pubs.acs.org/Langmuir © 2009 American Chemical Society
Competitive Adsorption and Assembly of Block Copolymer Blends on Nanopatterned Surfaces Houyang Chen,*,† Xueqian Chen, Zhencheng Ye, Honglai Liu,* and Ying Hu State Key Laboratory of Chemical Engineering and Department of Chemistry, East China University of Science and Technology, Shanghai 200237, China. †Present Address: Department of Chemical and Biological Engineering, State University of New York at Buffalo, Buffalo, NY. Received October 21, 2009. Revised Manuscript Received November 23, 2009 By employing off-lattice Monte Carlo simulations, the competitive adsorption and assembly of block copolymer blends on a nanopatterned surface were investigated. The segment distributions and polymer configurations are examined by varying the chemical structures of polymers, the interactions between segments and adsorbing stripe domains of the nanopatterned surface, and the width of stripe domains in the nanopatterned surface. The simulation results show that by modulating the affinities between a copolymer and the adsorbing stripe domain, one can adjust the density distributions and adsorption properties of block copolymer blends. With decorating the chemical structure of a surface, the targeted molecules would be actively recognized and separated. This offers a versatile way for novel separation materials and for the fabrication of nanomaterials.
1. Introduction Polymer adsorption is of central importance in both academics and industry. Recently, polymer recognition on nanopatterned surfaces has received great attention. In the theoretical aspect, the interactions between copolymer and heterogeneous surfaces1,2 and the density distributions of copolymer near a chemically heterogeneous patterned surface3-5 were investigated by employing self-consistent field theory. By developing and extending density functional theories, Nath et al.6 analyzed the ordering of block copolymers near patterned surfaces, and Chen et al.7 reported polymer recognition at patterned surfaces. Kriksin et al.8,9 suggested that a marked pattern recognition is possible for a copolymer with relatively short blocks at high surface affinities by using a semianalytical statistical mechanics model. In the computer simulation aspect, Semler and Genzer10,11 found that both the monomer sequence distribution of the copolymer with the size and the spatial distribution of adsorbing surface sites play a critical role in copolymer adsorption on patterned surfaces. A two-stage pattern recognition mechanism was proposed by Muthukumar for the adsorption of polyelectrolyte chains on a patterned surface, that is, complexation without registry and rearrangement.12 Later, a similar mechanism was found by Kriksin et al.8,9 and Sumithra et al.13,14 Striolo15 *To whom correspondence should be addressed. E-mail:
[email protected]. cn (H.L.);
[email protected] (H.C.).
(1) Genzer, J. Adv. Colloid Interface Sci. 2001, 94, 105. (2) Genzer, J. Macromol. Theory Simul. 2002, 11, 481. (3) Petera, D.; Muthukumar, M. J. Chem. Phys. 1997, 107, 9640. (4) Petera, D.; Muthukumar, M. J. Chem. Phys. 1998, 109, 5101. (5) Balazs, A.; Singh, C.; Zhulina, E. Macromolecules 1998, 31, 6369. (6) Nath, S. K.; Nealey, P. F.; de Pablo, J. J. J. Chem. Phys. 1999, 110, 7483. (7) Chen, H. Y.; Ye, Z. C.; Peng, C. J.; Liu, H. L.; Hu, Y. J. Chem. Phys. 2006, 125, 204708. (8) Kriksin, Y. A.; Khalatur, P. G.; Khokhlov, A. R. J. Chem. Phys. 2005, 122, 114703. (9) Kriksin, Y. A.; Khalatur, P. G.; Khokhlov, A. R. J. Chem. Phys. 2006, 124, 174904. (10) Semler, J. J.; Genzer, J. J. Chem. Phys. 2003, 119, 5274. (11) Semler, J. J.; Genzer, J. Macromol. Theory Simul. 2004, 13, 219. (12) Muthukumar, M. J. Chem. Phys. 1995, 103, 4723. (13) Sumithra, K. J. Chem. Phys. 2009, 130, 194903. (14) Sumithra, K.; Brandau, M.; Straube, E. J. Chem. Phys. 2009, 130, 234901. (15) Striolo, A. J. Chem. Phys. 2006, 125, 094709.
