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Recognition of Multiblock Copolymers on Nanopatterned Surfaces: Insight from Molecular Simulations Houyang Chen, Changjun Peng, Zhencheng Ye, Honglai Liu,* and Ying Hu Lab for AdVanced Material and Department of Chemistry, East China UniVersity of Science and Technology, Shanghai 200237, China
Jianwen Jiang* Department of Chemical and Biomolecular Engineering, National UniVersity of Singapore, 4 Engineering DriVe 4, Singapore 117576 ReceiVed October 6, 2006. In Final Form: NoVember 24, 2006 The recognition of multiblock copolymers on nanopatterned surfaces has been investigated by molecular simulations. All the copolymers (AnB12-n)5 are composed of 60 square-well segments, but with various architectures by changing n. Segment density profiles, radii of gyration, pattern transfer parameters, and three adsorption conformations (tail, loop, and train) are examined quantitatively. It is found that the copolymer can recognize the adsorbing stripes on surface and the surface vicinity. The recognition affinity becomes stronger with increasing the stripe width, the adsorption strength, and the number of adsorbing segments in copolymer chain. From surface to bulk phase, the shape of copolymer changes from elongated to elliptical, and finally to globular. Among the three adsorption conformations, tail has the greatest average size while train has the smallest. With the increased number of nonadsorbing segments, the average size shows an increase in tail but a decrease in train.
1. Introduction Adsorption on patterned surface has a wide range of industrial applications, such as the protective coating of electronic devices, the rational design of high-performance lubricants and adhesives, and the stability control of colloidal suspensions. In particular, with the emerging of nanotechnology, considerably increasing interest has recently focused on the fabrication of nanodevices from “bottom-up”, which is expected to substitute the current “top-down” lithographic method. Toward that end, polymers or biomolecules have been used to recognize or hybridize nanostructured building blocks into complex architectures.1 Over the years, a large number of experiments have been carried out to study the adsorption of polymers and biopolymers on chemically heterogeneous substrates.2-7 Pallandre et al.2 and Agheli et al.3 investigated protein adsorption on hydrophilic substrates bearing regularly spaced hydrophobic nanopatterns. Lei et al.4 examined the site-selective adsorption and the directional diffusion of a single molecule as well as the molecular clusters of copper phthalocyanine. Shi et al.5 used chemically modified patterned surface as a good matrix for selective adsorption of polystyrene nanoparticles with both positive and negative charges. Kim et al.6 demonstrated the integration of thin films of block copolymer with advanced lithographic techniques to induce the self-assembled epitaxial domains. Their * To whom correspondence should be addressed. (H.L.) Tel.: 86-2164252921; fax: 86-21-64252921; e-mail:
[email protected]. (J.J.) Tel: 65-65165083; fax: 65-67791936; e-mail:
[email protected]. (1) Joachim, G.; Gimzewski, J. K.; Aviram, A. Nature 2000, 408, 541. (2) Pallandre, A.; Meersman, B.; Blondeau, F. J. Am. Chem. Soc. 2005, 127, 4320. (3) Agheli, H.; Malmstrom, J.; Larsson, E. M.; Textor, M.; Sutherland, D. S. Nano Lett. 2006, 6, 1165. (4) Lei, S.; Wang, C.; Wan, L.; Bai, C. J. Phys. Chem. B 2004, 108, 1173. (5) Shi, F.; Wang, Z.; Zhao, N.; Zhang, X. Langmuir 2005, 21, 1599. (6) Kim, S. O.; Solak, H. H.; Stoykovich, M. P.; Ferrier, N. J.; de Pablo, J. J. Nealey, P. F. Nature 2003, 424, 411. (7) Wang, Y.; Liu, Z.; Huang, Y. et al. Langmuir 2006, 22, 1928. (8) Muthukumar, M. J. Chem. Phys. 1995, 103, 4723.
