Article pubs.acs.org/Macromolecules
Self-Assembly of Linear ABCBA Pentablock Terpolymers Hsuan-Hung Liu,† Ching-I Huang,*,† and An-Chang Shi‡ †
Institute of Polymer Science and Engineering, National Taiwan University, Taipei 10617, Taiwan R. O. C. Department of Physics and Astronomy, McMaster University, Hamilton, Ontario Canada, L8S 4M1
‡
ABSTRACT: The phase behavior of linear ABCBA pentablock terpolymers is examined and compared with corresponding linear ABC triblock terpolymers by using the 3-D selfconsistent field theory. In particular, phase diagrams of the melts are constructed and used to discuss how the selfassembled morphologies are influenced by the compositions of the three components and the block number per chain. Since the two free ends of A blocks in the ABCBA copolymers enable the macromolecules to relieve the packing frustration within the structures as well as more types of chain conformation, the ABCBA pentablocks exhibit diverse complex network structures and binary crystalline phases of cylinders and spheres. Compared with most linear diblock and triblock copolymers, for which the gyroid phase occupies a narrow region in the phase space, the ABCBA pentablocks tend to form a variety of continuous networks including diamond, hexagonally perforated lamellae, Fddd network, and gyroid. Moreover, the ABCBA pentablocks exhibit different packing orders of alternating A/C spheres and cylinders than ABC. By varying the length of the B-blocks and the ratio of compositions of A and C, a large number of binary metallic and ionic crystals, such as NaCl, CsCl, ZnS, CaF2, Li3Bi, Nb3Sn (A15), and Cu3Au, and alternating A/ C cylinders with coordination numbers of A/C equal to 4/4, 6/3, and 4/2, are obtained from the ABCBA pentablock terpolymers. As our simulated ABCBA pentablock terpolymers have synthetic advantages, the fascinating self-assembling results displayed in this study enable the ABCBA as being one of the most efficient routes to functional materials.
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INTRODUCTION Because of their rich phase behavior, block copolymers are widely applied in many nanotechnologies. With the development of synthetic techniques, a variety of multiblock copolymers, which could form hierarchical self-assembled microstructures, have been successfully synthesized. The unique character of forming multiple-length-scale structures opens vast opportunities for block copolymers as electrical, optical and other functional materials.1−4 Linear multiblock copolymers have been shown to be excellent candidates to generate hierarchical microstructures.5−19 The resultant selfassembling behavior by designing and increasing the number of blocks continues to attract considerable scientific attention in recent years. Generally speaking, the simplest AB linear diblock copolymers form microphase-separated structures with one characteristic length scale usually within the 10−100 nm range. The ordered equilibrium morphologies include body-centered cubic spheres (SBCC), hexagonally packed cylinders (CHEX), gyroid (G), Fddd network, and lamellae (L).20 When a third monomer type C is included, the resulting ABC linear triblock terpolymers can form much more complicated and hierarchically ordered structure-within-structure morphologies.21−43 Traditionally, the morphologies are divided into two types of so-called nonfrustrated and frustrated phases, according to the relative strength of the three Flory−Huggins interaction parameters.22 When the interaction parameter between the two end blocks is comparable to or larger than those between © 2015 American Chemical Society
the neighboring blocks, the systems tend to form a series of nonfrustrated morphologies with less A/C interfaces.23−32 In general, the morphologies in the nonfrustrated systems can be classified into several groups: (1) equilibrium diblock copolymer phases, such as L, G, CHEX, SBCC or disordered phase; (2) core−shell types of the G, CHEX, SBCC and two orthorhombic network phases with space groups Fddd (O70) and Pnna (O52), in which the middle-block is long enough to form a shell-domain around the core-structures of one of the end blocks; (3) alternating types of L, G, C and S phases, in which the two end blocks A and C form alternating comparable structures and the middle block B forms the matrix; (4) possible combination of the L, C, and S phases, including lamellae with cylinders inside a domain (L+C) and lamellae with spheres inside a domain (L+S). Experimentally, a number of nonfrustrated systems, such as poly(isoprene-b-styrene-bvinylpyridine) (PI−PS−PVP)27−29 and poly(isoprene-b-styrene-b-ethylene oxide) (PI−PS−PEO),30−32 have been synthesized and studied. On the other hand, when the interaction parameter between the two end blocks is much weaker than those between the neighboring blocks, the copolymers prefer to form morphologies with A/C interfaces, which however is not favored due to the chain topology.31,33−43 Thus, more complex ordered structures can be formed in these frustrated copolymer Received: June 25, 2015 Revised: August 14, 2015 Published: August 26, 2015 6214
