amphiphilic graft and block copolymers made of
PMMA and PEO blocks have received increasing atten-
Page 2 of 8 J Polym Res (2012) 19:9910
tions for the potential applications in modification of ker-
atoprosthesis [16], drug carriers [17] and biomedical ma-
terials [18, 19]. The study of PEO-b-PMMA copolymer
is of interest because of its crystallization behavior, and
Sun et al. had reported that the crystallization rate and
the degree of crystallinity decreased by an increase of
PMMA content [20], which means the PEO block in PEO-
b-PMMA copolymer is prone to crystallize. Furthermore,
there haven’t been any reports about the inducing effects of
surfaces on the miktoarm PEO-b-PMMA copolymers. We
gained some inspiring results in this paper, which can be
applied into nano-fabrication to improve its function.
Simulation method and model construction
Mesoscale structures are of utmost importance during the
production processes of many materials, such as polymer
blends, block copolymer systems, surfactant aggregates in
detergent materials, latex particles and drug delivery sys-
tems. Mesoscopic dynamics models are receiving increasing
attention, as they form a bridge between microscale and
macroscale properties [21–24]. As a useful simulation tech-
nique for fluids, MesoDyn has been successfully applied to
study the microphase separation of block copolymers in our
former researches [15, 25–28].
Our simulation processes were all carried out with the
MesoDyn package in the Materials Studio commercial soft-
ware provided by Accelrys on an SGI workstation. Meso-
Dyn is a state-of-the-art mesoscale simulation program. It
utilizes a dynamic variant of mean-field density functional
theory with Langevin-type equations to investigate polymer
diffusion, providing a coarse-grained method for the study
of complex fluids, their kinetics, and their equilibrium struc-
tures at large length and time scales. The thermodynamic
forces are found via mean-field DFT, using the Gaussian
chain as a model. The coarse-grained Gaussian chain con-
sists of beads with equal lengths and equal volumes. With
Table 1 Details of PEO/PMMA blending models and their input
parameters of MesoDyn at 400 K
Symbol wt% Input
Number molar ratio of PMMA parameter
1 1/6 93.16 0.00266
2 1/4 90.09 0.00217
3 1/3 87.20 0.00243
4 1/2 81.96 0.00197
5 1/1 69.43 0.00184
6 2/1 53.18 0.00636
7 3/1 43.09 0.00217
8 4/1 36.22 0.00878
9 6/1 27.46 0.01094
10 8/1 22.11 0.00217
a1 b1
b2a2
b3a3
Fig. 1 The schematic miktoarm PEO-b-PMMA copolymer models
used in this study. The black particles represent the PEO component
denoted as A, while the white particles the PMMA component denoted
as B
time evolution, the free energy of the system results in
no discernible changes, the phase separation is considered
completed.
We have obtained the representative chain lengths of
PEO and PMMA chain and the relevant parameters in our
former work [15, 27], and they are list in Table 1. Therefore,
the block copolymer chains are constructed by PEO (de-
noted as “A”) and PMMA (denoted as “B”) components as
A(A4B6)4, A5(B6)2, A3[A(B6)2]2, B(B5A5)4, B6(A5)2 and
B4[B(A5)2]2, named as 11111, 12112, 13114, 21111, 22121
Table 2 The molecular information of miktoarm PEO-b-PMMA
copolymer
Group Molar ratio Scheme
number of A5 to B6 Architecture Symbol in Fig. 1
Group 1 1:1 A(A4B6)4 11111 a1
1:1 A(A9B12)4 11211
Group 2 1:2 A5(B6)2 12112 a2
1:2 A10(B12)2 12212
Group 3 1:4 A3[A(B6)2]2 13114 a3
1:4 A8[A(B12)2]2 13214
Group 4 1:1 B(B5A5)4 21111 b1
1:1 B(B11A10)4 21211
Group 5 2:1 B6(A5)2 22121 b2
2:1 B12(A10)2 22221
Group 6 4:1 B4[B(A5)2]2 23141 b3
4:1 B10[B(A10)2]2 23241
J Polym Res (2012) 19:9910 Page 3 of 8
Table 3 Information of “ci”, “co”, “gra” and “rg” series surfaces
Type Included Example Scheme Mask type Name explanation
surfaces
ci-xxx ci-444, ci-444 S1 Semicircular balls Four semicircular balls in four
ci-882 surface sides, the radius is 4 nm
co-4xx co-444, co-444 S2 Equal spaced cubic Divided by equal space into four
