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Self-Assembly of the AB/BC Diblock Copolymer Mixture Based on Hydrogen Bonding in a Selective Solvent: A Monte Carlo Study Yuanyuan Han and Wei Jiang* State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China, and Graduate University of the Chinese Academy of Sciences
bS Supporting Information ABSTRACT: Monte Carlo simulation was used to study the selfassembly of the AB/BC diblock copolymer mixture based on hydrogen bonding (H-bonding) in a selective solvent. The simulative results indicate that the self-assembled micelle structure is a function of the intensity of the associative interaction (εhb) and the directional dependency (Phb) of H-bonding, and the intrinsic repulsive interaction (εAC) between A and C blocks. The Janus micelles, mixed micelles (micelles with a uniform mixing of different blocks in corona) and pure micelles (micelles with either AB or BC diblock copolymers) are obtained through the adjustment of εhb and εAC. Moreover, the simulative results reveal that decreasing directional dependency (Phb) and increasing H-bonding interaction (εhb) has an equivalent effect on the micelle structure and H-bonding association for the AB/BC diblock copolymer mixture in a selective solvent.
1. INTRODUCTION Hydrogen bonding is a donor-acceptor interaction specifically involving hydrogen atoms. The formation of a hydrogen bond is thermo-reversible and displays a high degree of cooperatively.1 This means hydrogen bonding offers possibilities to create materials which are sensitive to external stimuli. Hence, recently there has been growing interest in the phase behavior of the associating polymers based on hydrogen bonding in solutions.2-13 Jiang and co-workers2-11 reported on the preparation of “pseudo graft” copolymers from a homopolymers pair with one bearing a terminal H-bond donor (acceptor) and the other containing H-bond acceptors (donors) along the chain. Noncovalently connected micelles (NCCM), in which the core and shell are connected by hydrogen bonding, are formed by those pseudograft copolymers in block-selective solvents. These NCCMs are highly sensitive to changes in pH,5 temperature,8 and light irradiation10 due to the participation of hydrogen bonding. Another attractive quality of hydrogen bonding is that the self-assembly behavior in the copolymer systems based on hydrogen bonding is similar with the block copolymer systems if the hydrogen bonds are strong enough, whereas at the same time it is much simpler to prepare hydrogen bonding based samples than to synthesize the covalent analogues. Liu et al.12,13 recently reported the preparation of “pseudo” ABC triblock copolymers from two diblock copolymers AB and BC with an H-bonding nucleic acid pair adenine (A) and thymine (T) tagged at the end of the B block. The hydrogen bonding enhanced the mixing of different diblock chains in a micelle. Many intriguing micelles such as Janus micelles and flowerlike micelles were r 2011 American Chemical Society
obtained in block-selective solvents, and these micelles were supposed to have fascinating applications. Because of the large parameter space that characterizes the polymer architectures, chemical incompatibilities of different species and bonding strengths in the associating polymer systems based on hydrogen bonding, theoretical and simulated investigations14-24 undoubtedly play an important role in the studying of the effect of hydrogen bonding. Tanaka and co-workers first gave the theoretical description of the reversibly associating systems (different types of homopolymers are associated by reversible bonds instead of covalent bonds). They used the random phase approximation to study the microphase and macrophase separation transitions in the systems of AB pseudo diblock copolymers14 and pseudo graft copolymers.15 They found that macrophase separation, frequently involving at least one microphase separation, is a dominant feature in the systems based on reversible bonding. Later, ten Brinke et al.18 employed a combination study of theoretical method and Monte Carlo simulation to investigate the micro- and macrophase separation in pseudo AB diblock copolymer melt based on hydrogen bonding. Characteristic phenomena such as reappearing phases, macrophase separation and at least one of which is microphase separated were observed and discussed by them. Most recently, the group of Fredrickson employed self-consistent field theory to investigate the phase behavior of pseudo AB diblock22 and ABA triblock23 copolymer melts based on hydrogen bonding. Their investigations illustrate that the concentration of the copolymer are Received: November 7, 2010 Revised: January 22, 2011 Published: February 18, 2011 2167
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The Journal of Physical Chemistry B controlled by the bonding strength, segmental incompatibility, and the relative proportions and chain lengths of the homopolymers. Changing the ratio of homopolymer chain lengths has a dramatic effect on not only the extent of reversible bonding but also the phase morphology. However, to the best of our knowledge, the effect of hydrogen bonding on the micellization behavior in a selective solvent has seldom been investigated by theorists. As aforementioned, the phase behavior (reported by Liu et al.12) of AB and BC diblock copolymers based on hydrogen bonding in a selective solvent is very attractive. Many intriguing micelle morphologies were obtained, including the mixed micelles and Janus micelles which can be usually obtained in ABC triblock copolymer systems.25-28 Due to the introduction of hydrogen bonding, the associating system can exhibit more flexibility and hence variety in its phase behavior as compared to chemically connected or nonassociated systems. Thus in this paper, Monte Carlo simulation was used to study the phase behavior of AB and BC diblock copolymers based on hydrogen bonding in a selective solvent for A and C blocks. The purpose is to reveal the effect of hydrogen bonding on the self-assembly of the AB and BC diblock copolymer mixture in a selective solvent.
