asymmetric diblock copolymer thin film confined in a slit: microphase separation and morphology

556

Asymmetric Diblock Copolymer Thin Film Confined ina Slit: Microphase Separation and Morphology

Jie Feng, Honglai Liu,* Ying Hu

Department of Chemistry, East China University of Science and Technology, Shanghai 200237, ChinaFax: +86-21-64252485; E-mail: [email protected]

Keywords: cell dynamic system method; diblock copolymers; Monte Carlo simulation; phase separation; thin films;

1 IntroductionThe continuing demand for smaller, faster and densermicroelectronic systems is stimulating material scientiststo seek new methods for preparing nanosized struc-tures.[1–4] In general, features greater than 30 nm in sizeare routinely produced by photolithography or electronbeam lithography techniques. For those less than 30 nm,the traditional techniques fail. On the other hand, duringthe past decade, it has appeared that ordered diblockcopolymers would seem ideal as lithography templates[1]

for nanomaterials.Because the chemically distinct polymer blocks A and

B are joined end-to-end, phase separation in the tradi-tional sense is impossible for AB-diblock copolymers.Instead, microphase separation takes place[5] causingdense periodic patterns with feature sizes less than 30 nmto form; even features than 10 nm in size can be preparedby adjusting the interaction energy and the length of thechains. In practice, diblock copolymers are usually con-

fined between two plates for the sake of controlling themorphology and uniformity of microdomain. By adjust-ing the film thickness, segment composition and interac-tion between blocks and walls, one can obtain variousmicrodomain morphologies. At present, most of experi-mental studies have been carried out on symmetricdiblock copolymers, for instance, in the work of Manskyet al.,[6] Lambooy et al.[7] and Konneripalli et al.[8] Using astrong electric field, exceeding 30 kV N cm–1, Morkvel etal.[9] induced the cylinder microphase of an asymmetriccopolymer to align parallel to the field lines. Recently,Stone et al.[10] studied the self-assembling of sphere andcylinder microphases near walls below the order–disordertransition for asymmetric diblock copolymers. On theother hand, Geisinger et al.11] performed Monte Carlosimulations for symmetric diblock copolymer thin filmsconfined between two identical, hard, homogeneous, andparallel surfaces, where the copolymer had a repulsiveinteraction with one of the two blocks. Wang et al.[12] also

Full Paper: Microphase separation and morphology ofasymmetric diblock copolymer (f = 0.4) thin films con-fined in a slit with surfaces neutral or attractive towardsblock A or block B were studied by the cell dynamic sys-tem method (CDS). The size effect in CDS calculationswas carefully investigated. For asymmetric copolymers,the size effect is important even in the case of attractivewalls. Not only must we use boxes with larger sizes in theX- and Y-directions, the size is also dependent on the filmthickness. In contrast, for symmetric copolymers, the sizeeffect is not serious when we adopt attractive plates. Var-ious microdomain morphologies including regular lamel-lae adjacent to the surfaces, mesh-like layers with nano-sized spheres dispersed in a matrix of block A, and flexu-ous cylindrical phases are found in this work. A series ofconditions we can control, such as the chemical composi-tion of the copolymer, the thickness of the film, the selec-tive interactions between plates and blocks as well as theirstrength, all make the potential technology more adapta-

ble. To test the reliability of the CDS method, the resultsare compared with those from dynamical density func-tional theory and Monte Carlo simulation.

Macromol. Theory Simul. 2002, 11, No. 5 i WILEY-VCH Verlag GmbH, 69469 Weinheim 2002 1022-1344/2002/0506–0556$17.50+.50/0

Morphology of domain A of asymmetric copolymers (f = 0.4)confined between two A-attractive walls (HA = 0.2).

Macromol. Theory Simul. 2002, 11, 556–565

Asymmetric Diblock Copolymer Thin Film Confined in a Slit: Microphase Separation ... 557

studied symmetric diblock copolymer thin films confinedbetween two asymmetric, inhomogeneous walls viaMonte Carlo simulation based on a lattice model. Gener-ally, reports on asymmetric diblock copolymers are com-paratively rare.Most theoretical studies have been based on the time-

dependent Ginzburg–Landau equation (TDGL).[13, 14]

