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The impact of intramolecular polydispersity on the self-assembly of AB n miktoarm star copolymers. Phys Chem Chem Phys 2023; 25:20032-20041. [PMID: 37462012 DOI: 10.1039/d3cp00994g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/27/2023]
Abstract
The self-assembly behaviors of ABn miktoarm star copolymers as one typical type of asymmetric architecture have been studied well in the past few decades due to their deflected phase boundaries. In particular, recently, they have attracted renewed theoretical interest due to their expanded spherical phase region that stabilizes complex Frank-Kasper spherical phases. However, previous theoretical studies have never considered ABn copolymers with unequal arm lengths, which is more or less the case for synthesized copolymers. In this work, we investigate the self-assembly behaviors of ABn miktoarm star copolymers with unequal B-arms using self-consistent field theory. We propose an intramolecular polydispersity index (iĐ) to quantify the distribution of unequal B-blocks. Accordingly, we further propose a simple quantity of an effective arm number nequ = n/iĐ for quantitatively comparing the phase boundaries between various ABn copolymer samples with different arm numbers or different distributions of B-blocks. Our results indicate that different ABn copolymers with equal nequ exhibit similar phase diagrams. On the other hand, we also found that the phase boundaries of two different samples with same nequ are not exactly overlapped. We speculate that the effect of spontaneous curvature may be mainly controlled by nequ, but the packing frustration of B-blocks may also be dependent on the other quantities that are closely related to the shape of the distribution of B-arms, such as higher order polydispersity indexes.
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Theoretical Study of Phase Behaviors of Symmetric Linear B 1A 1B 2A 2B 3 Pentablock Copolymer. Molecules 2023; 28:molecules28083536. [PMID: 37110770 PMCID: PMC10146716 DOI: 10.3390/molecules28083536] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2023] [Revised: 04/08/2023] [Accepted: 04/16/2023] [Indexed: 04/29/2023] Open
Abstract
The nanostructures that are self-assembled from block copolymer systems have attracted interest. Generally, it is believed that the dominating stable spherical phase is body-centered cubic (BCC) in linear AB-type block copolymer systems. The question of how to obtain spherical phases with other arrangements, such as the face-centered cubic (FCC) phase, has become a very interesting scientific problem. In this work, the phase behaviors of a symmetric linear B1A1B2A2B3 (fA1 = fA2, fB1 = fB3) pentablock copolymer are studied using the self-consistent field theory (SCFT), from which the influence of the relative length of the bridging B2-block on the formation of ordered nanostructures is revealed. By calculating the free energy of the candidate ordered phases, we determine that the stability regime of the BCC phase can be replaced by the FCC phase completely by tuning the length ratio of the middle bridging B2-block, demonstrating the key role of B2-block in stabilizing the spherical packing phase. More interestingly, the unusual phase transitions between the BCC and FCC spherical phases, i.e., BCC → FCC → BCC → FCC → BCC, are observed as the length of the bridging B2-block increases. Even though the topology of the phase diagrams is less affected, the phase windows of the several ordered nanostructures are dramatically changed. Specifically, the changing of the bridging B2-block can significantly adjust the asymmetrical phase regime of the Fddd network phase.
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Asymmetric Binary Spherical Phases Self-Assembled by Mixing AB Diblock/ABC Triblock Copolymers. Macromolecules 2023. [DOI: 10.1021/acs.macromol.2c02217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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4
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Tuning conformational asymmetry in particle-forming diblock copolymer alloys. SOFT MATTER 2022; 19:90-97. [PMID: 36472126 DOI: 10.1039/d2sm01332k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Self-consistent field theory is employed to compute the phase behavior of binary blends of conformationally asymmetric, micelle-forming diblock copolymers with miscible corona blocks and immiscible core blocks (a diblock copolymer "alloy"). The calculations focus on establishing conditions that promote the formation of Laves phases by tuning the relative softness of the cores of the two different Laves phase particles via independent control of their conformational asymmetries. Increasing the conformational asymmetry of the more spherical particles of the Laves structure has a stabilizing effect, consistent with the expectations of increased imprinting of the Wigner-Seitz cells on the core/corona interface as conformational asymmetry increases. The resulting phase diagram in the temperature-blend composition space features a more stable Laves phase field than that predicted for conformationally symmetric systems. The phase field closes at low temperatures in favor of macrophase separation between a hexagonally-packed cylinder (hex) phase and a body-centered cubic phase. Companion calculations, using an alloy whose components do not produce a hex phase in the neat melt state, suggest that the Laves phase field in such a blend will persist at strong segregation.