results illustrate how hybridization strategy in nanofabrication allows for molecular-lever control in existing manufacturing processes. Wang et al.7 presented a facile method for fabricating polymer thin films with micropatterned surfaces by evaporating polymer solution. Thanks to the recent advances in statistical mechanics and the rapid growth in computational power, there have been increasing theoretical and simulation studies on polymer adsorption. Muthukumar8 and Zheligovskaya et al.9 separately examined the recognition affinity of a random heteropolymer and a copolymer and proposed a two-stage pattern recognition mechanism. In the first stage, a copolymer first binds to the selective adsorbing surface but usually not at the lowest energy state. Following that, the adsorbed copolymer rearranges its conformation to reach a perfect bound state as a consequence of the strong interaction with surface. Petera and Muthukumar,10 Balazs et al.,11 and Genzer12,13 calculated the density profile and the monomer distribution of a copolymer near a chemically heterogeneous patterned surface by a self-consistent field theory. Chakraborty and co-workers14,15 studied the recognition ability of random heteropolymers on multifunctional surfaces by combining the mean-field theory and Monte Carlo simulation and found a sharp transition from weak to strong adsorption regime. Kriksin and co-workers16,17 utilized a “minimal” statistically mechanical model to investigate the adsorption behavior of copolymer on (9) Zheligovskaya, E. A.; Khalatur, P. G.; Khokhlov, A. R. J. Chem. Phys. 1997, 106, 8598. Zheligovskaya, E. A.; Khalatur, P. G.; Khokhlov, A. R. Phys. ReV. E 1998, 59, 3071. (10) Petera, D.; Muthukumar, M. J. Chem. Phys. 1998, 109, 5101. (11) Balazs, A. C.; Singh, C.; Zhulina, E. B. Macromolecules 1998, 31, 6369. (12) Genzer, J. AdV. Colloid Interface Sci. 2001, 94, 105. (13) Genzer, J. Macromol. Theory Simul. 2002, 11, 481. (14) Chakraborty, A. K.; Bratko, D. J. Chem. Phys. 1998, 108, 1676. (15) Chakraborty, A. K.; Golumbfskie, A. J. Annu. ReV. Phys. Chem. 2001, 52, 537. (16) Kriksin, Y. A.; Khalatur, P. G.; Khokhlov, A. R. J. Chem. Phys. 2005, 122, 114703. Khokhlov, A. R.; Khalatur, P. G. Physica A 1998, 249, 253. Khokhlov, A. R.; Khalatur, P. G. Phys. ReV. Lett. 1999, 82, 3456. Yu, S.; Velichko; Khalatur, P. G.; Khokhlov, A. R. Macromolecules 2003, 36, 5047.
10.1021/la062930n CCC: $37.00 © 2007 American Chemical Society Published on Web 01/10/2007
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the selectively functionalized surfaces. They suggested that a marked pattern recognition is possible for a copolymer with relatively short blocks at polymer/surface affinities beyond a certain threshold. Furthermore, the recognition ability is found to enhance with an increase in the number of different monomer units and in the complementary adsorption sites arranged on a compact surface. Nath et al.18 employed a density functional theory to analyze the ordering of block copolymers near patterned surfaces. Huber and Vilgis19 found that the localization behavior is qualitatively affected by surface penetrability. Semler and Genzer20 simulated copolymer adsorption on chemically patterned planar surfaces and revealed that the commensurability between the sequence distribution in copolymer chain and the spatial distribution of adsorbing surface sites plays a critical role in copolymer adsorption. Patra and Linse21 investigated the structural properties of polymer brushes adsorbed on nanopatterned surfaces. The results showed that the central part of a patterned brush remains nearly unchanged as long as the pattern is several times wider than the height of brush, which agrees qualitatively with the recent experimental observation from atomic force microscopy. Recently, Striolo22 explained how the presence of a solid hard mask, used to mimic nanoscale patterns on an underlying hydrophobic surface, affects surfactant adsorption. There have been a large number of studies on the adsorption of homopolymers and diblock copolymers, however, the adsorption of multiblock copolymers is scarcely investigated. The present work aims to quantitatively investigate the recognition affinity of multiblock copolymers on nanopatterned surfaces using Monte Carlo molecular simulations. Different architectures of copolymers are examined on a variety of patterned surfaces consisting of adsorbing and nonadsorbing stripes. Adsorption conformations including tail, loop, and train are characterized, which are of central importance to better understand the pattern recognition ability of target-imprinted chemical sequences and the de novo design of conformation-dependent sequences.9,16 Following this introduction, the model and the interaction potential used are described in section 2. The simulation results are presented and discussed in section 3, including density distributions, polymer configurations, adsorption conformations, and so forth. Finally, section 4 gives some concluding remarks.