co-448, columns parts to form two columns in four
co-4412, surface sides, the height is 4 nm
co-4432
co-8xx co-884, co-884 S3 Equal spaced cubic Divided by equal space into eight
co-888, columns parts to form four columns in four
co-8812, surface sides, the height is 4 nm
co-8832
gra-xxx gra-444, gra-444 S4 The same widths, Divided by equal space into four
gra-888 gradually increasing parts in face-to-face sides to four
height columns, small surfaces with gradually
monodirectional increasing height, the highest
asymmetric height is 4 nm
gra-2(xxx) gra-2(444), gra-2(444) S5 The same as gra-xxx type, With the same two symmetric parts
gra-2(448), but monodirectional as gra-444 surface
gra-2(888) symmetric
rg-xxx rg-442, rg-442 S6 Similar as gra-xxx type, The highest height of both face-to-face
rg-884, but bidirectional symmetric sides is 4 nm, the divided surface
rg-16168 in one semi-section is two part
and 23141. Corresponding to these six schematic models in
Fig. 1, they are a1, a2, a3, b1, b2 and b3, respectively. The
latter three models are the component exchange between
“A” and “B” from the corresponding former three. When
double large these six models, we can gain other six mod-
els, A(A9B12)4, A10(B12)2, A8[A(B12)2]2, B(B11A10)4,
B12(A10)2 and B10[B(A10)2]2, named as 11211, 12212,
13214, 21211, 22221 and 23241, respectively. Table 2 lists
the grouping, molar ratio of blocks, molecular architecture,
symbol and corresponding scheme in details.
We designed four series patterned surfaces as substrates,
designated as “ci”, “co”, “gra” and “rg” series, to study
its inducing effects on the compatibility of PEO-b-PMMA
copolymers. The “ci” series of planes used half-spheres with
different radii as a mask that simulated different degrees
of surface roughness. The “co” series had equally spaced
cubic columns as a mask. The columns had different sizes
and heights to simulate different degrees of surface rough-
ness. The “gra” series were planes with different widths to
simulate different degrees of surface roughness. The mask
was generated by gradually increasing the column height
across the plane, so that it resembled stairs viewed side
on. In addition, monodirectional asymmetric planes, such
as gra-444 and gra-888, and monodirectional symmetric
planes, such as gra-2(444), gra-2(448) and gra-2(888), were
considered. The “rg” series were bidirectional symmetric
planes originating from monodirectional symmetric planes,
as used in the “gra” series. The details about these six
Fig. 2 The scheme of six
representative inducing surfaces
Page 4 of 8 J Polym Res (2012) 19:9910
types of designed surfaces were listed in Table 3, and six
representative surfaces (ci-444, co-444, co-884, gra-444,
gra-2(444) and rg-442) were showed in Fig. 2 as schemes
(S1, S2, S3, S4, S5 and S6, respectively).
Simulation results and discussion
We start the simulations by placing the block copolymers
randomly in the simulation box, followed by an equilibra-
tion of 10 ms until the free energy density (RT/Volume)
reaches a relative stable value. The time step is set as 50 ns
to stabilize the numerical calculations. The noise parameter
value is 75.002 by default, is used for the numerical speed
and stability. The adopted grid dimensions are 32 × 32 × 32
nm3, and the size of the mesh over which density variations
are to be plotted in MesoDyn length 1 nm.
The Flory-Huggins interaction parameter, χ data of ten
different compositions which can cover most composition at
400 K [15], and these data can be applied as the input para-
meters to deal with the miktoarm PEO-b-PMMA copolymer
in this work. The connection between the microscale and the
mesoscale is as follows:
IPM = χab RT,
where the parameter χab is calculated by atomistic simula-
tion for each blend composition at different temperature. Ris the molar gas constant, 8.314 J·mol
−1 · K−1
, and T is the
simulation temperature. IPM is the abbreviation of “Input
Parameter of MesoDyn” used to describe the interaction
between beads [15].