Besides TDGL, the cell dynamical system method (CDS)proposed by Oono and co-workers[15–17, 21] is also an effi-cient way to describe microphase separation on the meso-scale. Marko[18] applied CDS to the study of phase separa-tion of polymer blends confined by walls in two dimen-sions. Huinink et al.[19] used a dynamic density functionaltheory (DDFT) for polymeric systems to simulate the for-mation of microphases in a block copolymer melt (f = 1/3).In our previous work,[20] we studied symmetric diblockcopolymer thin films in three-dimensions and confinedbetween walls. When the walls are neutral, a parallelordered lamellar structure only exists over a short range,while an irregular microdomain morphology occurs overthe whole region. When directional quenching is appliedor the walls are attractive to one of the blocks, a periodicallamellar structure of alternating A- and B-rich layersoccurs over the whole film. Changing the space betweenthe two plates and the strength of interaction will influencethe period and arrangement of the lamellae. Furthermore,using boxes of extremely small sizes in the X- and Y-direc-tions will lead to incorrect results.In this work, we report results for asymmetric diblock

copolymer (f = 0.4) confined in a slit with two neutral orattractive plates using CDS. The paper is organized as fol-lows: in Section 2, we briefly describe the model. In Sec-tion 3, we discuss the size effect on the asymmetric systemin detail. Then we present main results on microdomainmorphology under various wall conditions and corre-sponding order parameter distributions in section 4, 5 and6. To test the reliability, we compare the results from theCDS with those from dynamical density functional theoryby Huinink et al.[19] and with those by Monte Carlo simula-tions in Section 7. Finally, a short summary is given.

2 Model in CDSAs presented by Oono and Puri.[15, 16] the CDS algorithmis written:[17]

w(x,y, z, t + 1) = Q [w(x,y, z, t)] – ppQ [w(x,y, z, t)]

– w(x,y, z, t)PP – a[w(x,y, z, t) – 1 + 2 f ] (1)

where w(x,y,z, t) = uB(x,y,z, t) – uA(x,y,z, t) is a local orderparameter, uA(x,y,z, t) and uB(x,y,z, t) are local concentra-tions of component A and component B, respectively, andf = NA/(NA +NB) is the molecular mass ratio of subchain A,and a = 0.02.Q [w(x,y,z, t)] is defined as:

Q[w(x,y, z, t)] = A tanh[w(x,y, z, t)] + D [ppw(x,y, z, t)PP

– w(x,y, z, t)] (2)

where A is a phenomenological parameter inversely pro-portional to temperature and D is a diffusion parameter.A periodic boundary condition is applied in the X- and Y-directions in this work. Since hard walls are placed atz = 0 and z = LZ + 1, the boundary condition in the Z-direction is introduced as follows[18]:

w(x,y,0, t) = w(x,y,1, t), w(x,y,LZ + 1, t) = w(x,y, z,Lz, t)

Q[w(x,y,0, t)] = Q[w(x,y,1, t)],

Q[w(x,y,LZ + 1, t)] = Q [w(x,y,LZ, t)] (3)

If the walls are attractive plates, algorithm is modifiedas:

Q[w(x,y, z, t)] = f (w(x,y, z, t)) + D[ppw(x,y, z, t)PP

– w(x,y, z, t)] – s(z)6 ln (A) (4)

s(z) = Hi6ui6dz, 1 or Lz (5)

Here, i denotes the attractive bead, A or B, Hi is thestrength of interaction between the walls and the attrac-tive bead, and dz, 1 or Lz is a Kronecker delta.

3 The Effect of Box Size in CDSAs we have mentioned in our previous work,[20] althoughthe periodical boundary condition is adopted to mimic apractical system, the effect of size in CDS has rarely beeninvestigated in the literature. We found that the size effectis serious for symmetric copolymers in a slit with neutralwalls in the X- and Y-directions. However, this restrictionis relaxed when the walls are attractive. Results for smal-ler boxes are the same as those for bigger box in the lattersituation.However, this is not the case for asymmetric copoly-

mers. As shown in Figure 1, when f = 0.4 and the wallshave a selective attraction towards block A, HA = 0.2, afive-layer structure is formed. Except for the two A-richlayers adjacent to the plates and the two B-rich layersnext to them, the intermediate layer shows a differentmorphology when differently sized boxes are adopted. Itexhibits parallel straight columns in a box of LX = LY = LZ

= 15, but regular mesh-like phase when the box size isexpanded to 40 in the X- and Y-directions. Further expan-sion will not cause much change.Figure 2 shows the morphology of the same diblock

copolymers (f = 0.4) confined between two surfaces asshown in Figure 1, but with attraction towards B; HB =0.2 and 1.0. Instead of five layers, a seven-layer structure

