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Self-assembly of ABA triblock copolymers under soft confinement
Chemical Physics 452 (2015) 46–52
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Self-assembly of ABA triblock copolymers under soft confinement Yuping Sheng a, Jian An a,⇑, Yutian Zhu b,⇑ a b
College of Materials Science and Engineering, Jilin University, Changchun 130022, People’s Republic of China State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 23 November 2014 In final form 14 February 2015 Available online 19 March 2015 Keywords: Self-assembly Soft confinement Monte Carlo simulation
a b s t r a c t Using Monte Carlo method, the self-assembly of ABA triblock copolymers under soft confinement is investigated in this study. The soft confinement is achieved by a poor solvent environment for the polymer, which makes the polymer aggregate into a droplet. Various effects, including the block length ratio, the solvent quality for the blocks B, and the incompatibility between blocks A and B, on the micellar structures induced by soft confinement are examined. By increasing the solvent quality of B blocks, the micellar structure transforms from stacked lamella to bud-like structure, and then to onion-like structure for A5B8A5 triblock copolymers, while the inner micellar structure changes from spherical phase to various cylindrical phase, such as inner single helix, double helixes, stacked rings and cage-like structures, for A7B4A7 triblock copolymers. Moreover, the formation pathways of some typical aggregates are examined to illustrate their growth mechanisms. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction The self-assembly of block copolymers has attracted great attention because of the potential applications in various areas, such as drug delivery [1–5], microreactors [6–8], nanoprobes [9] and so on. The block copolymers can spontaneously self-assemble into various nano-scale micelles, including spheres [10], cylinders [10,11], vesicles [10,12,13], rings [14–16] and multicompartment micelles [17–23], in solution. Comparing to the self-assembly in a bulk system, the confined self-assembly can lead to some unique structures that cannot be obtained under the classical equilibrium state. In previous studies, the self-assembly of polymer melts under rigid confinement have attracted intensive attention. For instance, the boundaries of flat walls (one-dimensional confinement) [24–26], cylindrical pores (two-dimensional confinement) [27–32], spherical pores (threedimensional confinement) [33–35] have been used in selfassembly of block copolymers, which induce a lot of unique nanostructures. In contrast to the rigid confinement, the boundaries with copolymer brushes [36,37] and the copolymer nanoparticles obtained by precipitation [38–40] or emulsions [41–46] can be termed as soft confinement. Because of the flexible boundaries, soft confinement will induce more complex and interesting structures. In experiment, the self-assembly under the soft confinement was achieved by confining the self-assembled ⇑ Corresponding authors. Tel.: +86 43185262866; fax: +86 43185262126. E-mail addresses: [email protected] (J. An), [email protected] (Y. Zhu). http://dx.doi.org/10.1016/j.chemphys.2015.02.019 0301-0104/Ó 2015 Elsevier B.V. All rights reserved.
units, i.e., block copolymers, in a small emulsion droplet. For instance, Tanaka et al. used polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) to prepare ‘‘onion-like’’ multilayered particles by slowly evaporating toluene from polymer/toluene droplets dispersed in aqueous media [41]. Zhu and coworkers tuned the content of 3-n-pentadecyphenol (PDP) and polystyrene-b-poly(4vinyl pyridine) (PS-b-P4VP) in emulsion droplets to generate unique nanostructures, including disorder spheres-within-sphere particles, spheres with dispersed spirals, prolate ellipsoids with stacked toroids, and onion-like nanoparticles [42]. Moreover, Zhu and coworkers obtained the Janus nanodics by stepwise disassembling disc-stacked particles formed by emulsion method [45]. Jeon et al. investigated the phase behavior of the colloidal particles prepared by the blends of polystyrene-b-polybutadiene (PS-b-PB) and polystyrene (PS) using emulsion method. They found that the microphases depended on the ratio of molecular weight and the ratio of the diameter of the emulsion droplet to the feature spacing [46]. Unlike the self-assembly of amphiphilic copolymer in the selective solvent, soft confinement can induce block copolymers to aggregate into nanoparticles with rich inner structures. On the other hand, computer simulation has been proved to be a powerful tool in the study of self-assembly of block copolymer. So far, however, there are only a few simulation works on the self-assembly of copolymers under soft confinement. For example, Fraaije and Sevink observed some remarkable bicontinuous structures proceeded by a sudden quench of a homogeneous droplet in solvent via self-consistent-field theory (SCFT) [47]. Svenik and Zvelindovsky demonstrated the kinetic pathways of self-assembly
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of diblock copolymers into complex vesicles based on dynamic SCFT [48]. Recently, Li and coworkers systematically studied the self-assembly of diblock copolymers under soft confinement using a simulated annealing method. It was found that the morphology was largely controlled by a competition between the bulk morphology of the copolymer and the solvent–polymer interaction. Their results demonstrated that polymer aggregated into a bulk droplet in a poor solvent environment, which can be used to mimic the soft confinement of polymer in experiment [49]. In this study, we apply Monte Carlo (MC) method to study the self-assembly of ABA triblock copolymers under soft confinement. The soft confinement is also achieved by a poor solvent environment for the polymer. It is observed that ABA triblock copolymers can spontaneously assemble into a series of nanoparticles under soft confinement. The effects of block length ratio, the solvent quality for the B blocks, and the incompatibility between A and B blocks on micellar morphologies are examined systematically.