DOI: 10.1021/acs.macromol.5b01395 Macromolecules 2015, 48, 6214−6223
Article
Macromolecules
Al2O3 are obtained. In more detail, the average coordination number (CN) of spherical phase is mainly determined by the length of the midde B-block, and the asymmetric degree of CNs is controlled by the relative length of the two end Bblocks. They also found that blending these tail-symmetric and asymmetric BABCB pentablock terpolymer with AB diblock or ABC triblock opens a vast opportunity to form more different types of binary crystals.50 These studies demonstrated that the crystal types of the spherical phases are greatly affected by the sizes of the A and C spheres. As multiblock terpolymers offer many parameters to control the spherical size, such as chain architecture and composition (length) of each block, discovering all possible packing types of spherical phases formed by the multiblock terpolymers with other chain architectures remains a highly interesting and important issue. Herein, we use linear ABCBA pentablock terpolymers as a model system and examine their self-assembling behavior. From the synthetic point of view, the ABCBA type of pentablock terpolymers is more symmetric than the BABCB or the ABCBC, and thus can probably be synthesized more efficiently. Experimentally, there have been a number of studies regarding the micelle formation of ABCBA pentablock terpolymer in aqueous solutions, aiming at potential applications in drug delivery and gene therapy.56−58 Besides, the ABCBA pentablocks can be compared with the ABC triblocks to understand the difference or advantages by increasing the number of covalently bonded blocks. For example, Meuler et al.59 reported that the symmetric poly(ethylene oxide-b-styrene-b-isoprene-b-styrene-b-ethylene oxide) (OSISO) pentablock terpolymers tend to form continuous morphologies and therefore have better mechanical properties than the OSI triblock terpolymers. Though the ABCBA pentablock terpolymers have been shown good mechanical properties, successful applications, and great potentials to exhibit diverse morphologies, there exist very few theoretical studies, in particular, of phase behavior of these systems. Ye et al.60 used two-dimensional (2-D) self-consistent field theory (SCFT) to investigate the self-assembling behavior of ABCBA linear pentablock terpolymers in melts at the same incompatibility parameters between each pair of components. In particular, they obtained a significant region of equilibrium lamellar phase in the interior phase triangle and three other equilibrium morphologies of the hexagonal lattice phase, the core−shell hexagonal lattice phase, and the two interpenetrating tetragonal lattice phase, surrounding the lamellar phase. On the basis of the fact that the linear multiblock terpolymers tend to form three-dimensional networks, a systematic selfassembling behavior via the 3-D numerical simulation techniques becomes a fundamentally interesting and crucial work. In this work, we employ three-dimensional (3-D) real-space SCFT method to investigate the self-assembling behavior of ABCBA linear pentablock terpolymers in melts. Specifically, the modified diffusion equations of SCFT are solved via the pseudospectral method,64 which takes the advantage of switching between real and reciprocal spaces. As it solves the modified diffusion equations by the split-step fast Fourier transformation, it provides a higher operating efficiency. The schematic plot of molecular structure of ABCBA linear pentablock terpolymers is displayed in Figure 1, where A, B, and C blocks are labeled in blue, red, and green, respectively. In order to reduce the parameter space, we assume equal segment sizes and the three Flory−Huggins interaction parameters are