The order parameter, P, is defined as the average volume
of the difference between local density squared and the
overall density squared, as given by the equation
Pi = 1
V
∫V
[η2
i (r) − η2
i
]dr,
where ηi is the dimensionless density (volume fraction) of
species i. The larger the value of P, the greater the phase
separation. A decrease in P indicates better compatibility or
miscibility, and the polymer phases mix more randomly.
We define a new parameter to describe the inducing effect
of being induced by surfaces. The order parameter value of
every miktoarm PEO-b-PMMA copolymer not introduced
by inducing surface effects (“plain”) is named as “a”, in
addition, the order parameter value of the corresponding
copolymer with inducing effect is named as “b”. The value
of (b−a)/a is defined as variation rates of order parameter
(VROP for abbreviation). By comparing the VROP values,
we can figure out the effective kind of inducing surfaces
on changing the phase morphology of miktoarm PEO-b-
PMMA copolymer. The larger the value of VROP, the
greater the inducing influence.
Modeling plain miktoarm PEO-b-PMMA copolymer
Figure 3 shows the P values of the 12 plain miktoarm PEO-
b-PMMA copolymers at 400 K. There are several features
in this figure that are worth noting:
(1) The P values of PEO-b-PMMA copolymers in the
same group at 400 K are the same, that is, P11111 =P11211 in Group 1, P12112 = P12212 in Group 2,
P13114 = P13214 in Group 3, P21111 = P21211 in Group
4, P22121 = P22221 in Group 5 and P23141 = P23241
in Group 6. Combined with the iso-density pictures
on the top, it suggests that when the copolymer with
the same architecture, long or short-chain copolymer
could presents the same mesoscale phase morphology.
(2) The order of P is P23141 = P23241 > P22121 = P22221 >
P21111 = P21211 = P11111 = P11211 > P12112 = P12212 >
P13114 = P13214, which can be converted into PGroup6 >
PGroup5 > PGroup4 = PGroup1 > PGroup2 > PGroup3. The
block ratio (PEO to PMMA) of them is 4:1, 2:1,
1:1, 1:1, 1:2 and 1:4, respectively, the more PEO
component in the copolymer, the higher the P value.
The composition of 11111 and 21111-type copolymer
is the same, both having four A5 and four B6
segments, though they have opposite block structure.
However, the compositions of 13114 and 23141-type
copolymer are different, 13114-type copolymer has
one A5 and four B6 segments, 23141-type copolymer
has four A5 and one B6 segments. Therefore, the
situation of P values of these two opposite block
copolymers are different.
(3) The remarkable high P values of Group 6 at 400
K, which is higher than 0.01, and the ordered iso-
density surfaces displayed both reveal its microscopic
phase separation. It can be explained from the special
architecture of 23141 and 23241-type copolymers in
Fig. 3 P values of 12 miktoarm PEO-b-PMMA copolymers at 400
K. Red represents PEO component; green PMMA. The iso-density
surfaces of these copolymers at 400 K are displayed at the top
J Polym Res (2012) 19:9910 Page 5 of 8
Group 6. They both are 4:1 (PEO to PMMA) block
ratio which have the highest PEO component content
in the 12 copolymers, when the temperature becomes
higher, the easier for the chain to move, combined
the nature of PEO block tending to crystallize [20],
then the PEO-rich region could be largened, further
microscopic separation could occur.
Modeling miktoarm PEO-b-PMMA copolymer induced
by surfaces
Subfigures a1, a2, a3, a4 and a5 in Fig. 4 shows the P values
for the 12 miktoarm PEO-b-PMMA copolymers induced by
10 kinds of surface at 400 K, respectively. Subfigures b1,
b2, b3, b4 and b5 show the corresponding VROP values for
these induced copolymers. A reference line is drawn through
R = 1 in subfigures b1, b2, b3, b4 and b5. When an VROPvalue lies above this line, the doping can be considered
to have a reinforcing effect; otherwise, the doping can be
considered to have a weakening effect. Thus, the main ob-
jective of modeling these cases is to determine the effective
surfaces that exerts the most influence on microscopic phase
separation. In addition, we also can explore which type of
miktoarm copolymer suffers the most with such inducing
effect on changing the phase morphology. The following
features of the plots are noteworthy:
(1) The P values of the copolymers in the same group with
the same surface’s inducing effect are also the same
in subfigure a1, a2, a3, a4 and a5. It reveals that the
architecture is more important than the chain length at
400 K. Furthermore, for the copolymers with the same
1:1 (PEO to PMMA) block ratio, that is, 11111, 11211,
21111 and 21211-type copolymers, their P values are
the same.