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the formation pathway of the micelle [13]. If the annealing rate is changed, the final self-assembled morphology may be changed correspondingly. In each annealing step, 9000 Monte Carlo steps (MCSs) are performed. One MCS means that each bead has one attempted exchange move on average. After 350 annealing steps, the inverse temperature 1/T is kept as 0.07, another 650 annealing steps are carried out to ensure that the final structures are under an equilibrium state. In this study, the concentration of the block copolymers is fixed as 10% and the chain length is set as Le = 18. The parameters between the same components are set as eAA = eBB = eSS = 0, and the interaction between different polymer segments is set as eAB P 1 to mimic their incompatibility. The interaction parameters eAS and eBS represent the interactions between blocks and the solvent. eAS is set as 2 and eBS is set as a positive value (eBS P 2) to ensure the solvent is poor for all the blocks. 3. Results and discussion
2. Model and method Lattice Monte Carlo method was used in this simulation to study the self-assembly of ABA triblock copolymer under soft confinement. All the simulations were carried out in a 40 40 40 simple cubic lattice. Periodic boundary condition was imposed in all three directions. A desired number of polymer chains were randomly dispersed in the lattice in initial state. Each polymer bead occupied one lattice site and single-site bond fluctuation pffiffiffi model [50–52] was used to restrict the bond length as 1 and 2. Moreover, excluded volume interactions were enforced to ensure that no more than one monomer occupied the same lattice site and no bond crossing is allowed. After the copolymer chains were generated, the remaining vacancies were regarded as the solvents. The partial-reptation algorithm [53,54] is used in the simulation, which allows for the possibility of co-operative motions over sections of the chains and increases the time efficiency of the simulation. This algorithm has been proved suitable for studying the dynamic process. A polymer bead was randomly selected to exchange with a bead on one of its 18 nearest neighbors. If the selected neighbor bead is a vacancy, the exchange is allowed when it is satisfied excluded volume conditions, no-bond-crossing and bond length restrictions. If the exchange breaks the chain, the vacancy will continue to exchange with the following monomers along the chain until the chain reconnecting. The acceptance or rejection of one attempted exchange is further governed by the Metropolis rule [55]. The attempted exchange is accepted if the energy change DE is negative or accepted with a probability of P p ¼ exp½DE=kB T, where DE ¼ ij DN ij eij is the energy change in one attempted exchange; kB is the Boltzmann constant and set as 1 in the whole simulation; T is the reduced temperature, DN ij is the number difference between the nearest neighbor pairs of components i and j before and after the exchange, eij is the reduced interaction between components i and j; i, j = A, B, and S (solvent) respectively. The annealing method is applied in this simulation. The inverse temperature 1/T is set as 0 at first and then gradually changes to 0.07, which represents the system changing from an athermal state to a relatively low temperature state. In experiment, as the organic solvent is evaporated, the block copolymers tend to aggregate together to avoid the contact with the water molecules. During this process, the movements of the hydrophobic block copolymers are gradually limited because they are gradually surrounded by the water. Therefore, 1/T is gradually increased from 0 to 0.07 to mimic the annealing process in the emulsion–evaporation induced selfassembly. The annealing rate is kept as 0.0002 per step in this study. It has been reported that the annealing rate will influence
In this study, it is found that ABA triblock copolymers can spontaneously self-assemble into bulk aggregates in poor solvent. The aggregates with abundant structures are showed in Figs. 1–6. The effects of block length ratio, solvent quality for the blocks B, and the incompatibility between blocks A and B on micellar morphologies are examined. Furthermore, the formation pathways of some typical aggregates are examined to illustrate their formation mechanisms. 3.1. Effect of block length ratio on the self-assembled morphology In this section, we examine the effect of block length ratio on self-assembled morphologies. The parameters eAB are fixed as 3. The total chain length of ABA triblock copolymers is set as Le = 18. To examine the effect of block length ratio, the length of middle B block (LeB) is increased from 2 to 12, while the lengths of A block (LeA) at the two ends are accordingly decreased because 2LeA + LeB = 18. Here, we first examine the case that A and B blocks have the equal hydrophobicity, i.e., eAS = eBS = 2. When LeB = 2 (A8B2A8 triblock copolymers), a spherical aggregate embedded with some spheres formed by B blocks is obtained in Fig. 1a. The B domains are totally covered by A blocks because B blocks are very short. When LeB increases to 4, the A7B4A7 triblock copolymers assemble into an ellipsoidal aggregate with spheres dispersed on the surface and a cylinder inside, as shown in Fig. 1b. A patchlike aggregate is obtained by A6B6A6 triblock copolymers when LeB is increased to 6 (Fig. 1c). As LeB is further increased to 8, and then to 10, stacked lamellae with alternate A and B domain are obtained from A5B8A5 and A4B10A4 triblock copolymers due to the comparable lengths of the total A blocks and B blocks (Fig. 1d and e). When LeB is increased to 12, the A3B12A3 triblock copolymers self-assemble into a patch-like aggregate with the cage-like B domain covering part of A domains, as shown in Fig. 1f. From Fig. 1, it is clear that B domains are likely to be exposed to solvent more and more as LeB is increased. On the other hand, we also investigate the case that B block has the higher hydrophobicity than the A block. Under this condition, it is expected that the block polymers will aggregate into the spherical droplets with the A domains on the outer surface. Here, we set eAS = 2 and eBS = 5 to mimic this case. In Fig. 2, we present a series of self-assembled morphologies as a function of LeB. When the triblock copolymer has a relatively short B block (LeB = 2), the A8B2A8 triblock copolymers self-assemble into a spherical aggregate with some small B spheres inside (Fig. 2a). Because of the difference in the hydrophobicity, weak hydrophobic A blocks always locate at the outside to cover the strong hydrophobic B domains. When LeB
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Fig. 1. Self-assembled morphologies as a function of the block length ratio with fixing eAS = eBS = 2: (a) A8B2A8; (b) A7B4A7; (c) A6B6A6; (d) A5B8A5; (e) A4B10A4; (f) A3B12A3. represents the A blocks; represents the B blocks. To clearly show the inner structures, the patterns with transparent A domains or only B domains are presented on the top of the corresponding snapshots.
Fig. 2. Self-assembled morphologies as a function of the block length ratio with fixing eAS = 2 and eBS = 5: (a) A8B2A8; (b) A7B4A7; (c) A6B6A6; (d) A5B8A5; (e) A4B10A4. The color codes are the same as that in Fig. 1. The domains of A blocks are transparent to show the inner B domains clearly and the cross-section snapshots are also given in the images (d) and (e). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
