Self-Assembled Morphologies of Diblock Copolymer Brushes in Poor

May 17, 2012 - Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada. Macromolecules , 2012, 45 (11), pp 4920–...
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Self-Assembled Morphologies of Diblock Copolymer Brushes in Poor Solvents Run Jiang, Baohui Li, Zheng Wang, and Yuhua Yin* School of Physics, Nankai University, Tianjin, 300071, China

An-Chang Shi* Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada ABSTRACT: Self-assembled morphologies of grafted linear AB diblock copolymers are investigated by a simulated annealing method. The copolymers are tethered to a flat substrate by the ends of the A blocks and immersed in a solution that is poor for both A and B components but exhibits a slight preference for one of the blocks. The morphological dependence of the system on the solvent selectivity, polymer grafting density, and the block lengths is investigated systematically. Phase diagrams for systems with two different grafting densities are constructed for the case where the chains are tethered by the less insoluble blocks. At a moderate grafting density, a variety of complicated morphologies, such as spherical pinned micelles, wormlike micelles, and stripe structures, are observed by varying the block lengths. Other complicated morphologies, such as perforated layers and complete layers, can be formed at a relatively high grafting density. More interestingly, by adjusting the length of copolymer chains and the volume fraction of the more insoluble block, some novel morphologies can be induced, ranging from “spheres-in-stripe” and “rods- in-stripe” structures at the moderate grafting density to “spheres-in-layer” and “rods-in-layer” structures at the higher grafting density. It is also observed that garlic-like and caterpillarlike structures can be obtained only when the solvent is more selective for the top block, consistent with previous theoretical results. Furthermore, the effect of the incompatibility of the two blocks on the structural evolution is also investigated.

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surface micelles formed by multichain at intermediate regime.4 If the grafting point is roughly uniform, such micelles appear as an ordered array. In the case of block copolymers, in addition to the grafting density, one also can vary the solvent affinities to each component and the interaction energy between the different monomers. Consequently, the system can be driven to form more complicated patterns than may be possible with homopolymers. There are extensive experimental27−29 and theoretical works as well as simulation studies30−32 on grafted AB diblock copolymer brushes in a selective solvent that is poor for one block but good for the other block. However, experimental investigations33,34 and theoretical35 and simulation studies31 of the behavior of grafted block copolymers immersed in a solvent that is poor for both blocks are less developed. Zhulina et al.35 used a two-dimensional self-consistent field calculations and scaling arguments to determine the behavior of grafted AB diblock copolymers, where the surrounding solution is assumed to be a poor solvent for both components. They focused on the situation where the Flory−Huggins interaction

INTRODUCTION Polymer brushes have been the subject of extensive theoretical and experimental studies1−7 due to their various applications including colloidal stabilization,8 chemical gates,9 lubrication, friction, and adhesion.10−12 In most of these traditional applications, the polymer and solvent readily mix together and the chains form a swollen polymer brush. However, much recent attention has been paid to the designing of nanopatterned surfaces or thin films by immersing these end grafted polymers in a poor solvent. In these systems, the polymer can only microphase separate into micelles in the tens to hundreds of nanometers range due to the immobile ends. The shape and size of polymer micelles can be controlled by the grafting density or molecular weight of the polymer. Therefore, such systems may provide an ideal platform for applications such as microelectronics,13 microreaction vessels and drug delivery14 and biomimetic material fabrication.15 The behavior of grafted homopolymers in poor solvent conditions has been addressed theoretically by self-consistent field (SCF),16−23 Monte Carlo24,25 and molecular dynamics simulations.26 So far, depending on the polymer grafting density three different regimes have been identified: individual “tadpole” globule formed by isolated chain at very low grafting density, collapsed polymer layers at very high density, and “octopus” © 2012 American Chemical Society

Received: March 19, 2012 Revised: May 6, 2012 Published: May 17, 2012 4920

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parameter between the A and B blocks (χAB) is close to zero, but the solvent affinities of the different blocks are significantly different. They demonstrated that the solvophobic interactions within the system drive the chains to self-assemble into a variety of structures, including “onion-” and “garliclike” pinned micelles. The specific morphology and dimensions of the micelles depend on the relative block lengths and whether the chains are grafted by the more or the less soluble component. More recently, Wang and Müller examined the microphase separation of diblock copolymer brushes in selective solvents using single-chain-inmean-field simulations.31 They obtained morphology diagrams in terms of fA (the fraction of the A block) and σ (the grafting density) for block copolymer brushes in different solvents. In particularly, when the solvent is poor for both A and B blocks, with a slight preference for the A block, with the increasing of fA, they observed a morphological sequence from continuous layers, to perforated layers, to ripple structures, to dimples and to unsegregated chains. However, due to the fluctuation of the grafting density for diblock copolymer brushes with a random pattern of grafting points, the morphology they observed lacks a long-range periodic order. On the experimental front, Zhao and Brittain presented evidence for the mechanism of the phase segregation predicted by the theoretical investigations.33 They synthesized a tethered block copolymer of polystyrene-blockPMMA (PS-b-PMMA) films, and observed that the tethered diblock copolymers underwent reversible changes in water contact angles as the film was treated with different solvents. Despites these previous studies, which have led to a good understanding of the physical behavior of diblock copolymers brushes in poor solvents, a comprehensive understanding of the system is still lacking. Therefore, it is desirable to construct detailed phase diagrams and to obtain understanding of the different scenarios of phase transformations sequences. In our previous studies, we have investigated the behavior of grafted linear AB diblock copolymers in selective solvents that is good for one block and poor for the other block32 and the morphologies and structural transitions of grafted Y-shaped ABC triblock copolymers in different solvents36 using the simulated annealing method. We demonstrated that the detailed morphology of grafted copolymer depends sensitively on the solvent selectivity, the grafting density, and the composition of the copolymer. Morphological transitions as well as size and spacing of the micellar aggregates can be manipulated by varying the block lengths. In this paper, we continue this line of research and examine the behavior of linear AB diblock copolymers that are grafted uniformly by one end onto a planar surface in selective solvents. As indicated by our previous study of tethered diblock copolymers,32 the competition between various interactions will give rise to various novel structures. Here, we focus on the situation where the copolymer is immersed in a solvent that is a poor for both components but exhibits a slight preference for one of the two blocks than the other. We use the simulated annealing method to investigate systematically the morphological dependences of the brushes on solvent quality, polymer grafting density, block length and the incompatibility of the two blocks. For the case where the chains are tethered by the less insoluble blocks, we also obtain morphology diagrams in terms of the relevant parameters. The paper is arranged as follows. In the next section, we describe our model and provide details of the simulation technique. In the subsequent section, we discuss the results of our simulations for grafted diblock copolymers in poor solvents. Finally, we summarize our conclusions from these studies.