(2) The general change tendency of P induced by the
same surface effect is P23141 = P23241 > P22121 =P22221 > P11111 = P11211 = P21111 = P21211 >
P12112 = P12212 > P13114 = P13214 at 400 K. How-
ever, the change tendency of the copolymers
induced by co-4412, co-4432, co-8812 and
co-8832 surfaces is different from it, that is,
P23141 = P23241 > P13114 = P13214 > P12112 = P12212 >
P11111 = P11211 = P21111 = P21211 > P22121 = P22221
at 400 K; in addition, the change tendency
of the copolymers induced by rg-442, rg-884
and rg-16168 surfaces is also different, that is,
P23141 = P23241 > P22121 = P22221 > P11111 = P11211 =P21111 = P21211 > P13114 = P13214 > P12112 = P12212
at 400 K. The reason leading to such differences
in the relationship above lies in the particularity of
the inducing surfaces. The 23141 and 23241-type
copolymers both are 4:1 (PEO to PMMA) block ratio
which have the highest PEO component content in the
12 copolymers, whose property depends on property
of PEO. For the copolymers with 1:1 (PEO to PMMA)
block ratio, they have equal opportunity to meet the
same block during mixing process compared with
other type copolymers.
(3) The top two largest P values for the copolymers in-
duced by surfaces are Pco−8832 and Pco−4432, except
23141 and 23241-type copolymer, whose top two
are Pco−8812 and Pci−882. It is the result from the
difference in PEO content. However, Pgra−2(888) and
Prg−16168 present the largest value in “gra” and “rg”
series inducing surface.
(4) The VROP values of the copolymers in the same group
with the same surface’s inducing effect are also the
same in subfigure b1, b2, b3, b4 and b5.
(5) The order of VROP is totally different from the
order of P for the copolymers induced by the
same kind of surface. For co-448, co-4412, co-888,
co-8812, gra-888, gra-2(444), gra-2(888), rg-442
and rg-884 surfaces, the order is VROP13114 =VROP13214 > VROP1 2112 = VROP12212 >
VROP1 1111 = VROP11211 = VROP21111 =VROP21211 > VROP23141 = VROP2 3241 >
VROP22121 = VROP22221; for co-4432, co-
8832, gra-444 and rg-16168 surfaces, the order is
VROP13114 = VROP132 14 > VROP12112 =VROP1 2212 > VROP11111 = VROP11211 =VROP21111 = VROP21211 > VROP2 2121 =VROP2 2221 > VROP23141 = VROP23241; for
co-444, co-884 and gra-2(448) surfaces, the order
is VROP13114 = VROP13214 > VROP12112 =VROP1 2212 > VROP23141 = VROP23241 >
VROP11111 = VROP11211 = VROP211 11 =VROP212 11 > VROP221 21 = VROP2 2221;
for ci-444 surface, the order is VROP12112 =VROP12212 > VROP13114 = VROP1 3214 >
VROP23141 = VROP2 3241 > VROP11111 =VROP11211 = VROP21111 = VROP21 211 >
VROP22121 = VROP22221; for ci-882 surface, the
order is VROP23141 = VROP23241 > VROP12112 =VROP12212 > VROP111 11 = VROP11211 =VROP21111 = VROP212 11 > VROP22121 =VROP22 221 > VROP13114 = VROP13214.
Furthermore, the VROP values are higher than 1,
which means the inducing surface play a reinforcing
effect on the cases as follows: 13114, 13214, 12112
and 12212-type copolymers induced by co-4432
surface; 13114, 13214, 12112 and 12212-type
copolymers induced by co-8812 surface; 13114,
13214, 12112, 12212, 11111, 11211, 21111, 21211,
22121, 22221, 23141 and 23241-type copolymers
induced by co-8832 surface. In addition, there is only
Page 6 of 8 J Polym Res (2012) 19:9910
Fig. 4 P and VROP values of 12 miktoarm PEO-b-PMMA copoly-
mers induced by 18 kinds of surfaces at 400 K, respectively. The iso-
density surface pictures of PEO-b-PMMA induced by ci-882 surface
is displayed in subfigures a1, a2 by co-4432 surface, a3 by co-8832
surface, a4 by gra-2(888) surface, and a5 by rg-16168 surface; the iso-
density surface pictures of PEO-b-PMMA induced by ci-444 surface is
displayed in subfigures b1, b2 by co-448 surface, b3 by co-888 surface,
b4 by gra-888 surface, and b5 by rg-442 surface. Red represents PEO
component; green PMMA
J Polym Res (2012) 19:9910 Page 7 of 8
23141 and 23241-type copolymer induced by co-4432
present negative values in VROP.