2. MODEL AND SIMULATION Lattice Monte Carlo simulation method was used in this study. The system is embedded in a simple cubic lattice of volume V = L L L with dimensions of L = 25. Periodic boundary conditions are imposed in all three directions. The monomer concentration is 15%. Each monomer occupies one lattice site, and the monomers are self- and mutually avoiding which insures that no more than one monomer existed per lattice site. The single-site bond fluctuation model29-31 with the permitted bond length of 1 and (2)1/2 was used in these simulations, thus, each lattice site has 18 nearest neighbor sites in a three-dimensional space. The evolution of the chain configuration was achieved through the exchange movement of monomers. In an exchange move, a monomer is randomly selected, and it can exchange with a solvent molecule on one of its 18 nearest neighbors. If the exchange move does not violate the bond length restriction and retains that no bond crossing occur, it is allowed. The acceptance or rejection of the attempted move is further governed by the Metropolis rule:32 that is, if the energy change ΔE is negative, it is accepted. Otherwise, it is accepted with a probability of p = exp[-ΔE/(kBT)]. In this study, the self-assembly of the A18-b-B3/B3-b-C18 diblock copolymer mixture was considered. The quantitative ratio of these two diblock copolymers was fixed as 1:1. There are functionalized monomers at the end of each chain, that is, A18B2-B0 and B00 -B2-C18. Between these two types of functionalized monomers B0 and B00 , there is associative interaction because of the hydrogen bonding (see Figure 1). Due to the uniqueness of hydrogen bonding, each functional monomer can only form one hydrogen bonding, and the interaction between these functional groups should be considered to have a strong directional dependency; that is, the interaction depends on the relative orientation of the two functional monomers. However, the monomers in the Monte Carlo simulation are coarse grained, and we cannot properly determine whether the hydrogen bonding will be formed through the external orientations of these coarse-grained groups. To appropriately and efficiently realize this directional dependency of hydrogen bonding in Monte
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Figure 1. Schematic diagram showing the associative interaction between the two different types of functionalized monomers in each diblock chain.