558 J. Feng, H. Liu, Y. Hu

is formed. As shown in Figure 2, a box size of LX = LY =40 is not enough to eliminate the size effect. We foundafter several tries that a box size of LX = LY = 80 is suita-ble to eliminate the size effect and to ensure the computa-tional efficiency for a reasonable description of themicrodomain morphology. In fact, the character of micro-domain morphology will not change if the box size isfurther enlarged. Besides the B-rich layers adjacent to thesurfaces, the morphology of the next nearest layers forthe two cases is virtually unchanged; it is a mesh-likephase when HB = 0.2 and an A-rich phase when HB = 1.0.However, for the middle layer, a straight parallel columnin the box of LX = LY = 40 is replaced by flexuous pat-terns when the size is increased to 80 or larger.Therefore we reach the conclusion that, in contrast to

the case of symmetric diblock copolymers with attractivewalls, the size effect must be carefully taken into consid-eration in the case of asymmetric diblock copolymers.We must make several attempts for each individual caseuntil an unchanged structure is formed.

4 Microdomain Morphology of AsymmetricDiblock Copolymers with a Composition off = 0.4 Confined Between Two NeutralPlates

Figure 3 shows the microdomain morphology for films ofdifferent thickness. Generally, a short, cylinder-like A-rich phase exists between two neutral plates. When the

thickness of the film is large, LZ = 40, the column micro-domain adopt a disordered arrangement. When the thick-ness is decreased until it approaches the length of a cylin-der, i.e., around 20 units, most columns become nearlyperpendicular to the surfaces. If the thickness is reducedto 1, the model is degraded to two dimensions: a sieve-like pattern with A-rich spheres dispersed in a bulk blockB is formed. It is known that hard walls influence theorientation of microdomains by restricting the motion ofpolymer chains, resulting a more regular pattern nearwalls because of the stereo-entropy effect. In addition A-rich spheres are the dispersed phase because block A is inpresent in a lower concentration. The narrower the dis-tance between two walls, the stronger is the effect onmicrodomain morphology.

5 Microdomain Morphology of AsymmetricDiblock Copolymers with a Composition off = 0.4 Confined Between Two PlatesAttractive Towards A

When the walls are attractive towards A, A-rich layersform adjacent to the surfaces and B-rich layers form nextto these. By adjusting the thickness of the film, differentnumbers of layers are produced, as shown in Figure 4.When the interaction parameter between the surfaces andA is HA = 0.2, the number of layers equals 13, 9, 7 and 5for LZ = 40, 30, 20 and 15, respectively. In comparison tothe layers adjacent to the surfaces and those next to them,

Figure 1. Morphology of asymmetric diblock copolymer (f = 0.4) confined between two attractive surfaces(HA = 0.2): (a) LX = LY = LZ = 15; (b) LX = LY = 40, LZ = 15; (c) LX = LY = 100, LZ = 15; (1) outwardappearance; (2) morphology of the middle layer.


the other layers are not so clearly separated. The mor-phology of those middle layers is mostly flexuous andcylinder-like, except when LZ = 15. In the latter case,there is only one A-rich layer and it is sieve-like becauseof the stronger influence exerted by the walls and theentropy effect as mentioned in the previous section.Obviously, because it is A-rich, the dispersed phase is B-rich spheres. The radius of each sphere is about the

dimension of 2 to 3 cells. In CDS, the size of a cell is lessthan that of a polymer chain.[18] Therefore, the featuresize of mesh hole or the radius of the cylinder is in thenanoscale. In reality, we may adjust the feature size byvarying the molar mass of the polymer.If the interaction between the walls and A is stronger,

i.e., HA is increased to 1.0, no obvious difference in thegeneral appearance is found from that with HA = 0.2,

Figure 2. Morphology of asymmetric diblock copolymers (f = 0.4) confined between two B-attractivesurfaces: (a) LX = LY = 40, LZ = 15, HA = 0.2; (b) LX = LY = 80, LZ = 15, HA = 0.2; (c) LX = LY = 40, LZ =15, HA = 1.0; (d) LX = LY = 80, LZ = 15, HA = 1.0; (1) outward appearance; (2) morphology of layersnear surfaces; (3) morphology of the middle layer.


except that the number of layers is reduced from 13 to 11when LZ = 40 as shown in Figure 5.Figure 6 shows the order parameter distribution along

the Z-axis when LZ = 15 for the cases of HA = 0.2 and HA

= 1.0. As shown in the Figure, the stronger the interac-tion, the more complete is the separation between blockA and block B. For the layers adjacent to the surfaces, theorder parameter w changes from –0.5, in the case of HA =0.2, to –0.9, in the case of HA = 1.0; w of the next layers(positive peak) also increases correspondingly. Figure 7shows the corresponding distributions when LZ = 40. Theorder parameters for the 13 layers of HA = 0.2 and 11layers of HA = 1.0 are correspond clearly to the patternsin Figure 5.