2. Simulation Methodology The multiblock copolymer (AnB12-n)5 is represented as a freely jointed chain composed of 60 segments with an identical diameter σ. By varying n (n ) 3, 5, 6, 7, 9), we can model different architectures for the copolymers. A and B are two types of segments, and the interaction between the segments is mimicked by the square-well potential:
{
rij > 1.5σ 0 - u(rij) ) ij σ < rij < 1.5σ ∞ rij < σ
(1)
Figure 1. A simulation box with two identical patterned surfaces in the z direction. Each surface bears with alternating nonadsorbing C stripes and adsorbing D stripes (with attractive interaction to B segments in copolymer). Each stripe has the same width w. Shown here are w ) 7.5σ and Ns ) 8.
and B-B have attractive interactions, however, A-B has a repulsive interaction. Monte Carlo simulations were performed in a canonical ensemble with a box of Lx × Ly × Lz ) 60σ × 60σ × 30σ, as schematically shown in Figure 1. The periodic boundary conditions were adopted in the x and y directions, while in the z direction two identical impenetrable nanopatterned surfaces were located at Lz ) 0 and Lz ) 30σ, respectively. The surfaces bear with alternating nonadsorbing C stripes and adsorbing D stripes. Each stripe is equally sized with a width of w, consequently, the number of stripes along the x direction is Ns ) Lx/w. The C and D stripes have different interactions with A and B segments,
{
ri-surface g σ 0 βi-wall ) βλmn 0 e ri-surface < σ ri-surface < 0 ∞
(2)
where ri-surface is the distance between i segment and the surface, and λmn is the interaction strength defined as
βλmn )
{
ΨB-D m ) B, n ) D 0 other
(3)
This definition indicates that D stripe has attractive interaction only with B segment, while C stripe has no interaction with either A or B segment. In the simulation, two copolymer chains were used, equivalent to a reduced segment density of 1.11 × 10-3. The reduced temperature was T* ) kBT/ ) 6, which is estimated to be above the critical point of the confined copolymers following our previous work23 and Hehmeyer et al.’s work,.24 Chain conformations were sampled in the semi-infinite three-dimensional space by two types of trial moves, namely, translation and jiggling. In translation, a randomly selected chain is translated with a random displacement in the x, y, or z direction. In jiggling, each bond is subject to a rotation. The new bond vector is calculated by rotating the old one in an arbitrary solid angle. More details can be found elsewhere.25-27 For a typical system, 107 trial moves were initially used to reach equilibration, and the ensemble averages were obtained from the subsequent 4 × 107 trial moves. The statistical error of our simulation was typically less than 1%.
where rij is the distance between two segments i and j; ij is the cross well depth obtained from the combining rule (iijj)1/2; ii is the well depth between segments of the same type, and for simplification we have AA ) BB ) . To better probe the recognition affinity of the block copolymer, we assume that A-A
3.1. Density Profiles. Figure 2a and b shows the threedimensional density profiles of B segment along the x and z
(17) Kriksin, Y. A.; Khalatur, P. G.; Khokhlov, A. R. J. Chem. Phys. 2006, 124, 174904. (18) Nath, S. K.; Nealey, P. F.; de Pablo, J. J. J. Chem. Phys. 1999, 110, 7483. (19) Huber, G.; Vilgis, T. A. Eur. Phys. J. B 1998, 3, 217. (20) Semler, J. J.; Genzer, J. J. Chem. Phys. 2003, 119, 5274. (21) Patra, M.; Linse, P. Nano Lett. 2006, 6, 133. (22) Striolo, A. J. Chem. Phys. 2006, 125, 094709.