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MODELS AND METHODS

The simulations were carried out using the simulated annealing technique37,38 applied to the “single-site bond fluctuation” model of polymers.39,40 Because details of the model system and simulation procedure have been given elsewhere,32,41 only a brief account of the model and method is given here. The model system is embedded in a simple cubic lattice of volume V = Lx × Ly × Lz. Periodic boundary conditions are applied in the x- and ydirections. Two homogeneous impenetrable surfaces are introduced atz = 0 and z = Lz, respectively. Polymers are not allowed to occupy these surface layers. The grafting points are distributed in the z = 1 plane, with equal “spacing” of d in both x- and y- directions; therefore, the grafting density of the copolymers is specified by σ = 1/d2. In our simulations, we consider the np linear AB diblock copolymer flexible chains each fixed onto a solid surface by the end of the A block. The dimensions are Lx = Ly = 54 if not specified, and Lz is much large than the chain length N. Therefore, the number of the copolymers is np = Lx × Ly × σ. The monomer number of each block is NA and NB respectively, thus, the total number of monomers in each chain is N = NA + NB. The bond length is set to be 1,√2, and √3 so that each site has 26 nearest-neighbor sites. The excluded volume effect is dealt with by enforcing the rule such that two or more monomers cannot occupy one lattice point at the same time. The starting configuration of the simulations is generated by putting an array of copolymer chains onto the lattice such that they are parallel to the z-axis with an extended conformation. After the desired number of chains has been generated, the remaining empty sites were assigned to solvent molecules. Starting from this initial configuration, the ground state of the system is obtained by executing a set of Monte Carlo simulations at decreasing temperatures. The energy of the system is the objective function in the simulated annealing. In our simulation, only the 26 nearest-neighbor interactions are considered. There are five types of effective pair interactions in the system, which are interactions of block A and block B, block A and solvent, block B and solvent, block A and surface, and block B and surface. These interactions are modeled by assigning an energy Eij = εijkBTref to each nearest-neighbor pair of unlike components i and j, where i,j = A, B, S(solvent), and W (surface or wall) and εij is a reduced interaction energy; kB is the Boltzmann constant; and Tref is a reference temperature. Without loss of generality, we assume εAB = 0.5 (unless otherwise specified) which ensures the immiscibility between the A and B monomers. When the solvent is selective for A blocks, we set εAS = 1.0 and εBS = 2.0, whereas when the solvent is selective for B blocks, we set εAS = 2.0 and εBS = 1.0. To avoid the adsorption of the blocks to the grafting surface, we set the interaction of the blocks with the surface the same as that with the solvent. Furthermore, we set all εii = 0 with i = A, B, S, W. We applied the usual annealing schedule with Tj = f Tj−1, where Tj is the temperature used in the jth annealing step and f is a scaling factor. The annealing was continued until the temperature reached a predetermined value (TF). In our simulations, f = 0.9, T1= 100Tref, and T reaches TF =T65 after 65 annealing steps. One Monte Carlo step (MCS) is defined as the average time required for all the lattice sites to be visited in an attempted move. At each annealing step, 15000 MCS are performed.

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RESULTS AND DISCUSSION In this paper, the solvent is assumed to be poor for both A and B blocks. Both blocks collapse in the solvent, but the solvent exhibits a slight preference for one of the blocks. The incompatibility between the AB blocks is assumed to be less than that between each block and the solvent. Results for two typical cases are presented in this section: (1) the solvent is more incompatible with the top B block; (2) the solvent is more incompatible with the grafted A block. As the primary aim of this work is to concentrate on morphological transition of multichain micelles, we do not show the simulation results for grafted copolymers with very low grafting density, where the chains do not overlap and interact. In this dilute regime the polymers 4921

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aggregate into individual core−shell micelles, with the less solvophobic blocks forming the core and the more solvophobic blocks forming the shell.35 Instead, we focus on the different morphologies formed at a moderate grafting density with σ = 0.111 and a high grafting density with σ = 0.25, and investigate the influence of the block length and the incompatibility of the two blocks on the morphology of the copolymer brushes. Solvent Selective for the Grafted Blocks: εAS = 1.0 and εBS = 2.0. This set of parameters is chosen so that the grafted copolymers are exposed to a solvent that is more compatible with the bottom, grafted A blocks, than the top B blocks. Therefore, the top blocks form the inner core and the grafted blocks form an outer coating. Depending on the grafting density and the lengths of the A and B blocks, the copolymer brushes exhibit several distinct morphologies. At the moderate grafting density with σ = 0.111, the morphologies of the brushes are summarized in the phase diagram shown in Figure 1. Four regions, denoted as spherical