Carlo simulation, ten Brinke et al. proposed an algorithm to change this orientational problem into a probabilistic problem.16,18 In this paper, we will take advantage of this algorithm to determine whether hydrogen bonding will be formed between two nearest neighbor nonbonded functional monomers. First, a parameter q was introduced to reflect the number of possible internal orientational states within a functional monomer. Thus, the number of all possible relative orientations of these two functional monomers is q2, and the interaction energy between them will be given as follows: εB0 B00 ¼ εhb ðCB0 , CB00 Þ þ εBB ½1 - δðCB0 , CB00 Þ
ð3Þ
where εhb and εBB are the energy of hydrogen bonding and the ordinary van der Waals interaction between B blocks, respectively. Ci is the variable number of internal states per monomer B0 or B00 (Ci = 1, 2, ..., q), and δ is the Kronecker delta function, which is equal to unity if CB0 = CB0 0 ; otherwise, its value is 0. Based on eq 3, it can be seen that only q pair states out of all q2 pairs have the energy of hydrogen bonding, which means that the probability of forming hydrogen bonding between two nearest nonbonded functional monomers is q/q2, i.e., 1/q. Hence, the form of interaction energy in the actual Monte Carlo process is given as follows: ( εhb if ξ e phb ð4Þ εB0 B00 ¼ εBB otherwise where ξ is a random number between 0 and 1. Phb is the probability of forming hydrogen bonding between two nonbonded functional monomers, i.e., Phb = 1/q (in this paper q = 10 if not specified). From the relationship between Phb and q, it is known that Phb can reflect the directional dependency of the hydrogen bonding. If the random number is less than Phb, it means that the relative orientations of the two functional monomers are suitable for forming hydrogen bonding, otherwise, they are not. Once the hydrogen bonding is formed, it will be maintained unless the movement of the bonded functional monomer violates the bond length restriction of hydrogen bonding. This condition means that the probability of breaking the hydrogen bonding mainly depends on the associative interaction of hydrogen bonding. When the associative interaction is strong, the possibility of breaking the hydrogen bonding is lower due to the strong energy constraint for the functional monomers. The experimental process for preparing micelles from AB/BC diblock copolymer mixture in the solution includes mixing the two diblock copolymers in a solvent that is good for the three blocks and then adding a block-selective solvent for the A and C blocks dropwise.12 To simulate this process, first, a disordered state was generated as a starting configuration. Then in order to 2168
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Figure 2. Morphologies formed by block copolymers in a selective solvent with different repulsive interactions between A and C blocks: (a) AB/BC diblock copolymer mixture and (b) ABC triblock copolymer.
mimic mixing of the diblock copolymers in a solvent that is good for the three blocks, all interactions were set to 0, except the interaction between functional monomers (εhb) and the intrinsic repulsion between A and C blocks (εAC). The simulation time at this step is sufficiently long to obtain a homogeneous solution. Then we changed εBB from 0 to -0.7 with a step of -0.05 per 1.0 104 Monte Carlo step (MCS) while keeping the interactions εhb and εAC unchanged to mimic the situation of adding a block-selective solvent for A and C dropwise. This step will also last for a sufficiently long time until the micelles are formed and become stable. It is worth noting that, from the relation between reduced interaction ε and Flory-Huggins interaction parameter χ, it can be obtained that: χBS = (1/kBT)[εBS - 1/2(εBBþεSS)], and χBS = -(1/(2kBT))εBB in the case of εBS = εSS = 0. Thus, it can be known that the value of χBS is positive while the value of εBB is negative, and in this case the solvent quality is poor for B blocks. In this paper, the temperature remains constant (1/kBT = 1), and the time t is measured in units of MCS. One MCS means that on the average, every monomer has attempted exchange once.
3. RESULTS AND DISCUSSION In this paper, we mainly focus on the effect of the associative interaction of hydrogen bonding εhb and the repulsive interaction between A and C blocks εAC on the micelle structures formed by the AB/BC diblock copolymer mixture in a selective solvent. First, two ultimate conditions of the bonding between these two diblock copolymers are investigated: (1) the bonding between these two diblock copolymers is inexistent and (2) the bonding is very strong to be considered an ABC triblock copolymer. Figure 2a shows the simulation results of the micelle morphologies that were formed by the AB and BC diblock copolymer mixture without the bonding between the two diblock copolymers. It is shown that the insoluble blocks B form the core of the micelle, whereas the soluble blocks A and C form the corona, and the patterns in the corona seem very different with an increase in εAC. When the values of εAC are relatively small, a uniform mixing of diblock copolymers in the corona is observed (see Figure 2, a1∼a2). However, when the values of εAC are relatively large, a mixture of pure micelles with either AB or BC diblock copolymers is observed (see Figure 2, a3∼a4). Figure 2b shows the simulation results under the other ultimate condition; that is, the AB and BC diblock copolymers are covalently bonded,