is increased to 4, the A7B4A7 triblock copolymers form an aggregate with double helix structure inside, as shown in Fig. 2b. When LeB = 6, the A6B6A6 triblock copolymers aggregate into a nanoparticle with cage-like structure formed by B blocks inside (Fig. 2c). The onion-like nanoparticle is obtained when LeB is increased to 8 (A5B8A5 triblock copolymers), as the integral and cross-section images showed in Fig. 2d. When LeB is further increased to 10 (A4B10A4 triblock copolymers), the onion-like structure is also observed. However, the outer A layer cannot completely cover the inner concentric B layer because A block is too short to form a perfect layer (Fig. 2e). From Fig. 2, it is found that the inner selfassembled structure changes from separated small spheres to double helixes, cage-like structure, and then to concentric layer, indicating that the inner structure formed by B blocks becomes more and more continuous as LeB is increased from 2 to 10. 3.2. Effect of hydrophobicity of blocks B on self-assembled morphology To study the effect of the hydrophobicity of B blocks on selfassembled morphology, the parameter eBS is varied in this section. Other parameters, such as eAB and eAS, are fixed as eAB = 3 and eAS = 2. Two different triblock copolymers are examined, i.e., A5B8A5 and A7B4A7. For the A5B8A5 triblock copolymers, when eBS = 2 (Fig. 3a), the stacked lamellae with alternate A and B domains are obtained as the same hydrophobicities of A and B blocks. Similar stacked lamellar structures were observed in the self-assembly of AB diblock copolymers when both the length ratio and the hydrophobicities of A and B blocks were comparable [48,49]. When eBS increases to 3, the aggregate with bent stacked lamellae (bud-like structure) is obtained, and the outmost layers are A domains due to the slight difference in solvent selectivity (Fig. 3b). When eBS P 4, the morphology changes into the onionlike nanoparticle (Fig. 3c and d). Due to the increased hydrophobicity, the concentric lamellae structure is formed and B domain is always covered by A domain to avoid B-solvent contacting. In recent experiment, Zhu and coworkers studied the reversed transformation of nanostructures formed by PS-P4VP confined in droplets [56]. The nanostructures transformed from stacked lamellae to bud-like structures, and then to onion-like structures by decreasing the concentration of poly(vinyl alcohol) (PVA). PVA
Fig. 3. Transformation of the morphologies as the increasing of the hydrophobicity of B blocks for the A5B8A5 triblock copolymers. (a) eBS = 2; (b) eBS = 3; (c) eBS = 4; (d) eBS = 5. The color codes are the same as that in Fig. 1. The snapshots (a) and (b) show the structures with true colors while snapshots (c) and (d) are drew with the transparent A domains to show the inner B domains. The patterns that only show the B domains or cross-sections are shown on the top of the corresponding snapshots. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
plays a role in neutralizing the particle interface. As the decreasing of the PVA, more and more block copolymers are directly exposed to solvent. Therefore, P4VP segments are likely to form the outer lay to cover the strong hydrophobic PS domains to minimize the surface free energy. Our simulation result agrees well with the transition pathway in experiment. For A7B4A7 triblock copolymer, a more complex morphological transition is observed by increasing eBS, as shown in Fig. 4. When eBS = 2, the ellipsoidal aggregate with spheres dispersed on the surface and a cylinder inside is observed (Fig. 4a). When eBS increases to 3, the spherical aggregate with some cylinders inside is formed, but the two ends of cylinders are exposed to the solvent (Fig. 4b). The inside cylinders then transform into double helixes when eBS = 4 and eBS = 5 (Fig. 4c and d). When eBS is further increased to 6, and then to 6.5, the internal structure changes into ring with cylinder and single helix, as shown in Fig. 4e and f, respectively. Then the spherical aggregates with stacked rings and cage-like structure inside are obtained when eBS = 7 and eBS = 8 (Fig. 4g and h). Comparing Fig. 3 with Fig. 4, it is found that the shapes of morphologies change from ellipsoid to sphere and the domains formed
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Fig. 4. Transformation of the morphologies as the increasing of the hydrophobicity of B blocks for the A7B4A7 triblock copolymers. (a) eBS = 2; (b) eBS = 3; (c) eBS = 4; (d) eBS = 5; (e) eBS = 6; (f) eBS = 6.5; (g) eBS = 7; (h) eBS = 8. The color codes are the same as that in Fig. 1. The domains of A blocks are transparent to show the inner B domains. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
by blocks B become more continuously with the increase of eBS. In experiment, Zhu and coworkers demonstrated a route to prepare the mesoporous nanoparticles via supramolecular assembly of PS-P4VP (PDP) in emulsion droplets [42]. PDP can hydrogen bond to the units of P4VP to change its hydrophilicity. By increasing the PDP content, the internal structures of the nanoparticles changed from dispersed spheres to spirals, stacked toroids, and then to concentric lamellae. Correspondingly, the internal structures transform from spherical phases to various cylindrical phases in our simulation. 3.3. Effect of the incompatibility between blocks A and B on the selfassembled morphology
connected cylinders, as shown Fig. 6b. A double-helix structure in a spherical aggregate is obtained when eAB = 3 (Fig. 6c). When eAB increases from 4 to 5, the inner structure changes from one side connected double helixes to two separated helixes with different lengths (Fig. 6d and e). When eAB further increases to 6 and 7, the inner structure turns to some dispersed cylinders with the two ends exposed to solvent, as shown in Fig. 6f and g. Figs. 5 and 6 indicate that the inner B domains distribute uniformly when the incompatibility is weak, such as concentric lamella (Fig. 5a) and dispersed spheres (Fig. 6a), while the B domains become more stretched, such as lamella (Fig. 5e) and straight cylinders (Fig. 6f), when the incompatibility is strong. 3.4. Formation pathways of some typical aggregates
In this section, we choose two different triblock copolymers, i.e., A5B8A5 and A7B4A7 triblock copolymers, to examine the effect of the incompatibility between blocks A and B on the self-assembled morphology. The parameters eAS and eBS are fixed, i.e., eAS = 2 and eBS = 5. When eAB is increased from 1 to 3, the self-assembled morphology is always the onion-like morphology for A5B8A5 triblock copolymers. For simplicity, we only put resulting morphologies at eAB = 3 in Fig. 5a. Then some holes appear on the concentric lamellae formed by blocks B when eAB increases from 4 to 6 (Fig. 5b–d). Moreover, it is also found that the hole number is increased as the increase of eAB. When eAB is further increased to 7, the B blocks form a lamella with the edge exposed to the solvent, due to the strong incompatibility between blocks A and B (Fig. 5e). For the A7B4A7 triblock copolymers, a spherical aggregate with dispersed spheres and shot rods inside is obtained when eAB = 1 (Fig. 6a). When eAB = 2, the inner structure changes into irregularly
In this section, the formation pathways of some typical aggregates, i.e., stacked lamellae, onion-like structure, droplet with internal double helixes, and droplet with internal stacked rings are examined to study their formation mechanisms. Fig. 7 shows the variation of the contact number between B-type monomer and solvent (NBS) of the onion-like structure (Fig. 3c) as a function of the annealing time (t), which can be used to monitor the micellization degree of the B blocks. Fig. 7 shows that NBS decreases considerably at first and then remains almost unchanged after 400 steps, which indicates that the micellization of B blocks is almost finished after t = 400. In other words, the final structure at t = 1000 should be an equilibration state. In the current study, all the results are captured at t = 1000 to ensure that the results are at the equilibration state. Moreover, using a different homogeneous state as the initial state, the resulting structures can be well
Fig. 5. Transformation of the morphologies of A5B8A5 triblock copolymers as the increasing of the incompatibility between blocks A and B. (a) eAB = 3; (b) eAB = 4; (c) eAB = 5; (d) eAB = 6; (e) eAB = 7. The color codes are the same as that in Fig. 1. The A domains are transparent to show the inner B domains. The cross-section and true color images are shown on the right of the corresponding snapshots in (a) and (e), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Transformation of the morphologies of A7B4A7 triblock copolymers as the increasing of the incompatibility between blocks A and B. (a) eAB = 1; (b) eAB = 2; (c) eAB = 3; (d) eAB = 4; (e) eAB = 5; (f) eAB = 6; (g) eAB = 7. The color codes are the same as that in Fig. 1. The A domains are transparent to show the inner B domains. The true color images are shown on the right of the corresponding snapshots in (f) and (g). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 7. Variation of the contact number NBS as a function of time (the annealing time) during the formation of onion-like structure (Fig. 3c).