Figure 2. Morphologies of grafted diblock copolymers with various lengths of the B blocks at σ = 0.111 and NA = 9: (a) NB = 3; (b) NB = 15; (c) NB = 30. In this and following figures, the A blocks are shown as light color and B blocks as dark color.

surface contact (see Figure 2a). The micelles appear to pack in the 2D x−y surface with a hexagonal symmetry. With the increase of NB, the number of chains in the core and in the entire micelle increases, so the size and the extent of the core in the z direction increase. At the same time the number of micelles in simulation box decreases. Because of the tethered A blocks at the bottom, A shells cannot shield the core effectively. The upper-part of the B cores will be exposed to the solvents eventually. The structure of wormlike micelles with NB = 15 is shown in Figure 2b, where the inner B cores are short rods in shape with legs formed by the A blocks. When the length of B blocks increases up to NB = 30, the AB stripe structures are observed (see Figure 2c), in which a semicylinder is formed by the B blocks parallel to the bottom, whose legs are formed by the A blocks. Because the A blocks are relatively short and tethered to the substrate, they only can enrich on the bottom to prevent the contact between B and the substrate. With a further increase in NB, the height of the semicylinders increases. As shown in Figure 1, morphological transitions also occur with the increase of NA at a fixed NB . In this case, a morphological sequence, from spherical micelles to wormlike micelles, and then to stripe structure, is also observed with the increase of NA. The typical morphologies with NB = 9 are shown in Figure 3. Similar

Figure 1. Phase diagram for system at σ = 0.111 in the NA and NBspace. The circles represent spherical pinned micelles; the up-triangles, wormlike micelles; the close squares, AB stripes structures; and the open squares, A stripes structures.

micelles, wormlike micelles, A stripe structures (where A component forms stripe structures, in which B component forms spheres or short rods) and AB stripe structures (where both A and B components form stripe structures) are observed in this case. Before a detailed description of the phase behavior, a number of observations should be made: (1) In our simulations, the shape of the wormlike micelles can be ellipsoid, short rod or mixed structure of spheres and rods. However, these morphologies are found not to be stable when the simulations were repeated with different random number seeds. (2) Because of the limitation of the simulation box size, we only perform simulations on systems with 3 ≤ N ≤ 66. So we do not locate a morphological transition from stripes to other morphologies in this case. As shown in Figure 1, when the length of the A block and B block are both short, the block copolymers form core−shell spherical micelles (or onion-like micelles), where the outer shell is composed of A blocks around the inner spherical B core. At a fixed NA, morphological transitions from spherical micelles to elongated wormlike micelles, then to stripe structures may occur with the increase of NB. As an example, the morphological sequence with NA = 9 is presented in Figure 2. For NB ≤ 12, core−shell spherical micelles are formed. Especially, when the B blocks are very short, the A blocks form a thick outer shell around the inner B core to minimize the B/solvent contact and the B/

Figure 3. Morphologies of grafted diblock copolymers with various lengths of the A blocks at σ = 0.111 and NB = 9: (a) NA = 3; (b) NA = 27; (c) NA = 33.

to the former case, for NA ≤ 12, spherical micelles are formed. However, when the length of the A blocks is very short, they only contribute to forming the legs of the spherical micelles, whose cores are almost composed of pure B blocks (see Figure 3a). By increasing NA, morphological transitions from spherical micelles to elongated wormlike micelles, then to a stripe structure, are observed. The structure of wormlike micelles with NA = 27 is shown in Figure 3b, where the inner B core is a short rod around by the outer A shell. With a further increase of NA, the A shell becomes sufficiently large that adjacent shells are driven to merge and thereby minimize their contact with solvent. In this case the multiple rod-like cores are simultaneously shielded by a common A shell, which resembles a long cylinder (see Figure 3c), namely an A stripe structure. 4922

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Figure 4. Density profiles of monomers along the z-direction for the typical pinned micelle morphologies of grafted diblock copolymers at σ = 0.111 and N = 18: (a) f B = 0.167; (b) f B = 0.50; (c) f B = 0.833. The corresponding snapshots are provided in the inset.

Figure 5. Density profiles of monomers along the z-direction for the typical stripe structures of grafted diblock copolymers at σ = 0.111 and N = 36: (a) f B = 0.083; (b) f B = 0.167; (c) f B = 0.5; (d) f B = 0.833. The corresponding snapshots are provided in the inset.

core and A legs are formed. Second, Figure 5 shows the snapshots and the density profiles of monomers along the z-direction for the typical stripe structures observed for N = 36. At a very small value of f B (f B = 0.083), it is interesting to note that the “spheresin-stripe” structures are observed, where B spherical micelles are formed in the center of an A stripe. When f B = 0.167, the transition of the shape of B domain from spheres to short rods is observed. In these two morphologies, with an enhancement in the outer layer, the inner B domains are effectively shielded from the energetically unfavorable solvent. As the fraction of B block increases, f B → 0.5, the block copolymer assemble into core− shell stripes, where the A component forms an outer shell around the inner B core. Each stripe has a perfectly cylindrical cross-

It should be also noticed that the exact internal separated structures depend on the volume fraction of the B block, f B = NB/ N, though the overall shape of microphase separation morphologies is determined by the total number of monomers in each chain. This can be illustrated by the following two examples shown in Figure 4 and Figure 5. First, the snapshots and the density profiles of monomers along the z-direction for the typical spherical micelles observed with N = 18 are shown in Figure 4. From Figure 4a, it is noted that at f B = 0.167 (NA ≫ NB), the spherical micelles are composed of perfect spherical B cores and thick A shells. At f B = 0.5, the spherical B cores have deformed and the A shells become relatively thin. At f B = 0.833 (NA ≪ NB), the spherical micelles with a semispherical pure B 4923