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explained how the presence of a solid hard mask, used to mimic nanoscale patterns on an underlying hydrophobic surface, affects surfactant adsorption. We have reported the recognition of multiblock polymers and polymer blends on nanopatterned surfaces using Monte Carlo (MC) simulations.16,17 Our results showed that the recognition affinity becomes stronger with increasing stripe width, adsorption strength, and number of adsorbing segments in the block copolymer chain. The results also indicated that an ordered film could be modulated by tuning adsorption energy between the surface and polymer or by adjusting the width of the stripes on the surface. Patra and Linse’s results18 noted that the central part of a patterned brush changes little when the pattern is several times wider than the height of the brush. Jayaraman et al.19,20 successfully developed a simulation technique to generate optimal surfaces that can recognize and adsorb preferentially a certain sequence in a copolymer. The target in studying interactions between block copolymers and patterned surfaces is to adjust the adsorption affinities and develop new materials. In our previous work, we discussed the cooperative interaction on binary mixtures adsorbed on the nanopatterned surfaces.17 In this work, we focus on the competitive adsorption of block copolymer blends and later adjust the adsorption ability of the block copolymer blend on the patterned surface. Subsequently, the corresponding properties of block copolymer blends are changed. This Article is organized as follows. In section 2, the details of the Monte Carlo simulations are described. In section 3, competitive adsorption of block copolymer blends is examined. Then the effect of adsorption properties of block copolymer blends is investigated by adjusting adsorption affinities between block copolymers and adsorbing stripe domains on nanopatterned surfaces. The last section summarizes the conclusions. (16) Chen, H. Y.; Peng, C. J.; Ye, Z. C.; Liu, H. L.; Hu, Y.; Jiang, J. W. Langmuir 2007, 23, 2430. (17) Chen, H. Y.; Peng, C. J.; Sun, L.; Liu, H. L.; Hu, Y.; Jiang, J. W. Langmuir 2007, 23, 11112. (18) Patra, M.; Linse, P. Nano Lett. 2006, 6, 133. (19) Jayaraman, A.; Hall, C. K.; Genzer, J. Phys. Rev. Lett. 2005, 94, 078103. (20) Jayaraman, A.; Hall, C. K.; Genzer, J. J. Chem. Phys. 2005, 123, 124702.
Published on Web 12/08/2009
DOI: 10.1021/la904001h
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2. Simulation Details The block copolymer blends under consideration include five mixtures of block copolymers (A30/mB30/m)m (m = 1, 2, 3, 5, 30), that is, A30B30, (A15B15)2, (A10B10)3, (A6B6)5, and (AB)30; and each of them has one chain in the system. (A30/mB30/m)m (m = 1, 2, 3, 5, 30) is considered as a freely jointed chain of 60 segments with an identical diameter σ for both A and B segments. The interaction between segments is given by 8 1:5σ σ < rij < 1:5σ rij < σ
ð1Þ
where rij is the center-to-center distance between segments i and j; εij is the cross-well-depth calculated by the geometric combining rule (εiiεjj)1/2; εii is the well-depth between segments of the same type, and for simplification we have εAA = εBB. The nanopatterned surface is mimicked by a plain surface with alternating adsorbing and nonadsorbing stripes along the x direction. Each stripe is equally sized with a width of w. The adsorbing and nonadsorbing stripes have different interactions with segments A and B,
βεi -wall
8 < 0 ri -surface gσ ¼ -λm 0eri -surface < σ : ¥ ri -surface < 0
ð2Þ
where ri-surface is the distance between segment i and the surface. We assume that the adsorbing stripe only attracts B segments, while the nonadsorbing stripe has no preference for either segment A or B, that is, λm means the interaction between B segments of block copolymer (A30/mB30/m)m (m = 1, 2, 3, 5, 30) and the adsorbing stripe domains of the nanopatterned surface. MC simulations were carried out in a Canonical ensemble with a box of Lx Ly Lz = 60σ 60σ 30σ, as schematically shown in Figure 2f. The number of stripes along the x direction is Ns = Lx/w. The periodic boundary conditions were exerted in the x and y directions, while two identical impenetrable nanopatterned surfaces were in the z direction located at Lz = 0 and Lz = 30σ. Two types of trial moves, namely, translation and jiggling, were employed. In the former movement, a randomly selected chain was translated with a random displacement in the x, y, or z direction. In the latter one, a bond between three successive segments was subject to a random rotation. The details can be found in the literature.21-24 The reduced temperature was selected as T* = kBT/εAA = 6. In our simulations, 5 107 trial moves were employed, and the latter 4 107 trial moves were for the ensemble averages. It should be noted that the modeling presented here is better for dilute solution systems because of the enormous computing cost.