forming A18-B6-C18 triblock copolymers. It is shown that the results at larger εAC values, that is, εAC g 0.5, are totally different from those found in Figure 2a. The micelles with laterally segregated coronas, which are typical Janus micelles, are found when εAC is in the range of 0.5-1.0 (see Figure 2, b3∼b4). To compare with the aforementioned ultimate conditions, two values of εhb are chosen, that is, -1 and -10. Figure 3 shows the simulation results of the micelle structures formed by the AB/ BC diblock copolymer mixture based on H-bonding with different values of εAC. It is shown that a uniform mixing of diblock copolymers in the corona is observed at relatively small εAC values in both systems (see Figure 3, a1∼a2, b1∼b2). However, when the values of εAC are relatively large, the simulation results are totally different between these two systems: a mixture of pure micelles with either AB or BC diblock copolymers is observed in the case of εhb = -1 (see Figure 3, a3∼a4), whereas the Janustype micelle is observed in the case of εhb = -10 (see Figure 3, b3∼b4). Based on these simulation results, we can see that the phase behavior of the AB/BC diblock copolymer mixture based on H-bonding is quite similar to that of the nonbonded system (AB/BC) or the chemically bonded system (ABC) when the values of εhb are properly chosen. However, when we change the value of εhb to -2, the patterns of the corona turn to be much richer, as shown in Figure 4a. To clearly observe the micelle types, the morphologies of each single micelle in Figure 4a are respectively drawn, and the typical morphologies in each system are shown in Figure 4b. A uniform mixing of diblock copolymers in the corona is observed at εAC = 0.1. A typical Janus-type micelle is observed when εAC is increased to 0.3. With a further increase in εAC, the micelle finally becomes a mixture of pure micelles with either AB or BC diblock copolymers. So far, three types of micelles (that is, mixed micelles or micelles with a uniform mixing of different blocks in corona, Janus micelles, and pure micelles) have been obtained. To further probe the formation conditions for each micelle type, series values of εhb and εAC are investigated, and the morphologies of each micelle are examined in detail. Figure 5 shows the structural variation with εhb and εAC, in which the regions for each type of micelles are compartmentalized by dot lines. It is obvious that the mixed micelles are always observed at lower values of εAC, whereas the Janus and pure micelles tend to appear at higher values. Furthermore, the detail regions of the Janus and pure micelles can be observed in Figure 5. When |εhb| is large, the 2169
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Figure 3. Morphologies formed by the AB/BC diblock copolymer mixture based on hydrogen bonding in a selective solvent with different repulsive interactions between A and C blocks: (a) εhb = -1 and (b) εhb = -10.
Figure 4. Morphologies formed by the AB/BC diblock copolymer mixture based on hydrogen bonding in a selective solvent with different repulsive interactions between A and C blocks for εhb = -2. (a) A full view of the morphologies. (b) The typical morphology in each system.
Janus micelles become a dominating structure. Otherwise, the pure micelles become the major structure. Note that some experimental results in the literature are consistent with our simulation results. Liu et al. found that different soluble blocks mix together in the corona when H-bonding nucleic acid pairs tag at the end of insoluble blocks in premixed micelles, whereas the segregation of different diblock copolymers took place in the system without H-bonding.12 This observation is consistent with the simulation result for lower values of εAC (that is, εAC = 0.2), as shown in Figure 5. Furthermore, from Figure 5 it can be found that the Janus micelle appears in the range of εAC = 0.2-1.0 in the case of |εhb|, while it appears in the range of εAC = 0.3-2.0 when the value of |εhb| is increased to 3.0. These results indicate that the region of Janus micelle shifts to higher values of εAC with increasing |εhb|. The aforementioned results illustrate that the associative interaction of H-bonding and the repulsive interaction between A and C blocks have a strong influence on the micelle morphologies formed by the AB/BC diblock copolymer mixture. To quantitatively investigate this property, the contact number of the A and C blocks (NAC) and the fractions of the H-bonded diblock copolymers (φhb) are introduced in this paper. Here, NAC is the number of A and C pairs of segments within the
√ distance of 2, and its value reflects the degree of the segregation between A and C blocks in the corona. The fractions of the bonded diblock copolymers φhb can reflect the amount of bonded diblock copolymers. All values of NAC and φhb in this paper are counted after the micelle structures become stable in each system. In Figure 6, log(NAC) is plotted against εAC for various values of εhb. It can be seen that NAC decreases from a high value (about 600) to almost 0 with increasing εAC for different values of εhb. This indicates that an increase in εAC can lead to the phase segregation between A and C blocks. However, the NAC decreasing rates are different for different values of εhb. For lower |εhb| (i.e., |εhb| e 1.5), NAC reduces rapidly, whereas it decreases slowly with an increase in εAC for higher |εhb| (i.e., |εhb| g 2.0). This indicates that decreasing |εhb| and increasing εAC are favorable for the phase segregation between A and C blocks. In other words, the phase segregation is the result of the competition between εAC and |εhb|. Besides the phase segregation, the formation of the H-bonded diblock copolymers is also the result of the competition between εAC and |εhb|. Figure 7 is the variation of the fractions of the H-bonded diblock copolymers (φhb) with εAC for different values of |εhb|. It is seen that φhb rapidly decreases up to about 0 with the increase of εAC for lower |εhb|. This indicates that only a small 2170
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Figure 7. Variations of φhb with εAC for the AB/BC diblock copolymer mixture based on hydrogen bonding in a selective solvent.