reproduced (results not shown in this work). To visualize the formation pathways of the stacked lamellae and the onion-like structure, a series of snapshots at different annealing time (t) are presented in Fig. 8. When t = 40 (Fig. 8a1), only some very small aggregates are formed by ABA triblock copolymers. At t = 150, ABA triblock copolymers start to assemble into a disordered and incompact aggregate (Fig. 8a2). Thereafter, the ABA triblock copolymers form a compact aggregate and the microphase-separation between A and B phases is appeared, as shown in Fig. 8a3 (t = 200). As the microphase-separation between A and B phases is completed, the stacked lamellae with alternate A and B domains is formed (Fig. 8a4, t = 1000). From Fig. 8b, it is observed that ABA triblock copolymers form an incompact aggregate at first (Fig. 8b1 and b2, t = 40 and t = 100, respectively.) and then B blocks aggregate into a cage-like structure covered by A domains (Fig. 8b3, t = 170). Thereafter, the holes on the cage-like structure of B domain start to close up, and the nanostructure transforms into a onion-like structure (Fig. 8b4 and b5, t = 200 and t = 1000, respectively). The formation pathways for the droplets with internal double helixes or stacked rings are presented in Fig. 9a and b, respectively. It is clear that their formation pathways are similar to the stacked lamellae and onion-like structure. ABA triblock copolymer form a incompact and disordered aggregate at first (Fig. 9a1–a3 and Fig. 9b1–b3, respectively). Thereafter, the microphase separation between A and B phase is occurred, resulting in the formation of double B-type helix (Fig. 9a4–a6)
and stacked rings inside the A-type spheres (Fig. 9b4–b6). From Figs. 8 and 9, it is clear that A domains start to dominate the outermost layer around t = 100, whether in the formations of onion-like structure, droplet with inner double helixes or stacked rings. Moreover, it is found that onion-like structure are formed by the fusion of cake-like structure, rather than the bending of lamellae reported in the previous work [48]. To further study the inner nanostructures, we calculate the density distribution of segment A, B, and solvent along r (the radii around the mass center of the self-assembled aggregate) in Fig. 10 for some typical aggregates, i.e., the stacked lamellae (Fig. 10a), onion-like structure (Fig. 10b), droplets with internal double helixes (Fig. 10c) and internal stacked rings (Fig. 10d). From density curves of the solvent, it is clear that there are no solvents in the core of the aggregates, as shown in Fig. 10a–d. For the stacked lamellae (Fig. 10a), the A density is higher than B density at first (r 6 4) because the mass center is located in the A lamella. Thereafter, A and B densities become almost equal when r > 4 because of the alternating A and B lamellae. For the onion-like structure (Fig. 10b), two peaks of the A density are observed, corresponding to the innermost core and outmost surface. From the curve of B density, a single peak is observed, corresponding an internal B lamella in the range of r = 6 to r = 10. For the droplets with internal double helixes (Fig. 10c) or stacked rings (Fig. 10d), their A density curves are similar to that of the onion-like structure (Fig. 10b), i.e., there are two peaks on the curve, which correspond to the innermost core and outmost surface of the A domain. However, the peak of B density is significantly lower than that of the onion-like structure (Fig. 10b) because B blocks only form internal helixes or rings instead of a continuous internal lamella. In the current study, the self-assembly of ABA triblock copolymer is accomplished under soft confinement. Some self-assembled nanostructures agree well with the previous works under rigid confinement. For example, Arsenault et al. obtained the onion-like structures via the confined self-assembly of polystyrene-block-poly (ferrocenylethylmethylsilane) (PS-b-PFEMS) diblock copolymer in 3D silica template [33]. Under a rigid spherical confinement, Chen et al. observed the droplets with inner spheres, cage-like structure and other complex symmetric structures from the selfassembly of diblock copolymers [34]. Moreover, Yu and coworkers observed the self-assembled nanostructures with stacked rings, single helix and double helixes from the confined self-assembly of diblock copolymers in the spherical pores [35]. In the current study, all these self-assembled structures were also obtained via
Fig. 8. The formation pathways of the stacked lamellae (a1–a4) and onion-like structure (b1–b5): (a1) t = 40; (a2) t = 150; (a3) t = 200; (a4) t = 1000; (b1) t = 40; (b2) t = 100; (b3) t = 170; (b4) t = 200; (b5) t = 1000. The color codes are the same as that in Fig. 1. The A domains are transparent to show the inner B domains in b3–b5.
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Fig. 9. The formation pathways of the droplets with internal double helixes (a1–a6) and internal stacked rings (b1–b6): (a1) t = 40; (a2) t = 100; (a3) t = 150; (a4) t = 200; (a5) t = 300; (a6) t = 1000; (b1) t = 40; (b2) t = 80; (b3) t = 100; (b4) t = 150; (b5) t = 200; (b6) t = 1000. The color codes are the same as that in Fig. 1. The A domains are transparent to show the inner B domains in a3–a6 and b3–b6, respectively.
Fig. 10. Variation of the densities of the segment A, B, and solvent with r (r is the radii around the mass center). (a) stacked lamellae; (b) onion-like structure; (c) droplet with internal double helixes; (d) droplet with internal stacked rings.
the self-assembly of ABA triblock copolymer under the soft confinement. However, the self-assembled aggregates from rigid three-dimensional confinement always keep the spherical shapes because of the rigid confinement boundary, while the aggregates under soft confinement can be the alterable shapes, such as the ellipsoidal shape (Fig. 1e).