3. Results and Discussion Figure 1 presents the segment density profiles of block copolymer blends along the z-axis at λm = 1.0 (m = 1, 2, 3, 5, 30), w/σ = 30 (i.e., Ns = 2), and x/σ = 45, the center of the adsorbing domain (the adsorbing domain is located in the range x/σ = 30-60). The density profiles of B segments of block copolymer (21) Dickman, R.; Hall, C. K. J. Chem. Phys. 1988, 89, 3168. (22) Chen, H. Y.; Ye, Z. C.; Cai, J.; Liu, H. L.; Hu, Y.; Jiang, J. W. J. Phys. Chem. B 2007, 111, 5927. (23) Cai, J.; Liu, H. L.; Hu, Y. Fluid Phase Equilib. 2002, 194-197, 281. (24) Chen, H. Y.; Cai, J.; Ye, Z. C.; Peng, C. J.; Liu, H. L.; Hu, Y.; Jiang, J. W. J. Phys. Chem. B 2008, 112, 9568.
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Figure 1. Segment density profiles of block copolymer blends along the z-axis at λm = 1.0 (m = 1, 2, 3, 5, 30), w/σ = 30 (i.e., Ns = 2), and x/σ = 45, the center of the adsorbing domain (the adsorbing domain is located in the range x/σ = 30-60). (a) A segments; (b) B segments. (circle) A30B30; (square) (A15B15)2; (triangle up) (A10B10)3; (triangle down) (A6B6)5; (tilted square) (AB)30.
blend (A30/mB30/m)m adsorb near the surface because B segments have attractive interaction with the adsorbing stripe domains. The curves decrease sharply at about z/σ = 1 due to the square well potential of the adsorption domain for the segments. In the domain of 0 < z/σ < 1, the density of B segments in the block copolymer blend decreases as the length of adsorbing blocks in block copolymer blend decrease; that is, the density of B segments in block copolymer A30B30 is the largest and that in (AB)30 is the smallest. The adsorption of A segments in each block copolymer (A30/mB30/m)m is near the surface due to the chain connectivity between the A and B segments in each block copolymer. From the surface to bulk, the peak position that appears in each curve (A density profiles) is from (AB)30 to (A6B6)5 to (A10B10)3 to (A15B15)2 to A30B30. The tail of the curve for density profiles of A segments is longer for longer nonadsorbing blocks; that is, the curve for density profiles of A segments in A30B30 has the longest tail. This occurs because the longer nonadsorbing block prefers to locate in the domain, which departs away the surface, to get larger entropy. The compositional polydispersity can profoundly influence the adsorption of the block copolymer. A similar result was presented in a recent paper by Jhon et al.25 From Figure 1, a film containing two layers is observed. The first layer next to the surface consists of B segments of a block copolymer blend, and the second layer further from the surface has both A and B segments. By employing a similar method, Chen and Ruckenstein generated nanochannels with two or three layers under cylindrical confinement.26-28 To have a full landscape for block copolymer blend adsorption near patterned surfaces, the contours of B segments in block copolymer blend (A30/mB30/m)m (m = 1, 2, 3, 5, 30) are presented (25) Jhon, Y. K.; Semler, J. J.; Genzer, J.; Beevers, M.; Gus’kova, O. A.; Khalatur, P. G.; Khokhlov, A. R. Macromolecules 2009, 42, 2843. (26) Chen, H.; Ruckenstein, E. J. Chem. Phys. 2009, 130, 024901. (27) Chen, H.; Ruckenstein, E. J. Chem. Phys. 2009, 131, 114904. (28) Chen, H.; Ruckenstein, E. Langmuir 2009, 25, 12315.