(23) Chen, T.; Liu, H. L.; Hu. Y. Macromolecules 2000, 33, 1904. (24) Hehmeyer, O. J.; Arya, G.; Panagiotopoulos, A. Z. J. Phys. Chem. B 2004, 108, 6809. (25) Cai, J.; Liu, H. L.; Hu, Y. Fluid Phase Equilib. 2002, 94-197, 281. (26) Dickman, R.; Hall, C. K. J. Chem. Phys. 1988, 89, 3168. (27) Ye, Z. C.; Chen, H. Y.; Cai, J.; Liu, H. L.; Hu, Y. J. Chem. Phys. 2006, 125, 124705.
3. Results and Discussion
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Figure 2. Density profiles of B segment along the x and z directions for copolymer (A7B5)5 on patterned surfaces with ΨB-D) -1.0 at (a) Ns ) 60 and (b) Ns ) 6. The snapshots are shown on the right (A segment: gray, B segment: black).
directions for asymmetrical copolymer (A7B5)5 on patterned surfaces. Different perspectives of the density profiles are shown in the Supporting Information. The two patterned surfaces are identical and the density profiles along the z direction are symmetrical from the box center, consequently, only half of the profiles are plotted. The adsorption energy between B segment and D stripe is set as ΨB-D) -1.0, and the number of stripes Ns along the x direction is 60 and 6, respectively, in Figure 2a and Figure 2b. Also shown are the typical simulation snapshots at equilibrium. At Ns ) 60 with narrow stripes (w ) 1σ), the density of B segment near the surface along the z direction is comparably close to the bulk density, implying that the copolymer prefers to stay in the bulk region to gain a larger configurational entropy. The copolymer chain cannot shrink on a narrow stripe and instead tends to “stick” onto the interfaces between neighboring nonadsorbing C and adsorbing D stripes. This behavior was previously observed by Kriksin et al.16 Near the adsorbing domain (i.e., D stripe), the density first appears as a peak because of the attractive interaction and then drops beyond the range of the square-well potential because of the excluded-volume effect. At this small w, the nanopatterned surface becomes nearly structureless. As a counterbalance of the entropic and energetic effects, the density distribution is largely governed by both the excludedvolume effect and the surface attraction. However, it is expected that the energetic effect will play a dominant role upon increasing the attractive strength between surface and copolymer.
At Ns ) 6 with wide stripes (w ) 10σ), the copolymer shows pronounced recognition on the attractive D stripes. Along the x direction, the density profile exhibits alternating peaks at D domains. Along the z direction, the density profile has the largest peak at z ≈ 0.9σ and then begins to oscillate with increasing z. Interestingly, at z ≈ 4.7σ, there is a small but indistinct peak, suggesting that the copolymer can be weakly recognized in the vicinity of the striped surface. At large z, density reaches the bulk density. As a consequence, it can be concluded that copolymer is subject to be recognized near the patterned surface when Ns is small, or equivalently, the width w of stripe is considerably large enough to accommodate the whole adsorbing block in such a way that the copolymer is able to wrap on the attractive stripe. 3.2. Pattern Transfer Parameters. Density profile gives us only intuitional information about the distribution of the copolymer chain, nevertheless, the recognition affinity on patterned surface cannot be quantitatively evaluated. Following Genzer,13 the pattern transfer parameter (PTP) is defined to estimate the pattern recognition of B segment along the z direction:
PTP(z) )
∫x ,y
D D
Φa(x,y,z)/AD -
∫x ,y
C C
Φa(x,y,z)/AC
∫x,y Φa(x,y,z)/(AC + AD)
(4)
where Φa(x, y, z) is the volume fraction of B at (x, y, z), and AC
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Table 1. PTP for Copolymer (A7B5)5 on Patterned Surfaces PTP ΨB-D