4. Conclusions Using Monte Carlo method, we investigated the self-assembly of ABA triblock copolymer under soft confinement. Some novel
self-assembled nanostructures, such as the aggregates with inner single helix, double helixes, stacked rings and cage-like structure, are predicted. The effects of block length ratio, the solvent quality for the blocks B, and the incompatibility between blocks A and B on the self-assembled morphologies are examined. As B block length is increased, more and more B domains are exposed to solvent when the solvent qualities of A and B blocks are equal, while the inner structure of the aggregate changes from sphere to cylinder, and then to concentric lamella when the solvent qualities for A and B blocks are different. As the increase of eBS, the morphology transforms from stacked lamella to bud-like structure and then to onion-like structure for A5B8A5 triblock copolymers, while the
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inner structure of aggregate changes from spherical phases to various cylindrical phases for A7B4A7 triblock copolymers. Moreover, as the incompatibility between A and B is increased, the self-assembled morphology will correspondingly be changed because A and B blocks are more likely to move away from each other. Furthermore, the formation pathways of some typical aggregates are examined to illustrate their formation mechanisms. 5. Conflict of interest
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There is no conflict of interests regarding the publication of this article. Acknowledgments This work was financially supported by the National Natural Science Foundation of China for General Program (51373172), Major Program (51433009) and the Open Project of State Key Laboratory of Supramolecular Structure and Materials (sklssm2015030). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
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Chemical Physics journal homepage: www.elsevier.com/locate/chemphys
Self-assembly of ABA triblock copolymers under soft confinement Yuping Sheng a, Jian An a,⇑, Yutian Zhu b,⇑ a b
College of Materials Science and Engineering, Jilin University, Changchun 130022, People’s Republic of China State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 23 November 2014 In final form 14 February 2015 Available online 19 March 2015 Keywords: Self-assembly Soft confinement Monte Carlo simulation
a b s t r a c t Using Monte Carlo method, the self-assembly of ABA triblock copolymers under soft confinement is investigated in this study. The soft confinement is achieved by a poor solvent environment for the polymer, which makes the polymer aggregate into a droplet. Various effects, including the block length ratio, the solvent quality for the blocks B, and the incompatibility between blocks A and B, on the micellar structures induced by soft confinement are examined. By increasing the solvent quality of B blocks, the micellar structure transforms from stacked lamella to bud-like structure, and then to onion-like structure for A5B8A5 triblock copolymers, while the inner micellar structure changes from spherical phase to various cylindrical phase, such as inner single helix, double helixes, stacked rings and cage-like structures, for A7B4A7 triblock copolymers. Moreover, the formation pathways of some typical aggregates are examined to illustrate their growth mechanisms. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction The self-assembly of block copolymers has attracted great attention because of the potential applications in various areas, such as drug delivery [1–5], microreactors [6–8], nanoprobes [9] and so on. The block copolymers can spontaneously self-assemble into various nano-scale micelles, including spheres [10], cylinders [10,11], vesicles [10,12,13], rings [14–16] and multicompartment micelles [17–23], in solution. Comparing to the self-assembly in a bulk system, the confined self-assembly can lead to some unique structures that cannot be obtained under the classical equilibrium state. In previous studies, the self-assembly of polymer melts under rigid confinement have attracted intensive attention. For instance, the boundaries of flat walls (one-dimensional confinement) [24–26], cylindrical pores (two-dimensional confinement) [27–32], spherical pores (threedimensional confinement) [33–35] have been used in selfassembly of block copolymers, which induce a lot of unique nanostructures. In contrast to the rigid confinement, the boundaries with copolymer brushes [36,37] and the copolymer nanoparticles obtained by precipitation [38–40] or emulsions [41–46] can be termed as soft confinement. Because of the flexible boundaries, soft confinement will induce more complex and interesting structures. In experiment, the self-assembly under the soft confinement was achieved by confining the self-assembled ⇑ Corresponding authors. Tel.: +86 43185262866; fax: +86 43185262126. E-mail addresses: [email protected] (J. An), [email protected] (Y. Zhu). http://dx.doi.org/10.1016/j.chemphys.2015.02.019 0301-0104/Ó 2015 Elsevier B.V. All rights reserved.
units, i.e., block copolymers, in a small emulsion droplet. For instance, Tanaka et al. used polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) to prepare ‘‘onion-like’’ multilayered particles by slowly evaporating toluene from polymer/toluene droplets dispersed in aqueous media [41]. Zhu and coworkers tuned the content of 3-n-pentadecyphenol (PDP) and polystyrene-b-poly(4vinyl pyridine) (PS-b-P4VP) in emulsion droplets to generate unique nanostructures, including disorder spheres-within-sphere particles, spheres with dispersed spirals, prolate ellipsoids with stacked toroids, and onion-like nanoparticles [42]. Moreover, Zhu and coworkers obtained the Janus nanodics by stepwise disassembling disc-stacked particles formed by emulsion method [45]. Jeon et al. investigated the phase behavior of the colloidal particles prepared by the blends of polystyrene-b-polybutadiene (PS-b-PB) and polystyrene (PS) using emulsion method. They found that the microphases depended on the ratio of molecular weight and the ratio of the diameter of the emulsion droplet to the feature spacing [46]. Unlike the self-assembly of amphiphilic copolymer in the selective solvent, soft confinement can induce block copolymers to aggregate into nanoparticles with rich inner structures. On the other hand, computer simulation has been proved to be a powerful tool in the study of self-assembly of block copolymer. So far, however, there are only a few simulation works on the self-assembly of copolymers under soft confinement. For example, Fraaije and Sevink observed some remarkable bicontinuous structures proceeded by a sudden quench of a homogeneous droplet in solvent via self-consistent-field theory (SCFT) [47]. Svenik and Zvelindovsky demonstrated the kinetic pathways of self-assembly
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of diblock copolymers into complex vesicles based on dynamic SCFT [48]. Recently, Li and coworkers systematically studied the self-assembly of diblock copolymers under soft confinement using a simulated annealing method. It was found that the morphology was largely controlled by a competition between the bulk morphology of the copolymer and the solvent–polymer interaction. Their results demonstrated that polymer aggregated into a bulk droplet in a poor solvent environment, which can be used to mimic the soft confinement of polymer in experiment [49]. In this study, we apply Monte Carlo (MC) method to study the self-assembly of ABA triblock copolymers under soft confinement. The soft confinement is also achieved by a poor solvent environment for the polymer. It is observed that ABA triblock copolymers can spontaneously assemble into a series of nanoparticles under soft confinement. The effects of block length ratio, the solvent quality for the B blocks, and the incompatibility between A and B blocks on micellar morphologies are examined systematically.