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Emergence and Stability of Exotic “Binary” HCP-Type Spherical Phase in Binary AB/AB Blends. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01957] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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6
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Emergence of Multi-strand Helices from the Self-Assembly of AB-Type Multiblock Copolymer under Cylindrical Confinement. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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10
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Emergence of Hexagonally Close-Packed Spheres in Linear Block Copolymer Melts. J Am Chem Soc 2021; 143:14106-14114. [PMID: 34448579 DOI: 10.1021/jacs.1c03647] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
The hexagonally close-packed (HCP) sphere phase is predicted to be stable across a narrow region of linear block copolymer phase space, but the small free energy difference separating it from face-centered cubic spheres usually results in phase coexistence. Here, we report the discovery of pure HCP spheres in linear block copolymer melts with A = poly(2,2,2-trifluoroethyl acrylate) ("F") and B = poly(2-dodecyl acrylate) ("2D") or poly(4-dodecyl acrylate) ("4D"). In 4DF diblocks and F4DF triblocks, the HCP phase emerges across a substantial range of A-block volume fractions (circa fA = 0.25-0.30), and in F4DF, it forms reversibly when subjected to various processing conditions which suggests an equilibrium state. The time scale associated with forming pure HCP upon quenching from a disordered liquid is intermediate to the ordering kinetics of the Frank-Kasper σ and A15 phases. However, unlike σ and A15, HCP nucleates directly from a supercooled liquid or soft solid without proceeding through an intermediate quasicrystal. Self-consistent field theory calculations indicate the stability of HCP is intimately tied to small amounts of molar mass dispersity (Đ); for example, an HCP-forming F4DF sample with fA = 0.27 has an experimentally measured Đ = 1.04. These insights challenge the conventional wisdom that pure HCP is difficult to access in linear block copolymer melts without the use of blending or other complex processing techniques.
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11
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Enlarged Stable Phase Region of Hybrid Lamella-sphere Phase Enabled by A1B1A2(B2)m Branched Tetrablock Copolymer. CHINESE JOURNAL OF POLYMER SCIENCE 2021. [DOI: 10.1007/s10118-021-2554-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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12
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Frank-Kasper Phases Self-Assembled from a Linear A 1B 1A 2B 2 Tetrablock Copolymer. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:5642-5650. [PMID: 33929198 DOI: 10.1021/acs.langmuir.1c00503] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The Frank-Kasper (FK) phases self-assembled from block copolymer systems have attracted abiding interest. In this work, the formation mechanism of the complex FK phases from the self-assembly of simple A1B1A2B2 tetrablock copolymers is investigated using self-consistent field theory (SCFT). For a typical set of parameter spaces, we utilize SCFT to construct a number of phase diagrams. In these phase diagrams, the FK phases exhibit a notable stability region. The stable region of the FK phases reveals that the distribution of A1 and A2 blocks can be precisely regulated by tuning the ratio of the A1/A2 block, wherein the long A1 blocks can aggregate within the "core" while the short A2 blocks can form the "shell" of a spherical domain in the FK phases, respectively, to accommodate the sizes and shapes of the spherical domains in the complex spherical packing phases. Besides, we also demonstrate that the existence of the B2 block plays a crucial factor to stabilize the FK phases.
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Scattering Function and Spinodal Transition of Linear and Nonlinear Block Copolymers Based on a Unified Molecular Model. CHINESE JOURNAL OF POLYMER SCIENCE 2021. [DOI: 10.1007/s10118-021-2544-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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14
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Simplicity in mean-field phase behavior of two-component miktoarm star copolymers. J Chem Phys 2021; 154:014903. [PMID: 33412874 DOI: 10.1063/5.0037979] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
Using self-consistent field theory, we systematically explore the microphase separation in the class of two-component miktoarm star copolymers containing a single conjunction point between different blocks by considering an extended list of candidate microphases. We plot mean-field phase diagrams in the plane of segregation strength and composition for an array of representative star copolymers. Three principal phase diagram topologies, dictated by different phase stabilities, are exposed, displaying a hierarchy in complexity by increasing the molecular asymmetry. Our investigation indicates that the phase diagram topology depends on the ratios of arm numbers and Kuhn segment lengths, which highlights the role of the coordination number ratio between different polymers at the domain interface. These findings reveal the simplicity of the general phase behavior and suggest a complete list of stable microphases for the entire class, which provide useful insight into studying copolymers with more complicated architectures and conformational properties.