-1.0 -2.0 -4.0 -6.0 -10.0
Ns 2
6
12
20
40
60
1.98 2.00 2.00 2.00 2.00
1.89 1.97 2.00 1.96 2.00
1.73 1.80 1.93 1.96 1.97
1.57 1.90 1.98 2.00 2.00
1.07 1.66 1.96 1.99 2.00
1.07 1.32 1.55 1.64 1.71
and AD denote the surface areas of C and D domains on the surface, respectively. PTP ranges from +2.0 to -2.0. A value close to +2.0 indicates that the pattern is well replicated by the adsorbing segment. In contrast, a value of -2.0 means a complete inversion of the pattern, that is, the adsorbing segment adsorbs on the nonattractive domain. Finally, a value of zero implies that no recognition occurs. Table 1 gives the PTPs of B segment for copolymer (A7B5)5 on striped surfaces with various affinity strengths ΨB-D. When |ΨB-D| increases, PTP increases gradually as expected, implying that the adsorbing blocks are more easily adsorbed. In this case, the copolymer with longer adsorbing blocks is an ideal candidate to obtain a better recognition. At a given ΨB-D, PTP decreases with increasing Ns the number of stripes. Figure 3 illustrates the PTPs of B segment for five multiblock copolymers (AnB12-n)5 (n ) 3, 5, 6, 7, 9, respectively) versus the distance z from patterned surfaces with stripes of various widths. Both (A3B9)5 and (A9B3)5 are two multiblock copolymers with asymmetrical structures, in that the former has a longer adsorbing block, while the latter has a shorter one. (A5B7)5 and (A7B5)5 are also asymmetrical, but (A6B6)5 is symmetrical. Nevertheless, (A6B6)5, (A5B7)5, and (A7B5)5 show similar PTP, indicating that the recognition ability does not strongly depend on the copolymer symmetry. The multiblock copolymer can recognize not only the stripes on surface, but also the surface vicinity, primarily because of the chain connectivity and the attraction between B segments. This behavior is similar to the alternating and diblock copolymers.20 Compared to other copolymers, the recognition affinity of (A9B3)5 is weaker in the region near the surface. The bigger the Ns, the smaller is the region. At Ns ) 2 and Ns ) 6, PTP is close to zero at z ≈ 10σ, while at Ns ) 20 and Ns ) 40, it is close to zero at z ≈ 2.5σ. A closer analysis reveals that PTP does not change appreciably within z < σ, in other words, a flat region exists. This phenomenon is independent of the symmetry of copolymer and the width of stripe. Since σ is the segment diameter, the flat region is indeed a monolayer at the interface. When the distance z from the surface increases, PTP starts to drop with an extent depending on both molecular structure and Ns. Generally, PTP drops rapidly with increased Ns and decreased length of adsorbing block. The recognition ability (or the value of PTP) decreases with increasing Ns, however, there are three exceptions. First, the PTP of (A3B9)5 at Ns ) 6 is larger than that at Ns ) 2 for z > σ. This is because of a better match at Ns ) 6 between the length of the adsorbing segments (B9) and the width of the adsorbing stripe. Second, at Ns ) 60, the PTPs of all copolymers remain nearly a constant of about 0.67, instead of zero for z > 1.5σ. The reason is that at Ns ) 60 copolymer chains prefer to reside in the bulk region to gain a larger configurational entropy. A statistical mechanical model has demonstrated that there is a free-energy penalty to cross the C/D interface.16 Consequently, a difference exists in the bulk density along the x direction and PTP does not fall into zero. Similar behavior is observed from radii of gyration in the next section. Third, the copolymer with a longer adsorbing block is capable of better recognition given a certain width of adsorbing
Figure 3. Pattern transfer parameters of B segment for copolymers (AnB12-n)5 (n ) 3, 5-7, 9) on patterned surfaces with ΨB-D) -1.0 at different Ns. ], Ns ) 2; 0, Ns ) 6; 4, Ns ) 12; ×, Ns ) 20; /, Ns ) 40; +, Ns ) 60.