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section in a plane perpendicular to the x−ysurface (see Figure 5c). In fact, as N ≥ 36, for symmetric or nearly symmetric diblock copolymers, core−shell stripe structure is always observed at this grafting density. As further increase f B to 0.833 and up, B stripes with a semicylindrical cross section are formed, whose legs are formed by A blocks. Because the A blocks are very short and tethered on the substrate, they become more stretching to prevent the contact between B and the substrate. At a high grafting density with σ = 0.25, the simulation results are summarized in the phase diagram shown in Figure 6. Similar

formed only by A component (A stripes) disappear in the phase diagram with the high grafting density. Instead, the stripe structures are always formed by both of the two components (AB stripes) . From Figure 6, it can also be observed that, at the high grafting density, the morphological transition sequence of A component from stripes to a perforated layer with some holes filled with solvent molecules and then to a complete continues layer occurs by further increasing NA at a fixed NB. Several morphologies are formed by B component inside the A perforated layer or A complete layer depending on the relative length of A/B blocks. The representative snapshots with NB = 4 are plotted in Figure 7 where wormlike micelles and spheres are formed at NA = 12and NA = 14, respectively, by the more insoluble B component, while the less insoluble A component forms the continuous phase in the perforated layers. As shown in Figure7e, when NA ≥ 16, a complete layer of A component is observed, inside which the B component forms spherical micelles. On the other hand, by further increasing NB with a fixed NA the morphological transitions of both components from stripe morphology to perforated layers, then to complete layers simultaneously are observed. The representative snapshots for the morphological sequences with NA = 4 are shown in Figure 8. Especially, in this case, the diblock copolymers with small NA and relatively large NB may be viewed as grafted B homopolymers in a poor solvent. For grafted homopolymers in a poor solvent, Pattanayek et al.23 observed the similar sequence of structures: complete layer → hole (perforated layer) → lamella/cylindrical micelle (stripes) → fused spherical micelle with decreasing the grafting density or the chain length in the system. Compared with the morphologies formed at the moderate grafting density (σ = 0.111), two types of different structures, the perforated layer structures and complete layer structures, are formed at the high grafting density (σ = 0.25). Figure 9 shows the snapshots and the density profiles of monomers along the zdirection for the typical perforated layer structures observed at σ = 0.25. As shown in Figure 9a, when NB ≪ NA, a disordered morphology is formed by B component inside the A perforated layer. With increasing NB, the morphological transitions to B spheres, then to B short rods are observed. When NB → NA, the diblock copolymers become almost symmetry and the two components both form perforated layers, where the hole appear to pack in the 2D x-y surface with a hexagonal symmetry. And we notice that there is a tendency for the A domain to surround the B domain to avoid the unfavorable contact of B component with solvents in this AB perforated layer as shown in Figure 9d. An analogous morphology which was labeled as the bicontinuous honeycomblike morphology, was observed in the experiment of tethered diblock copolymer after selective solvent treatment.29 From the phase diagram shown in Figure 6, we find that in

Figure 6. Phase diagram for system at σ = 0.25 in the NA and NBspace. The circles represent spherical pinned micelles; the up-triangles, wormlike micelles; the squares, stripe structures; the open downtriangles, A perforated layers ; the close down-triangles, AB perforated layers; the open diamonds, A complete layers; and the close diamonds, AB complete layers.

as the case at σ = 0.111, spherical pinned micelles are formed for smaller NA and NB. By increasing NA or NB, morphological transitions from spherical micelles to wormlike micelles, then to stripe structure are observed. When compared with the phase diagram at the moderate grafting density (σ = 0.111), however, Figure 6 presents three differences. (1) The regions of spherical micelles, wormlike micelles, and stripe structure shrink to narrow intervals of NA and NB. Wang and Muller also studied morphologies of diblock copolymer brushes in poor solvents with a slight preference for the grafted A blocks using singlechain-in-mean field simulation. They found that the stability region of the laterally structured phases expands with decreasing grafting density.31 Recently, Matsen et al. also found such a feature in melt brushes.42 (2) The regular hexagonal symmetry formed by the spherical micelles is not observed in the case of the high grafting density. Because in this case the simulation size is multiplied up many times than the periodicity of microphase separation morphologies, this feature demonstrates that lateral structures lack long-range periodicity in the grafting diblock copolymers as predicted in ref 31. (3) The stripe structures

Figure 7. Morphologies of grafted copolymers in solvents selective for A blocks at σ = 0.25 and NB = 4: (a) spherical micelles with NA = 4; (b) stripe structures with NA = 8; (c) B wormlike micelles in A perforated layer with NA = 12; (d) B spheres in A perforated layer with NA = 14; (e) B spherical micelles in A complete layer with NA = 18. 4924

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Figure 8. Morphologies of grafted copolymers in solvents selective for A blocks at σ = 0.25 and NA = 4: (a) spherical micelles with NB = 2; (b) stripe structures with NB = 6; (c) perforated layer with NB = 12; (d) complete layer with NB = 16.