Figure 5. Diagram showing the variation of the structures formed by the AB/BC diblock copolymer mixture based on hydrogen bonding in a selective solvent with εAC and εhb.
Figure 6. Variations of NAC with εAC for the AB/BC diblock copolymer mixture based on hydrogen bondingin a selective solvent.
increase in εAC can break the H-bonding association between the two diblock copolymers for lower |εhb|. However, for higher |εhb| (|εhb| = 2.0), it can be seen that φhb remains almost unchanged first, and then decreases with increasing εAC. This reflects that it becomes quite difficult for such repulsive interaction to break the H-bonding association. Furthermore, when |εhb| g 3.0, φhb becomes more higher and almost remain unchanged with an increase in εAC. This means that most chains are connected end to end via H-bonding. According to the above discussions, it can be concluded that the competition between |εhb| and εAC is the key factor that determines the type of micelles. Increasing εAC leads to the decrease of NAC, inducing the phase separation between coronaforming blocks. Increasing |εhb| leads to the increase of φhb, promoting the aggregation of core-forming blocks. Mixed micelles are more likely to be formed at lower εAC. However, if εAC is high enough, two separations between A and C blocks, i.e., the intermicellar separation (leading to the formation of pure micelles) and the intramicellar separation (leading to the formation of
Janus micelles), can occur depending on the competition between |εhb| and εAC. If the effect of εAC becomes dominating, intermicellar separation occurs, and a mixture of pure micelles can be obtained. If the effects of |εhb| and εAC are well balanced, Janus micelles can be obtained. As a result, the region for Janus micelle shifts to higher values of εAC with an increase in |εhb|. Furthermore, the effect of directional dependency (Phb) of H-bonding and concentration of the solution are investigated. The detailed simulative results and discussion are given in the Supporting Information. The simulative results indicate that decreasing Phb and increasing εhb has an equivalent effect on the micelle structures formed by AB/BC diblock copolymer mixture based on H-bonding. However, the micelle structure is not sensitive to the concentration and it mainly depends on the H-bonding interaction (εhb) and the repulsive interaction (εAC).
4. CONCLUSION Monte Carlo simulation was used to study the self-assembly of the AB/BC diblock copolymer mixture based on hydrogen bonding in a selective solvent. Insoluble blocks B form the core of the micelles, whereas soluble blocks A and C form the coronas. The simulative results indicate that the self-assembled micelle structure is a function of the intensity of the associative interaction (εhb) and the directional dependency (Phb) of H-bonding, and the intrinsic repulsive interaction (εAC) between A and C blocks. The Janus micelles, mixed micelles and pure micelles are obtained through the adjustment of εhb and εAC. The competition between these two interactions determines the type of micelles. If the associative interaction predominate the repulsive interaction, mixed micelles will be formed. On the contrary, if the repulsive interaction predominate the associative interaction, segregation will occur between these two diblock copolymers, and a mixture of pure micelles with either AB or BC diblock copolymers will be formed. If these two interactions are well balanced, Janus micelles will be formed. Moreover, the simulative results reveal that decreasing directional dependency (Phb) and increasing H-bonding interaction (εhb) has an equivalent effect on the self-assembled micelle structure and H-bonding association for the AB/BC diblock copolymer mixture. ’ ASSOCIATED CONTENT
bS
Supporting Information. Detailed simulative results and discussion of the effect of directional dependency of H-bonding
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Telephone: þ86-431-85262151. Fax: þ86-431-85262126.