stripe, for instance, (A3B9)5 has a stronger recognizing ability than (A9B3)5. This is because each adsorbed block is confined within the corresponding favored stripe, and the chain shows a “zipped” configuration.16 Such a behavior is different from the adsorption of an asymmetric diblock copolymer on a checkerboard pattern,13 in which the copolymer with a shorter adsorbing block can be recognized better. PTP is observed to decrease with increasing Ns, and the influence of Ns on PTP can be classified into three types. First, at Ns ) 2 or 6, the stripe is wide with width of 30σ or 10σ, and PTP near the surface is close to +2.0, indicating a perfect recognition. Not unexpectedly, a wide stripe can completely accommodate the adsorbing block, and hence PTP is the highest. Second, at Ns ) 12 or 20, the surface has a moderate stripe width,
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Figure 5. Schematic illustration of tail (1), loop (2), and train (3).
Figure 4. Radii of gyration (Rg/σ)2 for copolymer (A7B5)5 versus the distance z from patterned surfaces with ΨB-D) -1.0 at (a) Ns ) 60 and (b) Ns ) 6. ]: (Rg,x/σ)2; 0: (Rg,y/σ)2; 4: (Rg,z/σ)2.
and PTP is between 1.0 and 2.0, whereas the recognition ability is a little stronger at Ns ) 12. Third, at Ns ) 40 or 60, the stripe is rather narrow with only 1.5σ or 1σ in width, which is not sufficiently wide for the surface to hold adsorbing block; therefore, PTP is close to 1.0 and the recognition ability is poor. In this case, the adsorbing segments either reside along the y-axis or jostle to the neighboring nonadsorbing stripes or even cross the neighboring stripes and adsorb on the next-neighboring adsorbing stripes. However, this adsorption phenomenon is not favorable on a patterned surface with narrow stripes because of the lose of the configurational entropy. Consequently, PTP becomes smaller when the width of the stripe is narrow unless the adsorption energy is sufficiently high. 3.3. Radii of Gyration. Because of the geometric restriction and surface interaction, upon adsorption the copolymer has a different conformation from the bulk phase. In this work, the conformation was characterized by the ensemble-averaged anisotropic radii of gyration Rg,x2, Rg,y2, and Rg,z2 separately in the x, y, and z directions
Rg,p2 )
〈∑ 1
N
i
〉
(pi - pcom)2
(5)
where p ) x, y, and z; pi is the coordinate of the ith segment; pcom is the center of mass (com) of a polymer chain; and N is the number of segments in the chain.29 Figure 4 shows the reduced radii of gyration (Rg/σ)2 for (A7B5)5 versus the distance z from patterned surfaces with ΨB-D) -1.0 at Ns ) 60 (Figure 4a) and Ns ) 6 (Figure 4b). Near the surface, Rg,y is larger than Rg,x, and both are larger than Rg,z, predominantly because of the “stripe effect” and the repulsion of the surface. Moving away from the surface, Rg,y and Rg,x decrease gradually, while Rg,z increases. Eventually, as expected they are nearly identical in the bulk phase. These indicate that there is a conformational transition of the polymer chain, from an elongated coil preferentially along the one-dimensional y direction, to an ellipsoid along the two-dimensional x and y directions, and finally (28) Cerda` J. J.; Sintes, T. Biophys. Chem. 2005, 115, 277. (29) Eisenriegler, E.; Kremer, K.; Binder, K. J. Chem. Phys. 1982, 77, 6296.