Figure 9. Density profiles of monomers along the z-direction for the typical perforated layer of grafted diblock copolymers at σ = 0.25 with: (a) N = 14, f B ≈ 0.143; (b) N = 18, f B ≈ 0.222; (c) N = 20, f B = 0.3; (d) N = 26, f B ≈ 0.462. The corresponding snapshots are provided in the inset.

insoluble A block in a poor solvents, two brush regime denoted by BA (A continuous layer) and BB (B continuous layer) have been predicted under similar situation by Zhulina et al. using scaling theory.35 They speculated that in these two regimes the discontinuous component could form micelle type structures, although they did not provide details of these structures. In our simulations, we find that only the B micelles can form in A continuous layer, but A micelles can not form in the continuous B domain in this case. Once a complete B layer is formed at the top of the brush, a lateral uniform A layer always forms at the bottom even at NB ≫ NA when the diblock copolymer brushes grafted by the less insoluble A blocks. In ref 31, Wang and Muller observed a similar morphological sequence at high grafting density when increasing the fraction of bottom A blocks in a solvent which is poor for both A and B blocks with a slight preference for the A block. However, there are some differences between their results and ours. In their case, the B domains are always on the top of the A layers, whereas in our case, they are inside or partly inside the A

perforated layer region this AB bicontinuous morphology can be formed when NB ≥ NA. It should be also noted that, for most cases in our simulations, the holes in AB perforated layer do not pack orderly and the number of the holes decreases with the increase of NB. However, when NB ≫ NA, the A block can only contribute to form the legs of the B perforated layer. Figure 10 shows the snapshots and the density profiles of monomers along the z-direction for the typical complete layer structures observed at σ = 0.25. For large NA, a complete continues layer of A component is formed. Similar to the perforated layer case, as NB gradually increases from a very small value, the morphological transitions of B component from disorder morphology (region I) to spherical micelles (region II), to wormlike micelles (region III), then to perforated layer (region IV), are observed inside or partly inside the A layer (see Figure 6). As NB → NA or NB > NA, a complete B layer is formed on top of the A layer, therefore bicontinuous AB layers are formed. For diblock copolymer brushes grafted by the less 4925

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Figure 10. Density profiles of monomers along the z-direction for the typical complete continuous layer structures of grafted diblock copolymers at σ = 0.25 and N = 36: (a) f B ≈ 0.056; (b) f B = 0.167; (c) f B ≈ 0.278; (d) f B ≈ 0.389; (e) f B ≈ 0.556. The corresponding snapshots are provided in the inset.

Figure 11. Morphologies of grafted diblock copolymers at σ = 0.111, NA = 9, and NB = 9: (a)εAB = 0.0; (b) εAB = 0.5; (c) εAB = 1.0; (d) εAB = 3.0.

Figure 12. Averaged density profiles along the z-direction corresponding to morphologies shown in Figure 11: (a) for A monomers; (b) for B monomers.

two blocks on the structure of grafted copolymer, especially for the case of f B = 0.5. For case of σ = 0.111, as shown in Figure 11, when NA = 9, NB = 9, and εAB ≤ 0.5, core−shell micelles are formed. With the increase of εAB, the segregation of the A and B

layer, which may be due to the difference in the degree of preference of the solvent for the A block. The above simulations are carried out for the case of εAB = 0.5. We also examine the influence of the incompatibility between the 4926

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Figure 13. Morphologies of grafted diblock copolymers with σ = 0.111, NA = 18, and NB = 18: (a) εAB = 0.0; (b) εAB = 0.5; (c) εAB = 1.0; (d) εAB = 2.0.

Figure 14. Averaged density profiles along the z-direction corresponding to morphologies shown in Figure 13: (a) for A monomers; (b) for B monomers.

Figure 15. Morphologies of grafted diblock copolymers at σ = 0.25, NA = 10, and NB = 10: (a)εAB = 0.0; (b) εAB = 0.5; (c) εAB = 2.0; (d) εAB = 3.0.

Figure 14, from the corresponding averaged density profiles of B monomers we find that the B cores are perfectly spheres when εAB = 2.0. In the case of σ = 0.25, as shown in Figure 15, when NA = 10, NB = 10, and εAB = 0, a sandwich structure is formed, where A monomers enrich both near the grafting surface and the film surface while B monomers distribute in the interior of the film in order to minimize the unfavorable contact of B/solvent (see Figure15a). When εAB < 0.5, an AB perforated layer is formed where circular holes, filled with solvent, appear to pack in the 2D x−y surface with a hexagonal symmetry (see Figure 15b). With the increase of εAB, more solvent molecules will be incorporated into the copolymer brush layer, and the shape of holes becomes short rod (see Figures 15c), because the formation of the elongated holes can increase the contacts of A/solvent. And it is interesting to observe the morphological transition from perforated layer to stripe structure when εAB = 3.0, as shown in Figure 15d. When the degree of polymerization of the copolymer chain increases at high grafting density (σ = 0.25), a sandwich structure is also formed with NA = 20, NB = 20, and εAB = 0 as shown in Figure16a. However, with the increase of εAB, instead of the AB perforated layer structure, a laterally homogeneous AB layer is

components in perpendicular (z-direction) direction becomes stronger, and finally results in a splitting of core−shell structure at high εAB. This can be seen clearly from the corresponding average density profiles along the z-direction (Figure 12), where ρA increases at small Z values with the increase of εAB, at the same time, the curve peak of ρB moves to a larger Z value. That indicates that A blocks enrich near the grafting surface while B cores are pushed away from there. If εAB is increased further, to decrease contact between A−B components, one A micelle splits into two or more micelles around one B core near the grafting surface. When εAB = 3.0, B cores become perfect spheres, which can be demonstrated by the symmetry of the density profiles of B monomers. For the case of large total number of monomers in each chain (NA = 18, NB = 18), the core−shell stripes can be formed with relatively small εAB as shown in Figure 13. With the increase of εAB, the segregation of the A and B components in perpendicular direction becomes stronger, that results in A blocks enriching near the grafting surface, whereas B cylinders are pushed away from there. Because the increasing of εAB will lead most of the B core exposed to the solvents, to minimize the unfavorable A/B and B/solvent contacts, the morphological transitions of B core from cylinders to short rods, and then to spherical micelles when εAB is further increased. As shown in 4927

