Fluctuations, Order, and Disorder in Short Diblock Copolymers

Lee, Sangwoo; Gillard, Timothy M.; Bates, Frank S.

doi:10.1002/aic.14023

Cited by 95 publications

(227 citation statements)

References 62 publications

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“…1A), arguably the simplest material to exhibit quasicrystalline symmetry. This finding builds on our recent work detailing the formation of the Frank-Kasper σ phase, a large unit cell periodic approximant of the DDQC in a related IL diblock copolymer specimen (11)(12)(13).…”

supporting

confidence: 71%

“…The SCFT calculations implicate asymmetry in the block statistical segment lengths as a key parameter, predicting that a minimal degree of asymmetry is required (b A > 1.5b B for AB diblocks) for a stable σ phase window to occur at f A < 1/2. This prediction has yet to be tested by systematic experiments but is in qualitative agreement with the modest statistical segment length asymmetry of the IL system (b L /b I ∼ 1.2) (12).…”

Section: Discussionmentioning

confidence: 57%

“…The experiments discussed in this article document the temperaturedependent structure and dynamics of a poly(1,4-isoprene-b-DL-lactide) diblock copolymer designated IL-5.1 synthesized by an established combination of anionic polymerization and ring-opening polymerization (12,15). IL-5.1 has a number-average molecular weight M n = 4,600 g/mol (dispersity M w /M n = 1.06) divided between the polyisoprene (PI; 3,540 g/mol) and polylactide (PLA; 1,070 g/mol) blocks, corresponding to a composition of 18% by volume PLA based on published densities (16,17).…”

Section: Results and Analysismentioning

confidence: 99%

“…It is important to note that the micelle-like particles do not emerge at the order-disorder transition temperature from a homogenous disordered phase as anticipated by mean-field theory (10,14). As a consequence of relatively long-lived thermally driven composition fluctuations the disordered state just above T ODT contains a dense array of soft but segregated micelles characterized by a distribution of shapes and sizes with a liquid-like arrangement in space (12). The ordered BCC phase, first predicted by Leibler, is widely accepted as the equilibrium morphology for asymmetric diblock copolymer melts just below the ODT (14).…”

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confidence: 99%

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Dodecagonal quasicrystalline order in a diblock copolymer melt

Gillard

Lee

Bates

2016

Proc. Natl. Acad. Sci. U.S.A.

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We report the discovery of a dodecagonal quasicrystalline state (DDQC) in a sphere (micelle) forming poly(isoprene-b-lactide) (IL) diblock copolymer melt, investigated as a function of time following rapid cooling from above the order-disorder transition temperature (T ODT = 66°C) using small-angle X-ray scattering (SAXS) measurements. Between T ODT and the order-order transition temperature T OOT = 42°C, an equilibrium body-centered cubic (BCC) structure forms, whereas below T OOT the Frank-Kasper σ phase is the stable morphology. At T < 40°C the supercooled disordered state evolves into a metastable DDQC that transforms with time to the σ phase. The times required to form the DDQC and σ phases are strongly temperature dependent, requiring several hours and about 2 d at 35°C and more than 10 and 200 d at 25°C, respectively. Remarkably, the DDQC forms only from the supercooled disordered state, whereas the σ phase grows directly when the BCC phase is cooled below T OOT and vice versa upon heating. A transition in the rapidly supercooled disordered material, from an ergodic liquid-like arrangement of particles to a nonergodic soft glassy-like solid, occurs below ∼40°C, coincident with the temperature associated with the formation of the DDQC. We speculate that this stiffening reflects the development of particle clusters with local tetrahedral or icosahedral symmetry that seed growth of the temporally transient DDQC state. This work highlights extraordinary opportunities to uncover the origins and stability of aperiodic order in condensed matter using model block polymers.quasicrystals | Frank-Kasper phases | block polymers T he discovery of aperiodic order, today referred to as quasicrystalline order, in rapidly cooled Al-Mn alloys by Shechtman and coworkers in 1984 heralded a paradigm shift in the understanding of what constitutes long-range order in matter (1, 2). More recently, quasicrystalline order has been found in an expanding variety of soft materials including self-assembling wedge-shaped dendrimers, mixtures of ligand coated nanoparticles, concentrated solutions of surfactant and block polymer micelles, multicomponent polymer blends containing ABC-type miktoarm star polymers, and an ABA′C-type linear multiblock polymer (3-8). The underlying principles that govern the formation of quasicrystals in soft materials remain largely unresolved.Block polymers are uniquely tunable self-assembling soft materials in which the nanoscale morphology, characteristic length scale, chemical and physical properties, and dynamics can be precisely controlled through the judicious choice of block repeat unit chemistries, block molecular weights, and molecular architecture (9, 10). Such exquisite control over structure, and the associated dynamics, makes block polymers ideal model materials for fundamental inquiries into the formation and stability of soft quasicrystals. In this article, we report the discovery of a long-lived metastable dodecagonal quasicrystalline phase (DDQC) in a (nominally) single-component poly(1,4-is...