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’ ACKNOWLEDGMENT Financial support was provided by the National Natural Science Foundation of China for Youth Science Funds (21004063), Major Program (50930001), Creative Research Groups (50621302), Outstanding Young Investigators (50725312), and the National Basic Research Program (2007CB808000) of China. ’ REFERENCES (1) ten Brinke, G.; Ruokolainen, J.; Ikkala, O. Adv. Polym. Sci. 2007, 207, 113–177. (2) Liu, S.; Pan, Q.; Xie, J.; Jiang, M. Polymer 2000, 41, 6919–6929. (3) Duan, H.; Chen, D.; Jiang, M.; Gan, W.; Li, S.; Wang, M.; Gong, J. J. Am. Chem. Soc. 2001, 123, 12097–12098. (4) Wang, M.; Zhang, G.; Chen, D.; Jiang, M.; Liu, S. Macromolecules 2001, 34, 7172–7178. (5) Dou, H.; Jiang, M.; Peng, H.; Chen, D.; Hong, Y. Angew. Chem., Int. Ed. 2003, 42, 1516–1519. (6) Duan, H.; Kuang, M.; Wang, J.; Chen, D.; Jiang, M. J. Phys. Chem. B 2004, 108, 550–555. (7) Kuang, M.; Duan, H. W.; Wang, J.; Jiang, M. J. Phys. Chem. B 2004, 108, 16023–16029. (8) Zhang, Y.; Jiang, M.; Zhao, J.; Ren, X.; Chen, D.; Zhang, G. Adv. Funct. Mater. 2005, 15, 695–699. (9) Chen, D.; Jiang, M. Acc. Chem. Res. 2005, 38, 494–502. (10) Liu, X.; Jiang, M. Angew. Chem., Int. Ed. 2006, 45, 3846– 3850. (11) Guo, M.; Jiang, M. Soft Matter 2009, 5, 495–500. (12) Hu, J.; Liu, G. Macromolecules 2005, 38, 8058–8065. (13) Yan, X.; Liu, G.; Hu, J.; Willson, C. G. Macromolecules 2006, 39, 1906–1912. (14) Tanaka, F.; Ishida, M.; Matsuyama, A. Macromolecules 1991, 24, 5582–5589. (15) Tanaka, F.; Ishida, M. Macromolecules 1997, 30, 1836–1844. (16) Huh, J.; Ikkala, O.; ten Brinke, G. Macromolecules 1997, 30, 1828–1835. (17) Dormidontova, E.; ten Brinke, G. Macromolecules 1998, 31, 2649–2660. (18) Huh, J.; ten Brinke, G. J. Chem. Phys. 1998, 109, 789–797. (19) Angerman, H. J.; ten Brinke, G. Macromolecules 1999, 32, 6813–6820. (20) Dormidontova, E. E.; ten Brinke, G. J. Chem. Phys. 2000, 113, 4814–4826. (21) Huh, J.; Jo, W. H. Macromolecules 2004, 37, 3037–3048. (22) Feng, E. H.; Lee, W. B.; Fredrickson, G. H. Macromolecules 2007, 40, 693–702. (23) Lee, W. B.; Elliott, R.; Katsov, K.; Fredrickson, G. H. Macromolecules 2007, 40, 8445–8454. (24) Lee., W. B.; Mezzenga, R.; Fredrickson, G. H. Phys. Rev. Lett. 2007, 99, 187801. (25) Walther, A.; M€uller, A. H. E. Soft Matter 2008, 4, 663–668. (26) Erhardt, R.; B€oker, A.; Zettl, H.; Kaya, H.; Pyckhout-Hintzen, W.; Krausch, G.; Abetz, V.; M€uller, A. H. E. Macromolecules 2001, 34, 1069–1075. 2172
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