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the formation pathway of the micelle [13]. If the annealing rate is changed, the final self-assembled morphology may be changed correspondingly. In each annealing step, 9000 Monte Carlo steps (MCSs) are performed. One MCS means that each bead has one attempted exchange move on average. After 350 annealing steps, the inverse temperature 1/T is kept as 0.07, another 650 annealing steps are carried out to ensure that the final structures are under an equilibrium state. In this study, the concentration of the block copolymers is fixed as 10% and the chain length is set as Le = 18. The parameters between the same components are set as eAA = eBB = eSS = 0, and the interaction between different polymer segments is set as eAB P 1 to mimic their incompatibility. The interaction parameters eAS and eBS represent the interactions between blocks and the solvent. eAS is set as 2 and eBS is set as a positive value (eBS P 2) to ensure the solvent is poor for all the blocks. 3. Results and discussion
2. Model and method Lattice Monte Carlo method was used in this simulation to study the self-assembly of ABA triblock copolymer under soft confinement. All the simulations were carried out in a 40 40 40 simple cubic lattice. Periodic boundary condition was imposed in all three directions. A desired number of polymer chains were randomly dispersed in the lattice in initial state. Each polymer bead occupied one lattice site and single-site bond fluctuation pffiffiffi model [50–52] was used to restrict the bond length as 1 and 2. Moreover, excluded volume interactions were enforced to ensure that no more than one monomer occupied the same lattice site and no bond crossing is allowed. After the copolymer chains were generated, the remaining vacancies were regarded as the solvents. The partial-reptation algorithm [53,54] is used in the simulation, which allows for the possibility of co-operative motions over sections of the chains and increases the time efficiency of the simulation. This algorithm has been proved suitable for studying the dynamic process. A polymer bead was randomly selected to exchange with a bead on one of its 18 nearest neighbors. If the selected neighbor bead is a vacancy, the exchange is allowed when it is satisfied excluded volume conditions, no-bond-crossing and bond length restrictions. If the exchange breaks the chain, the vacancy will continue to exchange with the following monomers along the chain until the chain reconnecting. The acceptance or rejection of one attempted exchange is further governed by the Metropolis rule [55]. The attempted exchange is accepted if the energy change DE is negative or accepted with a probability of P p ¼ exp½DE=kB T, where DE ¼ ij DN ij eij is the energy change in one attempted exchange; kB is the Boltzmann constant and set as 1 in the whole simulation; T is the reduced temperature, DN ij is the number difference between the nearest neighbor pairs of components i and j before and after the exchange, eij is the reduced interaction between components i and j; i, j = A, B, and S (solvent) respectively. The annealing method is applied in this simulation. The inverse temperature 1/T is set as 0 at first and then gradually changes to 0.07, which represents the system changing from an athermal state to a relatively low temperature state. In experiment, as the organic solvent is evaporated, the block copolymers tend to aggregate together to avoid the contact with the water molecules. During this process, the movements of the hydrophobic block copolymers are gradually limited because they are gradually surrounded by the water. Therefore, 1/T is gradually increased from 0 to 0.07 to mimic the annealing process in the emulsion–evaporation induced selfassembly. The annealing rate is kept as 0.0002 per step in this study. It has been reported that the annealing rate will influence
In this study, it is found that ABA triblock copolymers can spontaneously self-assemble into bulk aggregates in poor solvent. The aggregates with abundant structures are showed in Figs. 1–6. The effects of block length ratio, solvent quality for the blocks B, and the incompatibility between blocks A and B on micellar morphologies are examined. Furthermore, the formation pathways of some typical aggregates are examined to illustrate their formation mechanisms. 3.1. Effect of block length ratio on the self-assembled morphology In this section, we examine the effect of block length ratio on self-assembled morphologies. The parameters eAB are fixed as 3. The total chain length of ABA triblock copolymers is set as Le = 18. To examine the effect of block length ratio, the length of middle B block (LeB) is increased from 2 to 12, while the lengths of A block (LeA) at the two ends are accordingly decreased because 2LeA + LeB = 18. Here, we first examine the case that A and B blocks have the equal hydrophobicity, i.e., eAS = eBS = 2. When LeB = 2 (A8B2A8 triblock copolymers), a spherical aggregate embedded with some spheres formed by B blocks is obtained in Fig. 1a. The B domains are totally covered by A blocks because B blocks are very short. When LeB increases to 4, the A7B4A7 triblock copolymers assemble into an ellipsoidal aggregate with spheres dispersed on the surface and a cylinder inside, as shown in Fig. 1b. A patchlike aggregate is obtained by A6B6A6 triblock copolymers when LeB is increased to 6 (Fig. 1c). As LeB is further increased to 8, and then to 10, stacked lamellae with alternate A and B domain are obtained from A5B8A5 and A4B10A4 triblock copolymers due to the comparable lengths of the total A blocks and B blocks (Fig. 1d and e). When LeB is increased to 12, the A3B12A3 triblock copolymers self-assemble into a patch-like aggregate with the cage-like B domain covering part of A domains, as shown in Fig. 1f. From Fig. 1, it is clear that B domains are likely to be exposed to solvent more and more as LeB is increased. On the other hand, we also investigate the case that B block has the higher hydrophobicity than the A block. Under this condition, it is expected that the block polymers will aggregate into the spherical droplets with the A domains on the outer surface. Here, we set eAS = 2 and eBS = 5 to mimic this case. In Fig. 2, we present a series of self-assembled morphologies as a function of LeB. When the triblock copolymer has a relatively short B block (LeB = 2), the A8B2A8 triblock copolymers self-assemble into a spherical aggregate with some small B spheres inside (Fig. 2a). Because of the difference in the hydrophobicity, weak hydrophobic A blocks always locate at the outside to cover the strong hydrophobic B domains. When LeB
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Fig. 1. Self-assembled morphologies as a function of the block length ratio with fixing eAS = eBS = 2: (a) A8B2A8; (b) A7B4A7; (c) A6B6A6; (d) A5B8A5; (e) A4B10A4; (f) A3B12A3. represents the A blocks; represents the B blocks. To clearly show the inner structures, the patterns with transparent A domains or only B domains are presented on the top of the corresponding snapshots.
Fig. 2. Self-assembled morphologies as a function of the block length ratio with fixing eAS = 2 and eBS = 5: (a) A8B2A8; (b) A7B4A7; (c) A6B6A6; (d) A5B8A5; (e) A4B10A4. The color codes are the same as that in Fig. 1. The domains of A blocks are transparent to show the inner B domains clearly and the cross-section snapshots are also given in the images (d) and (e). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