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Figure 2. Segment density contours of B segment in block copolymer blend (A30/mB30/m)m in the xz plane at λm = 1.0 (m = 1, 2, 3, 5, 30) and w/σ = 30 (i.e., Ns = 2) (the adsorbing domain is located in the range x/σ = 30-60). Other conditions are the same as those in Figure 1. (a) A30B30; (b) (A15B15)2; (c) (A10B10)3; (d) (A6B6)5; (e) (AB)30; and (f) snapshot (A segments, gray; B segments, purple; black domain of a wall, nonadsorbing domain; white domain of a wall, adsorbing domain).
in Figure 2 with the conditions being the same as those in Figure 1. In these figures, two layers with only B segments are presented. The layer next to the adsorbing stripe domain of the surface, which is mainly composed of B segments, is more compact, while the other layer further from the surface is made up of both A and B segments and is looser. From the interface between the adsorbing domain and the nonadsorbing domain to the middle of the adsorbing domain of the surfaces, the density of B segments increases due to higher energy being needed if they locate near the interfaces. The length of the tail of the B segments of the block copolymer blend increases from A30B30 to (A15B15)2 to (A10B10)3 to (A6B6)5 to (AB)30, reflecting the length of the nonadsorbing block in different kinds of block copolymer blends. In addition, a snapshot is shown in Figure 2f for further illustration. To examine the effect of the width of each stripe in patterned surfaces, the segment density profiles of block copolymer blends along the z-axis are shown in Figure 3 at λm = 1.0 (m = 1, 2, 3, 5, 30), w/σ = 3 (i.e., Ns = 20), and x/σ = (4n - 1)w/2σ, the center of the adsorbing domains, n = 1, 2, ..., Ns/2 (the adsorbing domains are located in the range (2n - 1)w/σ < x/σ < 2nw/σ). Generally, the trends of the curves are similar to those for w/σ = 30 in Figure 1. However, as the width of the stripe domains of patterned surfaces decreases, the densities of both A and B segments near the surface decrease. Especially for A and B segments for block copolymer (AB)30, the density profiles in the middle of the slit are higher than those near the adsorbing domain of the surfaces. This is mainly caused by the following: (1) when the width of the stripe domains becomes smaller, the molecules would “pass” several nonadsorbing domains and locate on several stripe domains; (2) narrow stripe domains on a nanopatterned surface could not accommodate whole polymer, and hence, part of block copolymer departs away from the surface. Langmuir 2010, 26(9), 6663–6668
Figure 3. Segment density profiles of block copolymer blend along the z-axis at λm = 1.0 (m = 1, 2, 3, 5, 30), w/σ = 3 (i.e., Ns = 20), and x/σ = (4n - 1)w/2σ, the center of the adsorbing domains, n = 1, 2, ..., Ns/2 (the adsorbing domains are located in the range (2n - 1)w/σ < x/σ < 2nw/σ). (a) A segments; (b) B segments.
To understand the competitive adsorption behavior of copolymer blends, we vary the attractive interaction λ5 between the B segments in block copolymer (A6B6)5 while keeping the interaction of B segments of the other block copolymer λm = 1.0 DOI: 10.1021/la904001h
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Figure 4. B segment density profiles of block copolymer blend along the z-axis at the center of the adsorbing stripe domain at λm = 1.0 (m = 1, 2, 3, 30), λ5 = 2.0. (a) w/σ = 30 (i.e., Ns = 2), the adsorbing stripe domain is located in the range x/σ = 30-60, x/σ = 45, the center of the adsorbing domain; (b) w/σ = 3 (i.e., Ns = 20), x/σ =(4n - 1)w/2σ, the center of the adsorbing domains, n = 1, 2, ..., Ns/2 (the adsorbing domains are located in the range (2n- 1)w/σ < x/σ < 2nw/σ). (circle) A30B30; (square) (A15B15)2; (triangle up) (A10B10)3; (triangle down) (A6B6)5; (tilted square) (AB)30.