6 Microdomain Morphology of AsymmetricDiblock Copolymers with a Composition off = 0.4 Confined Between Two PlatesAttractive Towards B

Figure 8 shows the microdomain morphology of diblockcopolymers between two plates attractive towards B withHB = 0.2. Similarly to those with HA = 0.2 in Figure 4, thenumber of layers equals 13, 9, 7 and 5 for LZ = 40, 30, 20and 15, respectively. The layers adjacent to the surfacesare naturally rich in B. The layers next to these are most

interesting. They are all sieve-like with B-rich spheresdispersed in a bulk A-rich phase. The strong attractionstoward B and the entropy effect together strengthen theformation of the regular pattern near the walls. For moreinner layers, flexuous cylinders appear in the patterns.Again, those inner layers are not so clearly separated.When LZ = 20, as discussed in Section 3, the box withLX = LY = 40 is not enough to eliminate the size effect,and LX = LY = 80 is used. When LZ = 15, the microdomainof block A becomes two layers of a nanomesh mem-brane.When the interaction between walls and block B is

stronger, i.e., for HB = 1.0, the general behavior of thepatterns is similar to those for HB = 0.2. However,although the layers adjacent to the surfaces are still natu-rally rich in B, the layers next to them are not sieve-likebut A-rich homogeneous lamellae as shown in Figure 9.This is because of the very strong attraction towards Bthat causes more B to be assembled in these layers, form-ing a lamella-like phase instead of spheres.Figure 10 and 11 show the corresponding order param-

eter distributions along Z-axis when LZ = 15 and 40,respectively, in the cases of HB = 0.2 and HB = 1.0. Thegeneral behavior is similar to that illustrated in Figure 6and 7, however, the number of layers for LZ = 40 remainsunchanged when the interaction is strengthened.

Figure 3. Morphology of asymmetric copolymers (f = 0.4) confined between neutral walls: (a) LX = LY =LZ = 40; (b) LX = LY = 40, LZ = 20; (c) LX = LY = 40, LZ = 1: (1) outward appearance; (2) morphology ofdomain A.


7 Comparison with Results from OtherTheory, Monte Carlo Simulation andExperiment

Comparison with DDFT

Huinink et al.[19] have used DDFT for polymeric systemsto study the formation of microphases in a melt of an

asymmetric block copolymers (f = 1/3). The compositionratio of beads A is close to that in this paper. They haveobtained various microphases such as parallel lamellae,perpendicular cylinders, parallel cylinders and mesh-likephases, which also occur in this work. Huinink et al.claimed that a perpendicular cylindrical phase is stablewhen neither the A nor B block preferentially wets the

Figure 4. Morphology of asymmetric copolymers (f = 0.4) confined between two A-attractive walls (HA =0.2): (a) LX = LY = LZ = 40; (b) LX = LY = 40, LZ = 30; (c) LX = LY = 40, LZ = 20; (d) LX = LY = 40, LZ = 15; (1)outward appearance; (2) morphology of domain A; (3) microdomain morphology of the middle layer.


surfaces. In fact, such phenomena only can take place ina very narrow slit. As the degree of coarsening in theirwork is smaller than that in CDS, their work was carriedout in very narrow slit. The results of our work show thata slight enlargement of the distance between the twoplates can damage the stability of perpendicular cylindri-cal phase.

Comparison with Monte Carlo Simulation

We use a cubic lattice to generate a Monte Carlo simula-tion for an asymmetric diblock copolymer system (f =0.4). The chain length is set equal to 10 (five beads of A

and five beads of B); the bead density is about 0.91. Thedistance between two plates is set as LZ = 22 to mimic avery narrow slit. As shown in Figure 12, the finite sizeeffect is very serious in Monte Carlo simulation too. Inthe case of LX = LY = 22, parallel cylinders are obtained inthe middle layer when both plates are preferentiallyattractive toward A block (HA = 0.25). However, we findmesh-like microphase instead of parallel cylindricalphase if LX and LY are extended to 110.If the two plates are preferentially attractive toward B

block (HB = 0.25), the two layers adjacent to walls arenaturally covered by B blocks. The next two layers havemesh-like structures consisting of B microdomains dis-persed in a matrix of A, as shown in Figure 13. This pat-tern also appears in CDS results when LZ = 15 and HB =0.2, as shown in Figure 8d. The results obtained usingCDS are in accordance with those from Monte Carlosimulation.