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supporting

confidence: 71%

Section: Discussionmentioning

confidence: 57%

Section: Results and Analysismentioning

confidence: 99%

mentioning

confidence: 99%

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Dodecagonal quasicrystalline order in a diblock copolymer melt

Gillard

Lee

Bates

2016

Proc. Natl. Acad. Sci. U.S.A.

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188

264

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“…In the absence of solvent, and under conditions that favor segregation of the two blocks, these soft mesomorphic particles produce ordered structures with a lattice size that scales with the size of the particles, controlled by the overall length (degree of polymerization or molecular weight) of the constituent polymers (22). In this article we offer an analysis and interpretation of experimental data obtained from a short diblock copolymer reported earlier to form a FrankKasper σ-phase (23,24). The compositionally asymmetric poly (isoprene-b-lactide) (PI-PLA; IL) diblock copolymer considered in this work (22% PLA by volume; Fig.…”

mentioning

confidence: 99%

Sphericity and symmetry breaking in the formation of Frank–Kasper phases from one component materials

Lee

Leighton

Bates

2014

Proc. Natl. Acad. Sci. U.S.A.

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Frank-Kasper phases are tetrahedrally packed structures occurring in numerous materials, from elements to intermetallics to selfassembled soft materials. They exhibit complex manifolds of Wigner-Seitz cells with many-faceted polyhedra, forming an important bridge between the simple close-packed periodic and quasiperiodic crystals. The recent discovery of the Frank-Kasper σ-phase in diblock and tetrablock polymers stimulated the experiments reported here on a poly(isoprene-b-lactide) diblock copolymer melt. Analysis of small-angle X-ray scattering and mechanical spectroscopy exposes an undiscovered competition between the tendency to form self-assembled particles with spherical symmetry, and the necessity to fill space at uniform density within the framework imposed by the lattice. We thus deduce surprising analogies between the symmetry breaking at the body-centered cubic phase to σ-phase transition in diblock copolymers, mediated by exchange of mass, and the symmetry breaking in certain metals and alloys (such as the elements Mn and U), mediated by exchange of charge. Similar connections are made between the role of sphericity in real space for polymer systems, and the role of sphericity in reciprocal space for metallic systems such as intermetallic compounds and alloys. These findings establish new links between disparate materials classes, provide opportunities to improve the understanding of complex crystallization by building on synergies between hard and soft matter, and, perhaps most significantly, challenge the view that the symmetry breaking required to form reduced symmetry structures (possibly even quasiperiodic crystals) requires particles with multiple predetermined shapes and/or sizes.symmetry breaking | sphericity | Frank-Kasper phases | block polymers T he discovery of materials with aperiodic order, often referred to as "quasicrystals," 30 years ago (1, 2) heralded new and promising vistas for designing materials endowed with unique properties. In the 1950s Frank and Kasper (3, 4) recognized complex tetrahedral atomic-and molecular-packing geometries that bridge the familiar close-packed crystals [e.g., face-centered cubic (FCC), hexagonally close-packed (HCP), and body-centered cubic (BCC) structures] characterized by periodic order, and quasiperiodic crystals (QCs) that extend crystallography beyond the 230 space groups relevant to periodic crystals (5, 6). The scientific literature is replete with examples of Frank-Kasper phases in hard materials, particularly in the area of intermetallics (7-9), but also in a few complex elemental crystals, including manganese (10, 11) and uranium (12). Recently, this class of crystalline order has cropped up in a host of soft materials, including dendrimers (13), surfactant solutions (14), and block polymers (15, 16), often in close proximity to QC phases (17)(18)(19). To the best of our knowledge the principles underlying the formation of Frank-Kasper phases across both categories of materials have not been established, presenting enticing challenges to sc...

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Polymerization Induced Microphase Separation for the Fabrication of Nanostructured Materials

2023

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Polymerization induced microphase separation (PIMS) is a strategy used to develop unique nanostructures with highly useful morphologies through the microphase separation of emergent block copolymers during polymerization. In this process, nanostructures are formed with at least two chemically independent domains, where at least one domain is composed of a robust crosslinked polymer. Crucially, this synthetically simple method is readily used to develop nanostructured materials with the highly coveted co‐continuous morphology, which can also be converted into mesoporous materials by selective etching of one domain. As PIMS exploits a block copolymer microphase separation mechanism, the size of each domain can be tightly controlled by modifying the size of block copolymer precursors, thus providing unparalleled control over nanostructure and resultant mesopore sizes. Since its inception 11 years ago, PIMS has been used to develop a vast inventory of advanced materials for an extensive range of applications including biomedical devices, ion exchange membranes, lithium‐ion batteries, catalysis, 3D printing, and fluorescence‐based sensors, among many others. In this review, we provide a comprehensive overview of the PIMS process, summarize latest developments in PIMS chemistry, and discuss its utility in a wide variety of relevant applications.

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Fluctuations, Order, and Disorder in Short Diblock Copolymers

Cited by 95 publications

References 62 publications

Dodecagonal quasicrystalline order in a diblock copolymer melt

Dodecagonal quasicrystalline order in a diblock copolymer melt

Sphericity and symmetry breaking in the formation of Frank–Kasper phases from one component materials

Polymerization Induced Microphase Separation for the Fabrication of Nanostructured Materials

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