(m = 1, 2, 3, 30) (Figure 4). The density of B segments of (A6B6)5 near the surface increases as λ5 increases, reflecting more block copolymers (A6B6)5 adsorbed on the adsorbing domain. The density profiles of B segments in (A6B6)5 are larger than those in block copolymers (A30B30), (A15B15)2, (A10B10)3, and (AB)30 when λ5 increases. On the other hand, because of the excluded volume effect, the density of B segments of (A30B30), (A15B15)2, (A10B10)3, and (AB)30 decreases near the center of adsorbing domains. Furthermore, when w/σ changes from 30 to 3, the density distribution of B segments changes. The density profile of the B segment in (A6B6)5 is a bit larger than that in (A30B30). It is clearly shown that the width of the stripe domain would affect the results of the competitive adsorption. In Figure 4, as the interaction between B segments and adsorbing stripe domains changes, the competitive adsorption of the block copolymer blend occurs. It is interesting to see at which condition the block copolymer with different lengths of adsorbing block has the same density profiles, or at which condition the density profiles with shorter adsorbing blocks are higher than those with longer adsorbing blocks. To be clear, a critical energy is defined. For block copolymer blends, by varying λm (m = 2, or 3, or 5, or 30) and keeping λj constant (j ∈ [1, 2, 3, 5, 30], j ¼ 6 m), when the density of B segments in (A30/mB30/m)m at the center of adsorbing stripe domains equal to the B segments in another kind of copolymer (A30/jB30/j)j with longer adsorbing blocks, we named the interaction energy λm as a critical adsorp*. Figure 5 shows the densities of A and B segments tion energy λm,j in the block copolymer blend at the center of the adsorbing stripe domain of a nanopatterned surface as a function of λm (m = 2, or 3, or 5, or 30) between B segments of (A30/mB30/m)m (m = 2, 3, 5, 30) and the adsorbing domain at fixed λj = 1.0 (j ∈ [1, 2, 3, 5, 30], 6666 DOI: 10.1021/la904001h
Figure 5. Density of A and B segments of block copolymer blend near the surface at the center of the adsorbing domain as a function of the interaction λm [m = 2 (a1,b1), 3 (a2,b2), 5 (a3,b3), or 30 (a4,b4)] between the B segments and the adsorbing stripe domain of the patterned surfaces when fixed λj = 1.0 (j ∈ [2, 3, 5, 30], j 6¼ m) and w/ σ = 30 (Ns = 2). (ak) A segments; (bk) B segments; k = 1, 2, 3, 4. (circle) A30B30; (square) (A15B15)2; (triangle up) (A10B10)3; (triangle down) (A6B6)5; (tilted square) (AB)30.
j¼ 6 m) and w/σ = 30 (Ns = 2). When λ2 increases (Figure 5a1 and b1), the density of A segments in (A15B15)2 near the center of the adsorbing domain approaches to the density of A segments from (A10B10)3. On the other hand, by increasing λ2, the density of B segments from (A15B15)2 reaches the density from (A30B30) first and then exceeds the density from (A30B30). By increasing λ30 (Figure 5a4 and b4), the density of B segments in (AB)30 first approaches, exceeds the density of B segments in (A6B6)5, and later reaches and exceeds the density of B segments in (A10B10)3, (A15B15)2, and A30B30, respectively, upon further increase of λ30. From Figure 5, critical energies are obtained as follows: λ*2,1 ≈ 1.08, λ*3,2 ≈ 1.08, λ*3,1 ≈ 1.12, λ*5,3 ≈ 1.12, λ*5,2 ≈ 1.20, λ*5,1 ≈ 1.23, λ*30,5≈ 1.23, λ*30,3≈ 1.47, λ*30,2≈ 1.72, and λ*30,1≈ 1.81. In other words, a block copolymer with a shorter length of adsorbing/ nonadsorbing blocks has more adsorption near the surface by increasing interaction between B segments of that kind of block copolymer and the adsorbing stripe domains of the patterned Langmuir 2010, 26(9), 6663–6668
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Figure 6. Radii of gyration (Rg/σ)2 for block copolymer blend (A30/mB30/m)m (m = 1, 2, 3, 5, 30) versus the distance z from the patterned surface with λm = 1.0 (m = 1, 2, 3, 5, 30) and w/σ = 30 (i.e., Ns = 2). (a) (Rg.x/σ)2; (b) (Rg.y/σ)2; (c) (Rg.z/σ)2. (circle) A30B30; (square) (A15B15)2; (triangle up) (A10B10)3; (triangle down) (A6B6)5; (tilted square) (AB)30.