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unfavorable contact of A/B monomers, as shown in the corresponding average density profiles along the z-direction (see Figure16c). At a larger εAB (see Figure 16d), the contact of A/B becomes more unfavorable, the brush incorporates more solvent molecules into the interface between A and B blocks and more B monomers withdraw to the top of brush, resulting in a greater height of brush. Solvent Selective for the Top Blocks: εAS = 2.0 and εBS = 1.0. This set of parameters is chosen so that the grafted copolymers are exposed to a solvent that is more compatible with the top B blocks than the bottom, grafted, A blocks. At the moderate grafting density with σ = 0.111, when we fix the length of the A blocks at NA = 9 and gradually increase the length of the B blocks from 3 to 30 with a step of 3, the resulting morphological sequence is shown in Figure 17. For 3 ≤ NB ≤ 6 spherical micelles (onion-like structure) are observed where the inner core is formed by the more insoluble A blocks and the outer shell is formed by the more soluble B blocks. For 9 ≤ NB ≤ 12, an interesting morphology (see Figure 17c) is formed, where several small A cores are simultaneously shielded by one B shell. Zhulina et al.35 predicted such a morphology under similar conditions, and they termed this polymer micelles “garlics”, so we shall also use this terminology in this article. It is interesting to notice that with a further increasing of NB, a “caterpillar-like” structure (NB ≥ 15) is observed, where the body is formed by B stripes and feet are formed by small A pinned micelles. When we fix the length of the B blocks at NB = 9 and gradually increase the length of the A blocks from 3 to 30 with a step of 3, the typical morphologies are plotted in Figure 18. For NA < NB, the garlic-like structure is observed. With an increase of NA, several small A cores shielded by one B shell are merged into a bigger core, to better shield the A blocks from the solvent. With a further increasing of NB, short rods and then stripe structures of B component are formed. Figure 19 shows the typical morphologies obtained at the high grafting density with σ = 0.25, where we fix the length of the B blocks at NA = 4 and gradually increase the length of the A blocks from 2 to 20 with a step of 2. It is noticed that with increasing NB, the following morphological transitions of copolymer brushes take place: from a spherical micelles (NB = 2) to a wormlike structure (4 ≤ NB ≤ 6), then to a bicontinuous perforated layer (NB = 8). And with a further increase of NB, a complete B layer are formed on the top where A blocks form disorder micelles at the bottom (NB ≥ 10). For the longer A blocks, it is noticed that for NB ≥ NA, the layer of A component in bottom is also not laterally homogeneous but with some holes filled with B component. It is reasonable considering the preference for B blocks of surface due to εAW = εAS = 2.0 and εBW = εBS = 1.0 set in our model. Similar morphological transitions also occur with the increase of NAfor fixedNBas shown in Figure 20. Finally, we examine the effect of incompatibility of the AB blocks on structures when the solvent is selective for the top B block. First, we focus on the “garlic-like” structure formed at σ = 0.111, εAB = 0.5, NA = 9, and NB = 12 (see Figure 17c). As shown in Figure 21, when εAB = 0 as conditions in ref35, we do not observe the “garlic-like” morphology. Instead, an “onion” morphology is formed where only one A core shielded by one B shell. However, with the increase of εAB, one A core splits into two cores shielded by a common B shell (see Figure 21b), i.e., the garlic-like structures are formed. Further increasing in εAB to 2.0 or larger results in further splitting into more A cores (see Figure 21, parts c and d). At the same time, the morphology of B changes from shells to cores, which are pushed away from the

Figure 16. Density profiles for each species (A monomer, B monomer and solvent) along the z-direction for the laterally homogeneous AB layer structures at σ = 0.25,NA = 20, and NB = 20: (a) εAB = 0.0; (b) εAB = 1.0; (c) εAB = 3.0; (d) εAB = 4.0. The side view of the corresponding snapshots are provided in the inset.

formed where B monomers are pushed to the top layer and A monomers enrich on the bottom layer (see Figure 16b). A further increasing in εAB will lead solvent to be incorporated into the middle region between the A and B layers to reduce the most 4928

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Figure 17. Typical morphologies of grafted diblock copolymers for different length of the B block at σ = 0.111 and NA = 9: (a) NB = 3; (b) NB = 6; (c) NB = 12; (d) NB = 24. Top: perspective view. Bottom: bottom view.

Figure 18. Typical morphologies of grafted diblock copolymers for different length of the B block at σ = 0.111 and NB = 9: (a) NA = 6; (b) NA = 12; (c) NA = 15; (d) NA = 27. Top: perspective view. Bottom: bottom view.

Figure 19. Typical morphologies of grafted diblock copolymers for different length of B blocks at σ = 0.25 and NA = 4: (a) NB = 2; (b) NB = 4; (c) NB = 8; (d) NB = 10.

Figure 20. Typical morphologies of grafted diblock copolymers for different length of A blocks at σ = 0.25 and NB = 4: (a) NA = 2; (b) NA = 6; (c) NA = 10; (d) NA = 14.

grafting surface, and exposed to the solvents. This result can be understood considering that when εAB ≥ εAS, the contact between A blocks and solvents is favorable than that between A blocks and B blocks.