to a three-dimensional globoid. Similar behavior of homopolymers was observed by Striolo et al.30 This phenomenon of multiblock copolymer is relevant to the folding/unfolding of biomolecules. The variations of Rg,y, Rg,x, and Rg,z depend strongly on Ns. At Ns ) 60, Figure 4a shows that Rg,y is consistently greater than Rg,x because of the stripe effect. In the bulk phase, Rg,y and Rg,z are identical but slightly greater than Rg,x because of the interfacial free energy. A copolymer chain can cross over a few neighboring adsorbing and nonadsorbing stripes and sticks into the multiple C/D interfaces. However, there is an increase in free energy by +216 across the C/D interface, which facilitates the polymer chain to move into the bulk phase to gain a low free energy. As a consequence, a balance exists between the adsorption energy ΨB-D and the free energy for polymer chain to cross the C/D interface. At Ns ) 6, Figure 4b shows that Rg,x is close to Rg,y beyond z ) 2.5σ, and Rg,x, Rg,y, and Rg,z are nearly equal in the bulk phase. Under this condition, the whole polymer chain is located in a constant external potential instead of crossing the C/D interface. The chain conformation is dominantly determined by the adsorption potential ΨB-D near the surface but by the chain connectivity away from the surface, that is, beyond the range of square-well potential. Upon comparison with Figure 4a at Ns ) 60, here Rg,y is greater near the surface, an indicator that the stripe effect of wider stripes is stronger and B segments are better recognized. 3.4. Conformations. Adsorption conformations can be classified into three types: tail, loop, and train. A sequence of successive segments are referred to as tail if they start from the head or the end of a chain to the first segment in contact with surface, they are referred to as loop if they are between two nearest segments that are in contact with surface, and they are referred to as train if a sequence of successive segments are in contact with the surface. Consequently, the lengths of tail, loop, and train are in the range between 1 and N - 1, N - 2, and N, respectively. Figure 5 schematically illustrates the three conformations. Although not considered under this study, when the two surfaces are sufficiently close, adsorbed polymer chain can form another conformation, bridge, which is closely related to the stability of colloidal suspensions. The average size of a conformation q is estimated by31
Lq )
∑l Pq(l)/∑Pq(l)
(6)
where Pq(l) is the probability to find a conformation with length l:31
Pq(l) ) Nq(l)/
∑ Nq(l)
(7)
where Nq(l) is the number of a conformation with length l observed during simulation. Figure 6 shows the probabilities of tail, loop, and train as a function of length for copolymer (A7B5)5 on patterned surface with ΨB-D) -1.0 and at Ns ) 6. Both tail and loop exhibit alternating peaks, which is similar to what was observed by Jeon (30) Striolo, A.; Prausnitz, J. M.; Bertucco, A. Macromolecules 2000, 33, 9583. (31) Jeon, J.; Dobrynin, A. V. Phys. ReV. E 2003, 67, 061803.
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Figure 6. Size distributions of three conformations versus length for copolymer (A7B5)5 on patterned surfaces with ΨB-D) -1.0 at Ns ) 6. 0: tail; ]: loop; 4: train.
Figure 8. Average sizes of (a) tail, (b) loop, and (c) train for copolymers (AnB12-n)5 (n ) 3, 5-7, 9) on patterned surface with ΨB-D) -1.0. ], (A3B9)5; 0, (A5B7)5; 4, (A6B6)5; ×, (A7B5)5; +, (A9B3)5.
Figure 7. Average sizes of (a) tail, (b) loop, and (c) train for copolymer (A7B5)5 on patterned surface at different Ns. ], Ns ) 2; 0, Ns ) 6; 4, Ns ) 12; 3, Ns ) 20; /, Ns ) 40; +, Ns ) 60.
and Dobrynin.31 However, with increasing length, the peak of loop drops, while that of tail keeps nearly a constant, which is caused by the configurational entropy effect. As reported by Chen et al.,32 the probability to find a shorter train is higher and the length of train is mainly affected by two factors: (1) the higher adsorption energy which leads to a longer train but is limited by the length of adsorbing block and (2) a longer train occupies more adsorption sites and thus sterically hinders the further adsorbed polymer to form trains. Figure 7 shows the effect of the adsorption energy ΨB-D on the average sizes of tail, loop, and train for multiblock copolymer (A7B5)5 on patterned surfaces at various Ns. The average size of each conformation remains essentially unchanged when ΨB-D ranges from -10 to -4. Primarily, this is because when ΨB-D is negatively less than -4, all adsorbed segments are essentially (32) Chen, T.; Liu, H. L.; Hu, Y. J. Chem. Phys. 2001, 114, 5937.