surface. To adjust the interaction between B segments in a shorter adsorbing block, that is, m = 2, 3, 5, 30, a larger interaction is needed to have the same density of longer blocks near the surface. From Figure 5, the density of a selected kind of block copolymer can be modulated by adjusting λm (m = 1, 2, 3, 5, 30), and the competitive adsorption of block copolymer blend is controlled. By doing this, new and novel materials could be rationally designed. We have discussed above the control of competitive adsorption of block copolymer blends. We will then consider the properties after controlling competitive adsorption in detail. Hence, two quantities, the radii of gyration and pattern transfer parameter, are employed. The anisotropic radii of gyration (Rg.x/σ)2, (Rg.y/σ)2, and (Rg.z/σ)2 in the x, y, and z directions are defined as
Rg, p =σ
2
¼
1X ðpi - pcom Þ2 N i
ð3Þ
where p = x, y, or z, pi is the coordinate of the ith segment, pcom is the center of mass of a block copolymer chain, and N is the number of segments in the chain. Figure 6 presents the radii of gyration for block copolymer blend (A30/mB30/m)m (m = 1, 2, 3, 5, 30) versus the distance z from the patterned surface with λm =1.0 (m = 1, 2, 3, 5, 30) and w/σ = 30 (i.e., Ns = 2). (Rg.x/σ)2 is nearly equal to (Rg.y/σ)2, showing little stripe effect. Both are larger than (Rg.z/σ)2, indicating the Langmuir 2010, 26(9), 6663–6668
Figure 7. Radii of gyration (Rg/σ)2 for block copolymer blend (A30/mB30/m)m (m = 1, 2, 3, 5, 30) versus the distance z from the patterned surface with λm = 1.0 (m = 1, 2, 5, 30), λ3 = 1.3 and w/σ = 30 (i.e., Ns = 2). (a) (Rg.x/σ)2; (b) (Rg.y/σ)2; (c) (Rg.z/σ)2. (circle) A30B30; (square) (A15B15)2; (triangle up) (A10B10)3; (triangle down) (A6B6)5; (tilted square) (AB)30.
confinement effect. Such behavior was also presented in the binary mixture.17 It is also shown in Figure 6 that the center of mass of (AB)30 locates near the surface and it presents as a circle shape along the xy plane. The centers of mass of (A6B6)5, (A10B10)3, (A15B15)2, and A30B30 reside further away from the surface one by one. In addition, the former three show as circle shapes along the xy plane, and the area of these circle decreases as m decreases. For A30B30, it appears as a globule. In the center of the slit, all polymers are globular and the volumes of their shapes decrease from (AB)30 to A30B30. By adjusting λ3 (Figure 7), the conformation of the block copolymer blend changes significantly. The block copolymer (A10B10)3 stays near the surface as an ellipsoid, and the long axis along with x-axis, and the short axis along with y-axis. Moving away from the surface, it appears as a circle. Further from the surface, few (A10B10)3 are shown in the middle of the slit. Affected by prior adsorption of (A10B10)3, the block copolymer with shorter lengths of adsorbing/nonadsorbing blocks (i.e., (A6B6)5 and (AB)30) changes, while the block copolymer with longer lengths of adsorbing/nonadsorbing blocks (i.e., (A15B15)2 and A30B30) does not. This is because the center of mass of block copolymers with shorter lengths of adsorbing/nonadsorbing blocks is closer to the surface. When (A10B10)3 is adsorbed near the surface, other block copolymers will depart away from the surface due to the excluded volume effect. DOI: 10.1021/la904001h
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Figure 8. Pattern transfer parameter of block copolymer blend along the z-axis at λm = 1.0 (m = 1, 2, 3, 5, 30) and w/σ = 10 (i.e., Ns = 6). (a) A segments; (b) B segments. (circle) A30B30; (square) (A15B15)2; (triangle up) (A10B10)3; (triangle down) (A6B6)5; (tilted square) (AB)30.