(6) The P and VROP values of co-4432, co-8832, gra-888,
gra-2(888) and rg-16168 display nearly the most high-
est in “co-4xx”, “co-8xx”, “gra-xxx”, “gra-2(xxx)” and
“rg-xxx” series surface except its inducing effect on
some copolymers. Therefore, the rougher the surface,
the higher the P and VROP value.
(7) The inserted iso-surface pictures is different from
our previous works. For the inducing effects of
doped nanoparticles in PEO/PMMA blends [15], PS-
b-PMMA copolymer [25] or PEO-b-PMMA copoly-
mer [28], the iso-surfaces were almost presented as
cubic phase morphologies. In addition, less cases dis-
played as lammellar phase morphologies for PEO/
PMMA blends [27] and PS-b-PMMA copolymer [26]
induced by surfaces. In contrast, the lammellar phase
morphologies has uniform interval distance between
layers.
Special miktoarm PEO-b-PMMA copolymer: 23141 and
23241-type
Owing to the dramatically high P data for 23141 and 23241-
type copolymers induced by surfaces, it is necessary to
investigate such special miktoarm PEO-b-PMMA copoly-
mer deeply. Owing to the same P, VROP and phase mor-
phologies of these two copolymers, we take the 23141-type
copolymer for example to discuss further.
We can detect the particularity in the architecture and
property of 23141-type copolymer, whose scheme is the
subfigure b3 in Fig. 1: firstly, the ratio of PEO to PMMA
block is 4:1, which has the highest PEO percentage of
Fig. 5 Iso-density surfaces of
23141-type PEO-b-PMMA
copolymer induced by 18
surfaces at 400 K. Redrepresents PEO component;
green PMMA
Page 8 of 8 J Polym Res (2012) 19:9910
12 copolymers; secondly, each joint has two PEO blocks and
four PEO blocks in total, which could makes this copoly-
mer has much more opportunity to “meet” the same PEO
blocks, further form PEO-rich region; thirdly, the PMMA
block is flexible and lying in the middle of copolymer,
this can increase the “meeting opportunity” during adjusting
its placement and orientation; fourthly, the semicrystalline
nature of PEO could make it congregates easily, especially
at higher temperature such as 400 K.
Figure 5 displays the iso-density pictures induced by 18
surfaces at 400 K, respectively. We can seen the peculiar
microscopic phase separation clearly. The cases present
local phase separation due to the inducing effect of surfaces,
no matter what type of inducing surfaces.
Conclusions
We study about the phase morphologies of plain miktoarm
PEO-b-PMMA copolymers via MesoDyn simulation. It
shows that the values of P in the same group are the same at
400 K. The architecture of copolymers is the crucial factor
to determine the P values, but the chain length has little
relation with the P values.
We investigate the plain miktoarm PEO-b-PMMA
copolymers induced by 18 surfaces via mesoscopic simu-
lations. The simulation results show that introducing such
inducing surfaces is a good way of improving the degree of
order of the microscopic phases morphologies. No matter it
is a reinforcing or a weakening effect, the co-8832 and co-
4432 inducing surfaces exerts the top two most remarkable
influence on changing the phase morphologies of the mik-
toarm PEO-b-PMMA copolymers, except 23141 and 23241-
type copolymer. From the iso-surface pictures we can see
that the 23141 and 23241-type copolymers doped with no
matter which kind of inducing surfaces, they all present
special lamallae phase morphologies at 400 K, included its
plain copolymer.
Acknowledgements This work is supported by the Science-
Technology Foundation for Middle-Aged and Young Scientists of
Shandong Province (BS2010CL048), a Shandong Province Higher
School Science & Technology Fund Planning Project (J10LA61), and
a Zaozhuang Scientific and Technological Project (200924-2).
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