Comparison with Experiment

It is difficult to quantitatively compare our results withexperiment, as few experiments on an f = 0.4 asymmetricblock copolymer in a slit have been done at present.Therefore, we present only a qualitative comparison witha similar system. Morkved et al.[9] and Thurn-Albrecht etal.[22] placed thin film of asymmetric styrene/methylmethacrylate copolymer (PS/PMMA) between two hardwalls and obtained a perpendicular cylinder morphology,similar to that shown in Figure 3b. The morphologyreported in their work are more regular than ours becauseof the electric field applied.

8 ConclusionThis work again tells us that the size of the box chosenmust be carefully considered in CDS. As yet, we unableto formulate a general rule for choosing the box size. Forsymmetric copolymers, the size effect is not serious whenwe adopt attractive plates. For asymmetric copolymers, itis different. Not only must we use boxes which are larger

Figure 5. Morphology of domain A of asymmetric copolymers (f = 0.4) confinedbetween two A-attractive walls: (a) HA = 0.2; (b) HA = 1.0.

Figure 6. Order parameter distributions for systems with HA =0.2(h) and HA = 1.0 (f) when LZ = 15.

Figure 7. Order parameter distributions for systems with HA =0.2(h) and HA = 1.0 (f) when LZ = 40.


in the X- and Y-directions to eliminate the size effect; thesize is also dependent on the film thickness. As shown inthis work, when LZ = 20, we have to use a box with LX =LY = 80. In practice, we always have to search for theappropriate dimensions for the box by trail and error.For symmetric copolymers, the microdomains are

mostly lamellar, with the distances between A- and B-rich lamellae being in the nanoscale. For asymmetriccopolymers, the morphology displayed is mostly cylindri-cal, with the radii of the cylinders also in the nanoscale.

On some occasions, we have a sieve-like structure on thenanoscale. All these phenomena are interesting to mate-rial scientists searching for sophisticated nanomaterials.A series of conditions can be controlled in practice; thechemical composition of the copolymer, the thickness ofthe film, the selective interactions between the plates andthe blocks, as well as their strength, can all be optimizedmaking the potential technology quite flexible.We compare some results from CDS with those from

DDFT and Monte Carlo simulation. Although those pat-

Figure 8. Morphology of asymmetric copolymers (f = 0.4) confined between two B-attractive walls (HB = 0.2): (a) LX =LY = LZ = 40; (b) LX = LY = 40, LZ = 30; (c) LX = LY = 80, LZ = 20; (d) LX = LY = 40, LZ = 15; (1) outward appearance; (2)morphology of domain A; (3) microdomain morphology of the layer next to the surface layer; (4) microdomain morphol-ogy of middle layers.


Figure 9. Morphology of asymmetric copolymers (f = 0.4) confined between two B-attractive walls (HB =1.0): (a) LX = LY = LZ = 40; (b) LX = LY = 40, LZ = 30; (c) LX = LY = 80, LZ = 20; (d) LX = LY = 40, LZ = 15;(1) outward appearance; (2) morphology of domain A; (3) microdomain morphology of middle layers.Exception: (d) – the latter is the second or the fourth layer.

Figure 10. Order parameter distributions for systems withHB = 0.2(h) and HB = 1.0 (f) when LZ = 15.

Figure 11. Order parameter distributions for systems withHB = 0.2(h) and HB = 1.0 (f) when LZ = 40.


terns obtained in this work have appeared in some experi-mental work, an exact comparison between CDS andexperimental results is not an easy job at present. For thecase of a very narrow slit, the theoretical and experimen-tal results are consistent with each other. However, forbroader slits, further efforts are needed to test the reliabil-ity of the method.

Acknowledgement: This work was supported by the NationalNatural Science Foundation of China (Projects No. 29736170,20025618), and the Doctoral Research Foundation sponsored bytheMinistry of Education of China.

Received: October 22, 2001Revised: February 25, 2002

Accepted: April 1, 2002

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Figure 12. Morphology of microdomain of asymmetricalcopolymer system by Monte Carlo simulation, HA = 0.25: (a) LX

= LY = 110, LZ = 22 (minimized to half the original size); (b) LX

= LY = LZ; (1) outer appearance; (2) the middle layer.

Figure 13. Morphology of micro domain of asymmetricalcopolymer system by Monte Carlo simulation, HB = 0.25, LX =LY = 110, LZ = 22: (1) outer appearance (2) the second layer.

asymmetric diblock copolymer thin film confined in a slit: microphase separation and morphology

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