To examine the recognition ability of block copolymer blends, the pattern transfer parameter (PTP), which was first defined in off-lattice Monte Carlo simulations in our previous work,7 at different z from the wall was employed. R PTPi ðzÞ ¼
R
i i xa , ya Φ ðx, y, zÞ=Aa - xn , yn Φ ðx, y, zÞ=An R i x, y Φ ðx, y, zÞ=ðAa þ An Þ
ð4Þ
where Φ (x,y,z) is the volume fraction of the ith kind of segment and locates at the position (x,y,z), and Aa and An denote the surface areas of adsorbing domain and nonadsorbing domain on the surface, respectively. From this definition, PTP = 2.0 means that a perfect recognition has taken place, while PTP = -2.0 indicates a perfect inversion of the pattern. When no recognition happens, PTP = 0. Figure 8 presents the PTP of both A and B segments in block copolymer blend at λm= 1.0 (m = 1, 2, 3, 5, 30) and w/σ = 10. It shows that the B segments recognize the adsorbing stripe domain readily. Near the surface, nearly perfect recognition occurs. The PTPB decreases as the length of the adsorbing block decreases. For B segments in a selected polymer, the PTPB decreases by moving away from surface. Approaching to the middle of the slit, PTPs are closer to but not zero, indicating that there is a confinement effect. This result is in accord with the result we found in the above section for the radii of gyration. The PTPA was generated by chain connectivity. For the same length of block copolymer blend, a shorter length of block (both adsorbing block and nonadsorbing block), that is, greater number of blocks, would have a larger connectivity effect between the A and B segments.26 Hence, PTPA has inverse behavior with PTPB. Figure 9 presents the PTP of block copolymer blend along the z-axis at λm= 1.0 (m = 1, 2, 5, 30), λ3 = 1.3, and w/σ = 10 (i.e., Ns = 6). As expected, the PTPB of block copolymer (A10B10)3 has better recognition ability than that in other copolymers. With i
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Figure 9. Pattern transfer parameter of block copolymer blend along the z-axis at λm = 1.0 (m = 1, 2, 5, 30), λ3 = 1.3, and w/σ = 10 (i.e., Ns = 6). (a) A segments; (b) B segments. (circle) A30B30; (square) (A15B15)2; (triangle up) (A10B10)3; (triangle down) (A6B6)5; (diamond) (AB)30.
increasing λ3, the PTP of B segments of (A10B10)3 near the surface increases. Meanwhile, the PTP of B segments of A30B30 for 0 < z/σ < 7.5 decreases. Due to the chain connectivity between A and B segments, the PTP of A segments of (A10B10)3 near the surface increases somewhat.
4. Conclusions By employing Monte Carlo simulations, the competitive adsorption and assembly on nanopatterned surfaces were identified. The segment distributions and configurations of block copolymer blends depend on the chemical structures of copolymers, the interactions between segments and adsorbing domains, and the width of the stripe surface. For a selected case, as the length of adsorbing blocks in copolymers decreases, the density profiles in the domains near the surface (0 < z/σ < 1) decrease. As the width of the stripe domains becomes narrower, the density on the surface decreases. By adjusting the adsorbing energy between B segments of a selected block copolymer and adsorbing domain of the surface, the competitive adsorption affinities can be changed; subsequently, adsorption properties such as radii of gyration and PTP of block copolymer blends have a pronounced change. To adjust the interaction between B segments in a shorter adsorbing block, that is, m = 2, 3, 5, 30, a larger interaction is needed to have the same density of longer block near the surface. Acknowledgment. The authors are grateful to Dr. Jianwen Jiang for helpful discussions. This work is supported by the National Natural Science Foundation of China (Project Nos. 20736002, 20676030), the creative team development project of Ministry of Education of China (No. IRT0721), the 111 Project of Ministry of Education of China (No. B08021), and Outstanding Youth Research Funding from East China University of Science and Technology (YH0157118).
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