is increased to 4, the A7B4A7 triblock copolymers form an aggregate with double helix structure inside, as shown in Fig. 2b. When LeB = 6, the A6B6A6 triblock copolymers aggregate into a nanoparticle with cage-like structure formed by B blocks inside (Fig. 2c). The onion-like nanoparticle is obtained when LeB is increased to 8 (A5B8A5 triblock copolymers), as the integral and cross-section images showed in Fig. 2d. When LeB is further increased to 10 (A4B10A4 triblock copolymers), the onion-like structure is also observed. However, the outer A layer cannot completely cover the inner concentric B layer because A block is too short to form a perfect layer (Fig. 2e). From Fig. 2, it is found that the inner selfassembled structure changes from separated small spheres to double helixes, cage-like structure, and then to concentric layer, indicating that the inner structure formed by B blocks becomes more and more continuous as LeB is increased from 2 to 10. 3.2. Effect of hydrophobicity of blocks B on self-assembled morphology To study the effect of the hydrophobicity of B blocks on selfassembled morphology, the parameter eBS is varied in this section. Other parameters, such as eAB and eAS, are fixed as eAB = 3 and eAS = 2. Two different triblock copolymers are examined, i.e., A5B8A5 and A7B4A7. For the A5B8A5 triblock copolymers, when eBS = 2 (Fig. 3a), the stacked lamellae with alternate A and B domains are obtained as the same hydrophobicities of A and B blocks. Similar stacked lamellar structures were observed in the self-assembly of AB diblock copolymers when both the length ratio and the hydrophobicities of A and B blocks were comparable [48,49]. When eBS increases to 3, the aggregate with bent stacked lamellae (bud-like structure) is obtained, and the outmost layers are A domains due to the slight difference in solvent selectivity (Fig. 3b). When eBS P 4, the morphology changes into the onionlike nanoparticle (Fig. 3c and d). Due to the increased hydrophobicity, the concentric lamellae structure is formed and B domain is always covered by A domain to avoid B-solvent contacting. In recent experiment, Zhu and coworkers studied the reversed transformation of nanostructures formed by PS-P4VP confined in droplets [56]. The nanostructures transformed from stacked lamellae to bud-like structures, and then to onion-like structures by decreasing the concentration of poly(vinyl alcohol) (PVA). PVA
Fig. 3. Transformation of the morphologies as the increasing of the hydrophobicity of B blocks for the A5B8A5 triblock copolymers. (a) eBS = 2; (b) eBS = 3; (c) eBS = 4; (d) eBS = 5. The color codes are the same as that in Fig. 1. The snapshots (a) and (b) show the structures with true colors while snapshots (c) and (d) are drew with the transparent A domains to show the inner B domains. The patterns that only show the B domains or cross-sections are shown on the top of the corresponding snapshots. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
plays a role in neutralizing the particle interface. As the decreasing of the PVA, more and more block copolymers are directly exposed to solvent. Therefore, P4VP segments are likely to form the outer lay to cover the strong hydrophobic PS domains to minimize the surface free energy. Our simulation result agrees well with the transition pathway in experiment. For A7B4A7 triblock copolymer, a more complex morphological transition is observed by increasing eBS, as shown in Fig. 4. When eBS = 2, the ellipsoidal aggregate with spheres dispersed on the surface and a cylinder inside is observed (Fig. 4a). When eBS increases to 3, the spherical aggregate with some cylinders inside is formed, but the two ends of cylinders are exposed to the solvent (Fig. 4b). The inside cylinders then transform into double helixes when eBS = 4 and eBS = 5 (Fig. 4c and d). When eBS is further increased to 6, and then to 6.5, the internal structure changes into ring with cylinder and single helix, as shown in Fig. 4e and f, respectively. Then the spherical aggregates with stacked rings and cage-like structure inside are obtained when eBS = 7 and eBS = 8 (Fig. 4g and h). Comparing Fig. 3 with Fig. 4, it is found that the shapes of morphologies change from ellipsoid to sphere and the domains formed
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Fig. 4. Transformation of the morphologies as the increasing of the hydrophobicity of B blocks for the A7B4A7 triblock copolymers. (a) eBS = 2; (b) eBS = 3; (c) eBS = 4; (d) eBS = 5; (e) eBS = 6; (f) eBS = 6.5; (g) eBS = 7; (h) eBS = 8. The color codes are the same as that in Fig. 1. The domains of A blocks are transparent to show the inner B domains. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
by blocks B become more continuously with the increase of eBS. In experiment, Zhu and coworkers demonstrated a route to prepare the mesoporous nanoparticles via supramolecular assembly of PS-P4VP (PDP) in emulsion droplets [42]. PDP can hydrogen bond to the units of P4VP to change its hydrophilicity. By increasing the PDP content, the internal structures of the nanoparticles changed from dispersed spheres to spirals, stacked toroids, and then to concentric lamellae. Correspondingly, the internal structures transform from spherical phases to various cylindrical phases in our simulation. 3.3. Effect of the incompatibility between blocks A and B on the selfassembled morphology
connected cylinders, as shown Fig. 6b. A double-helix structure in a spherical aggregate is obtained when eAB = 3 (Fig. 6c). When eAB increases from 4 to 5, the inner structure changes from one side connected double helixes to two separated helixes with different lengths (Fig. 6d and e). When eAB further increases to 6 and 7, the inner structure turns to some dispersed cylinders with the two ends exposed to solvent, as shown in Fig. 6f and g. Figs. 5 and 6 indicate that the inner B domains distribute uniformly when the incompatibility is weak, such as concentric lamella (Fig. 5a) and dispersed spheres (Fig. 6a), while the B domains become more stretched, such as lamella (Fig. 5e) and straight cylinders (Fig. 6f), when the incompatibility is strong. 3.4. Formation pathways of some typical aggregates
In this section, we choose two different triblock copolymers, i.e., A5B8A5 and A7B4A7 triblock copolymers, to examine the effect of the incompatibility between blocks A and B on the self-assembled morphology. The parameters eAS and eBS are fixed, i.e., eAS = 2 and eBS = 5. When eAB is increased from 1 to 3, the self-assembled morphology is always the onion-like morphology for A5B8A5 triblock copolymers. For simplicity, we only put resulting morphologies at eAB = 3 in Fig. 5a. Then some holes appear on the concentric lamellae formed by blocks B when eAB increases from 4 to 6 (Fig. 5b–d). Moreover, it is also found that the hole number is increased as the increase of eAB. When eAB is further increased to 7, the B blocks form a lamella with the edge exposed to the solvent, due to the strong incompatibility between blocks A and B (Fig. 5e). For the A7B4A7 triblock copolymers, a spherical aggregate with dispersed spheres and shot rods inside is obtained when eAB = 1 (Fig. 6a). When eAB = 2, the inner structure changes into irregularly
In this section, the formation pathways of some typical aggregates, i.e., stacked lamellae, onion-like structure, droplet with internal double helixes, and droplet with internal stacked rings are examined to study their formation mechanisms. Fig. 7 shows the variation of the contact number between B-type monomer and solvent (NBS) of the onion-like structure (Fig. 3c) as a function of the annealing time (t), which can be used to monitor the micellization degree of the B blocks. Fig. 7 shows that NBS decreases considerably at first and then remains almost unchanged after 400 steps, which indicates that the micellization of B blocks is almost finished after t = 400. In other words, the final structure at t = 1000 should be an equilibration state. In the current study, all the results are captured at t = 1000 to ensure that the results are at the equilibration state. Moreover, using a different homogeneous state as the initial state, the resulting structures can be well
Fig. 5. Transformation of the morphologies of A5B8A5 triblock copolymers as the increasing of the incompatibility between blocks A and B. (a) eAB = 3; (b) eAB = 4; (c) eAB = 5; (d) eAB = 6; (e) eAB = 7. The color codes are the same as that in Fig. 1. The A domains are transparent to show the inner B domains. The cross-section and true color images are shown on the right of the corresponding snapshots in (a) and (e), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Transformation of the morphologies of A7B4A7 triblock copolymers as the increasing of the incompatibility between blocks A and B. (a) eAB = 1; (b) eAB = 2; (c) eAB = 3; (d) eAB = 4; (e) eAB = 5; (f) eAB = 6; (g) eAB = 7. The color codes are the same as that in Fig. 1. The A domains are transparent to show the inner B domains. The true color images are shown on the right of the corresponding snapshots in (f) and (g). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 7. Variation of the contact number NBS as a function of time (the annealing time) during the formation of onion-like structure (Fig. 3c).