on the striped surface and cannot move freely. In other words, chemical adsorption may occurr when ΨB-D is less than -4. When ΨB-D changes from -4 to -1, Ltail increases monotonically and Lloop increases marginally, whereas, Ltrain decreases. Because of the decrease in adsorbing energy, segments are not strongly adsorbed on the surface. With deceasing Ltrain, more segments participate in constructing loops and tails; consequently, Ltail and Lloop increase as the adsorption energy increases. When ΨB-D ) 0, there is no interaction between B segment and D stripe, and the patterned surface is essentially structureless. In such case, more segments move away from the substrate, and the spatial distribution of B near the surface monotonically decreases (data not shown here), which leads to a monotonic decrease in Ltail, Lloop, and Ltrain. In addition, we find that the average sizes of tail, loop, and train exhibit a weak dependence on Ns. Figure 8 shows the effect of molecular structure on the average sizes of tail, loop, and train for multiblock copolymers (AnB12-n)5 (n ) 3, 5-7, 9) on patterned surfaces with ΨB-D) -1.0 at different Ns. Similar to Figure 6, Ltail is the greatest and Ltrain is the smallest. At a given Ns, Ltail increases but Ltrain decreases with the increase of n. For a multiblock copolymer, the nonadsorbing A segments primarily participate in constructing tails and loops, while the adsorbing B segments primarily participate in constructing trains. Upon increasing the number of nonadsorbing A segments, that is, increasing n, the probability to form loops and tails is enhanced. Simultaneously, the number of adsorbing B segments decreases, and thus the probability to form trains decreases.
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The influence of Ns on the average sizes of tail, loop, and train is relatively complicated. Generally, when Ns increases, as Genzer has found,13 Ltail first increases and then remains unvaried, Ltrain decreases moderately once Ns is greater than 20, but Lloop has no distinct trend in variation. The reason might be that a wide adsorbing stripe can hold a whole adsorbing block when Ns is small. With increasing Ns, however, the stripe is not sufficiently wide and part of the block has to move into the bulk phase to gain the maximum entropy.
4. Conclusions Monte Carlo simulations have been performed to study the nanopattern recognition of multiblock copolymers. The recognition affinity are quantitatively characterized by the density profiles, pattern transfer parameters, and radii of gyration as well as adsorption conformations including tail, loop, and train. We find that the multiblock copolymer can readily recognize the wide adsorbing stripes on the patterned surface. The recognition affinity depends weakly on copolymer symmetry and is enhanced on wider stripes, with a larger number of adsorbing segments, and at a higher adsorption strength. Driven by the confinement effect, the copolymer chain exhibits an elongated shape near the surface.
Chen et al.
However, a shift to elliptical and finally to globular is observed moving away from the surface. The simulation results reveal that the average size of the tail is the greatest and that of the train is the smallest among the three adsorption conformations. Moreover, the tail becomes longer while the train becomes shorter with increasing number of the nonadsorbing segments in the copolymer chain. Acknowledgment. The authors are grateful to Dr. Alberto Striolo for helpful discussions. This work was supported by the National Natural Science Foundation of China (Projects No. 20236010, 20476025, 20490200), the Doctoral Research Foundation sponsored by the Ministry of Education of China (Project No. 20050251004), Shanghai Municipal Science and Technology Commission of China (No.05DJ14002), E-institute of Shanghai High Institution Grid (No. 200303), and the National University of Singapore. Supporting Information Available: Density profiles of B segment in multiblock copolymer (A7B5)5 on patterned surfaces. This material is available free of charge via the Internet at http://pubs.acs.org. LA062930N