systems. Typical ordered phases include (1) B-formed cylinders, rings, spheres, and helices on cylinders; (2) lamellae with B-cylinders or B-spheres at the interfaces and gyroid with B-spheres at the interfaces; and (3) knitting patterns. Modeled experimental systems of this class are poly(styrene-b-ethyleneco-l-butene-b-methyl methacrylate) (SEBM)36,37 and poly(styrene-b-butadiene-b-methyl methacrylate) (SBM).38−43 Current interest regarding ABC linear block terpolymers has been extended from triblock to multiblock classes of A(BC)n, A(BC)nB, and A(BC)nBA, with the number of alternating B and C blocks, n ≥ 2, both experimentally 5−11 and theoretically.12−19 In particular, most of these previous studies have focused on the copolymers containing one or two long end-blocks of A and multiple short midblocks of B and C. Accordingly, many fascinating hierarchical structure-withinstructures can be formed by varying the A composition and the interaction parameters. Followed the pioneering experimental work of undecablock terpolymers consisting of two long poly(2-vinylpyridine) (P) end-blocks and short polystyrene− polyisoprene (SI) alternating midblocks by Matsushita et al.,7 it has been well understood that for most interaction parameters between components I and J, χIJ, a series of spheres-withinlamellae, cylinders-within-lamellae, parallel lamellae-withinlamellae morphology, coaxial cylinders, and concentric spheres can be induced as a function of the A-composition.19 Moreover, the number of thin layers can be tuned by the interaction parameters and the relative length of the midblocks and endblocks.16−18 On the contrary, when the interaction parameters χBC ≫χAB > χAC, the segregated B and C small-length-scale domains tend to be perpendicular with respect to the largelength-scale morphologies. The formation of perpendicular hierarchical structure-within-structures has been observed in the hexablock terpolymers of CECEC-P (C, cyclohexylethylene; E, ethylene; P, propylene) with one long end-block of P by Fleury and Bates.8,9 The formation of more complex morphologies from multiblock copolymers, by varying the monomer types, block numbers, block sequence, and composition, continues to attract the attention of the research community. Very recently, one particular interest has been focused on how to build up the design principles of the multiblock copolymers for the packing of spherical domains into various crystalline lattices,25,44−50 as in ionic and metallic alloy crystals. For the simplest AB diblock copolymer melts and solutions, the most stable spherical phase formed by the minority component is the BCC,51−54 while the FCC packing of the spheres formed by the majority blocks in the presence of a selective solvent becomes more stable than BCC.55 The Frank−Kasper A15 and σ phases have been proposed as equilibrium phases in other complex architectures, such as dendrimer and multibranch copolymers.45−47,49 For ABC multiblock terpolymers, it is quite possible to form binary crystals when the two nonadjacent minority components of A and C form spheres in the B-matrix. For example, the alternating A and C spheres formed by the ABC linear triblock terpolymers have two characteristic packing orders of CsCl (with Pm3m symmetry) and NaCl (with Fm3m symmetry), which is greatly influenced by the composition of B, f B.25,48 Recently, Xie et al.48 explored a large number of possible crystalline lattices of A and C spheres formed by tail-symmetric and asymmetric BABCB pentablock terpolymers. By manipulating the lengths of the middle and terminal B-blocks, a variety of binary ionic and metallic crystals, such as NaCl, CsCl, ZnS, α-BN, AlB2, CaF2, TiO2, ReO3, Li3Bi, Nb3Sn (A15), and α6215
DOI: 10.1021/acs.macromol.5b01395 Macromolecules 2015, 48, 6214−6223
Article
Macromolecules
attributed to the diffusion of each A, B, and C monomer along the chains, respectively. To consider the contribution from the chain diffusion, we define a length parameter along the copolymer chain, s, so that there are (Δs)N monomers within any chain interval of length Δs. In order to solve the volume fraction profiles as well as the free energy in the equilibrium state, we begin with solving the copolymer partial partition
Figure 1. Schematic plot of ABCBA linear pentablock terpolymers.
the same, χABN = χBCN = χACN = χN = 80, which is strong enough to ensure the segregation from one another. We first construct a phase triangle of the system, from which the selfassembling behavior of ABCBA linear pentablock terpolymers will be systematically discussed as a function of composition (fA, f B, and f C). For a comparison, we also construct the phase triangle of corresponding ABC linear triblock terpolymers at the same χN = 80.
⇀
⇀
functions, qCO( r ,s) and qCO+( r ,s), which are defined as the end-integrated distribution functions and represent the probabilities to find the polymer segment of contour length s ⇀
at space coordinates of r starting from two free ends,
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⇀
⎧ ⇀ ⎪ ωA ( r ), 0 ≤ s ⎪ ⎪ ⎪ f ⇀ ⇀ ωI( r ) = ⎨ ωB( r ), A ≤ 2 ⎪ ⎪ fA ⎪ ω (⇀ + ⎪ C r ), ⎩ 2 ⇀