On the other hand, it should be also mentioned that, for the onion-like structure at σ = 0.111, εAB = 0.5, NA = 9, and NB = 3 (see Figure 17a), by slightly increasing εAB, a dumbbell-like structure similar to that predicted by Zhulina et al,35 is observed 4929

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Figure 21. Morphologies of grafted diblock copolymers at σ = 0.111, NA = 9and NB = 12 for different εAB: (a) εAB = 0; (b) εAB = 1.0; (c) εAB = 2.0; (d) εAB = 3.0. Top: A and B components are both shown. Bottom: only B components are shown.

When the grafting A block is more insoluble than the top B block, by increasing the length of the top block relative to that of grafting block at moderate grafting density, the copolymers associate to the garlic-like micelles or caterpillar-like structures which are not observed when the solvent is selective for the grafted blocks. Increasing the grafting density causes one or both components to form a continuous layer and eventually forms a laterally homogeneous brush for long blocks. The results are consistence with the theoretical prediction of Zhulina et al.35 We also examine the effect of the incompatibility of the A and B blocks on the copolymer morphologies. An increase in εAB will results in the segregation of the A and B components and a subsequent splitting of the structures. When the copolymer chains are tethered by the less insoluble A blocks, and the grafting density is moderate, for the limiting case of εAB = 0, the polymer− solvent interaction is the dominant contribution to the total energy. Thus, the formation of core−shell structures can reduce the polymer−solvent contacts effectively. With an increase of εAB, the A/B interfacial interaction becomes increasingly important. The stronger incompatibility of the A and B blocks results in the splitting of core−shell structures where the tethered A blocks enrich near the grafting surface while B cores to be pushed away from there. Especially, the morphological transition from core−shell stripes to spherical micelles is observed when εAB is sufficiently large. At a high grafting density, when εAB = 0, sandwich-like brushes in which the A component tends to wrap around the more solvophobic B component, can be observed. By increasing εAB, the copolymers can form AB perforated layer structures and then a stripe structures, or laterally homogeneous AB brushes depending on the length of the copolymer chains. On the other hand, when the copolymer chains are tethered by the more insoluble blocks, with the increase of εAB, the A and B micelles can coexist by the subsequent splitting of the onion-like or the garlic-like structures. In particular, an order array of dumbbell-like structures can be deduced from the onion-like structure by increasing εAB. On the other hand, when the copolymer chains are tethered by the more insoluble blocks, with the increase of εAB, the A and B micelles can coexist by the subsequent splitting of the onion-like or the garlic-like structures. In particular, an order array of dumbbell-like structures can be deduced from the onion-like structure by increasing εAB. Because of the capable of relatively unrestricted motion of the chemical linkage between the different block, this system exhibits novel structures which are significantly different from the grafted Y-shaped block copolymers in our previous study.36 First, for

in our simulation, where the B core is at the top of A domain (see Figure 22a). But if the incompatible of the A and B blocks are

Figure 22. Morphologies of grafted diblock copolymers atσ = 0.111, NA = 9 and NB = 3 with different εAB: (a) εAB = 2.0; (b) εAB = 3.0.

sufficiently strong that adjacent B cores are driven to merge and thereby their contact with A domain is minimized, and finally (εAB = 3.0), as shown in Figure 22b, we obtain a structure similar to that formed in garlic-like case.

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CONCLUSIONS In this paper, we use a simulated annealing method to investigate systematically the morphologies of grafted linear diblock copolymers with moderate and high grafting densities in poor solvents. The simulation results indicate that the detailed structures depend on the solvent selectivity, the grating density, and the composition of copolymer. The final morphology of a grafted copolymer is the result of the competition between these various interactions and controlling parameters. In the case where the copolymer chains are tethered by the less insoluble A blocks, phase diagrams for systems with a moderate density and a high grafting density are constructed to illustrate the dependence of the morphological transitions on the length of the blocks. When the grafting density is moderate, the diblocks self-assemble to form a variety of B micelles with morphologies ranging from spheres to worms to stripes, depending on the relative lengths of the A and B blocks. At the same time, the A segments contribute to the legs of the B micelles and also contribute to shielding the B core. By decreasing the fraction of the B block f B, single B core in a core−shell stripe structure can be also driven to form rods and spheres inside the A stripe shell. When the grafting density is relatively high, increasing the lengths of the blocks causes one or both components to form a continuous layer, in the middle of which the B component can form different micelles from spheres to rods depending on the relative lengths of the A and B blocks. 4930