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Impact of Architecture of Symmetric Block Copolymers on the Stability of a Dislocation Defect. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c01654] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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Abstract
Molecular architecture plays a key role in the self-assembly of block copolymers, but few studies have systematically examined the influence of chain connectivity on tetrahedrally close-packed (TCP) sphere phases. Here, we report a versatile material platform comprising two blocks with substantial conformational asymmetry, A = poly(trifluoroethyl acrylate) and B = poly(dodecyl acrylate), and use it to compare the phase behavior of AB diblocks, ABA triblocks, and (AB)n radial star copolymers with n = 3 or 4. Each architecture forms TCP sphere phases at minority A block compositions (fA < 0.5), namely, σ and A15, but with differences in the location of order-order phase boundaries that are not anticipated by mean-field self-consistent field theory simulations. These results expand the palette of polymer architectures that readily self-assemble into complex TCP structures and suggest important design considerations when targeting specific phases of interest.
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Accelerated Pseudo-Spectral Method of Self-Consistent Field Theory via Crystallographic Fast Fourier Transform. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01974] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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Emergence and Stability of Janus-Like Superstructures in an ABCA Linear Tetrablock Copolymer. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01328] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
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Synergistic Effect of Stretched Bridging Block and Released Packing Frustration Leads to Exotic Nanostructures. ACS Macro Lett 2020; 9:980-984. [PMID: 35648611 DOI: 10.1021/acsmacrolett.0c00313] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
The self-assembly of amphiphilic macromolecules into various mesocrystals has attracted abiding interest. Although many interesting mesocrystals have been achieved, mesocrystals of a low coordination number (CN) such as simple cubic are rarely reported. Here we purposely design an AB-type multiblock copolymer to target exotic spherical phases of low CNs. Self-consistent field theory reveals that two sophisticated mechanisms are realized in the copolymer, that is, stretched bridging block and released packing frustration, synergistically leading to the formation of three spherical phases with extremely low CNs, including the simple cubic spheres (CN = 6), the cubic diamond spheres (CN = 4), and normally aligned hexagonal-packing spheres (6 < CN < 8) in a considerable parameter region. Moreover, we demonstrate that these exotic phases are hard to be stabilized by either of the two mechanisms individually.
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Regulate the Stability of Gyroids of ABC-Type Multiblock Copolymers by Controlling the Packing Frustration. ACS Macro Lett 2020; 9:278-283. [PMID: 35638691 DOI: 10.1021/acsmacrolett.9b00966] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
We propose to regulate the stability of gyroids of ABC-type multiblock copolymers by controlling the packing frustration of majority-component B-blocks. Accordingly, we investigate the self-assembly behaviors of the BABCB linear terpolymer with a variable length ratio τ of the middle B-block relative to the total B-blocks using self-consistent field theory. It is observed that the gyroid region exhibits a maximal width with respect to τ, which is attributed by the nonmonotonical change of the packing frustration of three B-blocks in the morphology of discrete domains, for example, cylinders. Then we further purposely design another ABC-type copolymer composed of an ABC linear triblock tethered by another B-block at the middle of the B-block. In contrast, the packing frustration of B-blocks of the second terpolymer drops down continuously as the middle B-block shortens, thus, expanding the stable regions of cylinders and spheres while contracting those of lamella and gyroid.
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Tunable helical structures formed by ABC triblock copolymers under cylindrical confinement. Phys Chem Chem Phys 2019; 21:26333-26341. [PMID: 31782439 DOI: 10.1039/c9cp04978a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Block copolymers confined in nanopores provide unique achiral systems for the formation of helical structures. With AB diblock copolymers, stable single and double helical structures are observed. Aiming to obtain more different helical structures, we replace the AB diblock copolymer with linear ABC triblock copolymers. We speculate that a core-shell superstructure is formed within the nanopore, which is composed of a C-core cylinder wrapped by B-helices within the A-shell. Accordingly, the pore surface is set to be most attractive to the majority A-block and a typical set of interaction parameters is chosen as χACN ≪ χABN = χBCN = 80 to generate the frustrated interfaces. Furthermore, the volume fraction of B-block is fixed as fB = 0.1 to form helical cylinders. A number of helical structures with strands ranging from 1 to 5 are predicted by self-consistent field theory, and in general, the number of strands decreases as the volume fraction of C-block fC increases in a given nanopore. More surprisingly, the variation of helical strand in the confined system has an opposite trend to that in the bulk, which mainly results from the constraint of the cylindrical confinement on the change of the curvature between the outer A-layer and the inner B/C-superdomain. Our work demonstrates a facile way to fabricate different helical superstructures.
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Abstract
Well-defined miktoarm (polystyrene)4-(polylactic acid)4 ((PS)4-(PLA)4) block copolymers were synthesized and their phase behaviors were compared with linear PS-b-PLA block copolymers, in which the miktoarm architecture enhanced the phase segregation.
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