reproduced (results not shown in this work). To visualize the formation pathways of the stacked lamellae and the onion-like structure, a series of snapshots at different annealing time (t) are presented in Fig. 8. When t = 40 (Fig. 8a1), only some very small aggregates are formed by ABA triblock copolymers. At t = 150, ABA triblock copolymers start to assemble into a disordered and incompact aggregate (Fig. 8a2). Thereafter, the ABA triblock copolymers form a compact aggregate and the microphase-separation between A and B phases is appeared, as shown in Fig. 8a3 (t = 200). As the microphase-separation between A and B phases is completed, the stacked lamellae with alternate A and B domains is formed (Fig. 8a4, t = 1000). From Fig. 8b, it is observed that ABA triblock copolymers form an incompact aggregate at first (Fig. 8b1 and b2, t = 40 and t = 100, respectively.) and then B blocks aggregate into a cage-like structure covered by A domains (Fig. 8b3, t = 170). Thereafter, the holes on the cage-like structure of B domain start to close up, and the nanostructure transforms into a onion-like structure (Fig. 8b4 and b5, t = 200 and t = 1000, respectively). The formation pathways for the droplets with internal double helixes or stacked rings are presented in Fig. 9a and b, respectively. It is clear that their formation pathways are similar to the stacked lamellae and onion-like structure. ABA triblock copolymer form a incompact and disordered aggregate at first (Fig. 9a1–a3 and Fig. 9b1–b3, respectively). Thereafter, the microphase separation between A and B phase is occurred, resulting in the formation of double B-type helix (Fig. 9a4–a6)
and stacked rings inside the A-type spheres (Fig. 9b4–b6). From Figs. 8 and 9, it is clear that A domains start to dominate the outermost layer around t = 100, whether in the formations of onion-like structure, droplet with inner double helixes or stacked rings. Moreover, it is found that onion-like structure are formed by the fusion of cake-like structure, rather than the bending of lamellae reported in the previous work [48]. To further study the inner nanostructures, we calculate the density distribution of segment A, B, and solvent along r (the radii around the mass center of the self-assembled aggregate) in Fig. 10 for some typical aggregates, i.e., the stacked lamellae (Fig. 10a), onion-like structure (Fig. 10b), droplets with internal double helixes (Fig. 10c) and internal stacked rings (Fig. 10d). From density curves of the solvent, it is clear that there are no solvents in the core of the aggregates, as shown in Fig. 10a–d. For the stacked lamellae (Fig. 10a), the A density is higher than B density at first (r 6 4) because the mass center is located in the A lamella. Thereafter, A and B densities become almost equal when r > 4 because of the alternating A and B lamellae. For the onion-like structure (Fig. 10b), two peaks of the A density are observed, corresponding to the innermost core and outmost surface. From the curve of B density, a single peak is observed, corresponding an internal B lamella in the range of r = 6 to r = 10. For the droplets with internal double helixes (Fig. 10c) or stacked rings (Fig. 10d), their A density curves are similar to that of the onion-like structure (Fig. 10b), i.e., there are two peaks on the curve, which correspond to the innermost core and outmost surface of the A domain. However, the peak of B density is significantly lower than that of the onion-like structure (Fig. 10b) because B blocks only form internal helixes or rings instead of a continuous internal lamella. In the current study, the self-assembly of ABA triblock copolymer is accomplished under soft confinement. Some self-assembled nanostructures agree well with the previous works under rigid confinement. For example, Arsenault et al. obtained the onion-like structures via the confined self-assembly of polystyrene-block-poly (ferrocenylethylmethylsilane) (PS-b-PFEMS) diblock copolymer in 3D silica template [33]. Under a rigid spherical confinement, Chen et al. observed the droplets with inner spheres, cage-like structure and other complex symmetric structures from the selfassembly of diblock copolymers [34]. Moreover, Yu and coworkers observed the self-assembled nanostructures with stacked rings, single helix and double helixes from the confined self-assembly of diblock copolymers in the spherical pores [35]. In the current study, all these self-assembled structures were also obtained via
Fig. 8. The formation pathways of the stacked lamellae (a1–a4) and onion-like structure (b1–b5): (a1) t = 40; (a2) t = 150; (a3) t = 200; (a4) t = 1000; (b1) t = 40; (b2) t = 100; (b3) t = 170; (b4) t = 200; (b5) t = 1000. The color codes are the same as that in Fig. 1. The A domains are transparent to show the inner B domains in b3–b5.
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Fig. 9. The formation pathways of the droplets with internal double helixes (a1–a6) and internal stacked rings (b1–b6): (a1) t = 40; (a2) t = 100; (a3) t = 150; (a4) t = 200; (a5) t = 300; (a6) t = 1000; (b1) t = 40; (b2) t = 80; (b3) t = 100; (b4) t = 150; (b5) t = 200; (b6) t = 1000. The color codes are the same as that in Fig. 1. The A domains are transparent to show the inner B domains in a3–a6 and b3–b6, respectively.
Fig. 10. Variation of the densities of the segment A, B, and solvent with r (r is the radii around the mass center). (a) stacked lamellae; (b) onion-like structure; (c) droplet with internal double helixes; (d) droplet with internal stacked rings.
the self-assembly of ABA triblock copolymer under the soft confinement. However, the self-assembled aggregates from rigid three-dimensional confinement always keep the spherical shapes because of the rigid confinement boundary, while the aggregates under soft confinement can be the alterable shapes, such as the ellipsoidal shape (Fig. 1e).
4. Conclusions Using Monte Carlo method, we investigated the self-assembly of ABA triblock copolymer under soft confinement. Some novel
self-assembled nanostructures, such as the aggregates with inner single helix, double helixes, stacked rings and cage-like structure, are predicted. The effects of block length ratio, the solvent quality for the blocks B, and the incompatibility between blocks A and B on the self-assembled morphologies are examined. As B block length is increased, more and more B domains are exposed to solvent when the solvent qualities of A and B blocks are equal, while the inner structure of the aggregate changes from sphere to cylinder, and then to concentric lamella when the solvent qualities for A and B blocks are different. As the increase of eBS, the morphology transforms from stacked lamella to bud-like structure and then to onion-like structure for A5B8A5 triblock copolymers, while the
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inner structure of aggregate changes from spherical phases to various cylindrical phases for A7B4A7 triblock copolymers. Moreover, as the incompatibility between A and B is increased, the self-assembled morphology will correspondingly be changed because A and B blocks are more likely to move away from each other. Furthermore, the formation pathways of some typical aggregates are examined to illustrate their formation mechanisms. 5. Conflict of interest
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There is no conflict of interests regarding the publication of this article. Acknowledgments This work was financially supported by the National Natural Science Foundation of China for General Program (51373172), Major Program (51433009) and the Open Project of State Key Laboratory of Supramolecular Structure and Materials (sklssm2015030). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
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