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(7) (a) Singh, C.; Pickett, G. T.; Balazs, A. C. Macromolecules 1996, 29, 7559. (b) Singh, C.; Pickett, G. T.; Zhulina, B.; Balazs, A. C. J. Phys. Chem. B 1997, 101, 10614. (8) Pincus, P. Macromolecules 1991, 24, 2912. (9) Ito, Y.; Ochiai, Y.; Park, Y. S.; Imanishi, Y. J. Am. Chem. Soc. 1997, 119, 1619. (10) Leger, L.; Raphael, E.; Hervert, H. Adv. Polym. Sci. 1999, 138, 185. (11) Mansky, P.; Liu, Y.; Huang, E.; Russell, T. P.; Hawker, C. J. Science 1997, 275, 1458. (12) Ruths, M.; Johannsmann, D.; Rühe, J.; Knoll, W. Macromolecules 2000, 33, 3860. (13) Niu, Q. J.; Frechet, J. M. J. Angew. Chem., Int. Ed. Engl. 1998, 37, 66. (14) Balazs, A. C.; Singh, C.; Shulina, E.; Gersappe, D.; Pickett, G. MRS Bull. 1997, 16, 1. (15) Askay, A.; Trau, M.; Manne, S.; Honma, I.; Yao, N.; Zhou, L.; Fenter, P.; Eisenberger, P. M.; Gruner, S. M. Science 1996, 273, 892. (16) Halperin, A. J. Phys. (Fr.) 1988, 49, 547. (17) Shim, D. F. K.; Cates, M. E. J. Phys. (Paris) 1989, 50, 3535. (18) Huang, K.; Balazs, A. Macromolecules 1993, 26, 4736. (19) Zhulina, E. B.; Borisov, O. V.; Pryamitsyn, V. A.; Birshtein, T. M. Macromolecules 1991, 24, 140. (20) Singh, C.; Zhulina, E. B.; Gersappe, D.; Pickett, G. T.; Balazs, A. C. Macromolecules 1996, 29, 7637. (21) Zhulina, E. B.; Singh, C.; Balazs, A. C. J. Chem. Phys. 1998, 108, 1175. (22) Singh, C.; Balazs, A. J. Chem. Phys. 1996, 105, 706. (23) Pattanayek, S. K.; Pham, T. T.; Pereiraa, G. G. J. Chem. Phys. 2005, 122, 214908. (24) Lai, P. Y.; Binder, K. J. Chem. Phys. 1992, 97, 586. (25) Soga, K. G.; Guo, H.; Zuckermann, M. J. Europhys. Lett. 1995, 29, 531. (26) Grest, G. S.; Murat, M. Macromolecules 1993, 26, 3108. (27) Zhao, B.; Brittain, W. J.; Zhou, W.; Cheng, S. Z. D. Macromolecules 2000, 33, 8821. (28) Gao, X.; Feng, W.; Zhu, S.; Sheardown, H.; Brash, J. L. Langmuir 2008, 24, 8303. (29) Tomlinson, M. R.; Genzer, J. Langmuir 2005, 21, 11552. (30) Zhulina, E. B.; Singh, C.; Balazs, A. C. Macromolecules 1996, 29, 8254. (31) Wang, J.; Müller, M. Macromolecules 2009, 42, 2251. (32) Yin, Y.; Sun, P.; Li, B.; Chen, T.; Jin, Q.; Ding, D.; Shi, A.-C. Macromolecules 2007, 40, 5161. (33) Zhao, B.; Brittain, W. J. J. Am. Chem. Soc. 1999, 121, 3557. (34) Kent, M. S.; Majewski, J.; Smith, G. S.; Lee, L. T.; Satija, S. J. Chem. Phys. 1999, 110, 3553. (35) Zhulina, E. B.; Singh, C.; Balazs, A. C. Macromolecules 1996, 29, 6338. (36) Yin, Y.; Jiang, R.; Li, B.; Jin, Q.; Ding, D.; Shi, A.-C. J. Chem. Phys. 2008, 129, 154903. (37) Kirkpatrick, S.; Gelatt, C. D., Jr.; Vecchi, M. P. Science 1983, 220, 671. (38) Kirkpatrick, S. J. Stat. Phys. 1984, 34, 975. (39) Carmesin, I.; Kremer, K. Macromolecules 1988, 21, 2819. (40) Larson, R. G. J. Chem. Phys. 1989, 91, 2479; 1992, 96, 7904. (41) Sun, P.; Yin, Y.; Li, B.; Chen, T.; Jin, Q.; Ding, D.; Shi, A.-C. J. Chem. Phys. 2005, 122, 204905. (42) Matsen, M. W.; Griffiths, G. H. Eur. Phys. J. E. 2009, 29, 219.

grafted symmetric diblock, core−shell spherical micelles (onionlike micelles) or core−shell stripes with perfect B sphere or perfect B cylinder can be formed, while for grafted Y-shaped block copolymers, the B core is semisphere or semicylinder. Second, for the case of compatible blocks (εAB = 0), these two systems both form core−shell spherical pinned micelles, but an increase in εAB leads to different results. With the increase of εAB, the grafted Y-shaped block copolymers form core−shell micelles first and finally completely split micelles in the lateral direction, whereas the grafted linear diblock copolymers form core−shell micelles first and then each of these micelles splits into two micelles (dumbbell- like micelles) in perpendicular direction. To highlight the effects of solvent quality we also compare the findings here (case I) with those in our previous work on AB diblock copolymer brushes in a selective solvent that is poor for one block but good for the other one (case II).32 Specifically, when the solvent is preference for the grafted block (A) than the top block (B), the self-assembly behavior in the two different situation (for case I with εAS = 1.0, and εBS = 2.0, for case II with εAS = −1.0, and εBS = 1.0, whereas εAB = 0.5 in both cases) are quite different. For case II, the soluble A blocks basically form a stretched brush, whereas the insoluble B blocks exhibit several distinct morphologies, depending on the grafting density and the lengths of A and B blocks. Similar morphological transitions can be induced by increasing NA or by decreasing NB with a fixed grafting density, although the self-assembled morphologies are richer and more sensitive to the change of NB. On the other hand, For case I, both blocks collapse in the solvent. Because of the tethered feature the A blocks are confined at the bottom of the brush. The expulsion of the solvents from the brush layers makes this case more closely related to melt brushes.42 One interesting feature of the observed morphologies is that, for a fixed grafting density, the overall shape of the block copolymer brushes depends on the length of the copolymer chain N, whereas the exact internal separated structures depend on the volume fraction of the B block f B.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: (Y.Y.) [email protected]; (A.-C.S.) shi@mcmaster. ca. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research was financially supported by the National Natural Science Foundation of China (Grant Nos. 20904026, 20904027, and 20774052), by the National Science Fund for Distinguished Young Scholars of China (No. 20925414), and by the Fundamental Research Funds for the Central Universities. A.C.S. acknowledges support by the Natural Science and Engineering Council (NSERC) of Canada.

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REFERENCES

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