Landau theory of the orthorhombic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mi>d</mml:mi><mml:mi>d</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:math>phase

Ranjan, Amit; Morse, David C.

doi:10.1103/physreve.74.011803

Cited by 37 publications

(47 citation statements)

References 8 publications

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“…The gyroid (G) phase continues to dominate the complex phase channel, and the newly discovered Fddd (O 70 ) phase remains stable extending down to the mean-field critical point just as it does for diblock copolymer melts. 51 In the diblock copolymer system, the predicted O 70 regions are rather small and thus prone to the effect of fluctuations. 52 However, O 70 does evidently survive fluctuations given the fact that it has been identified by experiments in diblock copolymer melts, 13−15 although this may have been aided by conformational asymmetry.…”

Section: ■ Discussionmentioning

confidence: 99%

Effect of Architecture on the Phase Behavior of AB-Type Block Copolymer Melts

2012

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Equilibrium phase diagrams are calculated for a selection of two-component block copolymer architectures using self-consistent field theory (SCFT). The topology of the phase diagrams is relatively unaffected by differences in architecture, but the phase boundaries shift significantly in composition. The shifts are consistent with the decomposition of architectures into constituent units as proposed by Gido and co-workers, but there are significant quantitative deviations from this principle in the intermediatesegregation regime. Although the complex phase windows continue to be dominated by the gyroid (G) phase, the regions of the newly discovered Fddd (O 70 ) phase become appreciable for certain architectures and the perforated-lamellar (PL) phase becomes stable when the complex phase windows shift toward high compositional asymmetry. ■ INTRODUCTIONThe phase behavior of AB diblock copolymer melts has been well studied experimentally, 1 and self-consistent field theory (SCFT) 2 has been remarkably successful in explaining the equilibrium phase behavior.3−5 Vavasour and Whitmore 6 produced the first SCFT phase diagram, but it was limited to the classical lamellar (L), cylindrical (C), and bcc spherical (S) phases. Matsen and Schick 7 then extended it to include complex phases, predicting the gyroid (G) phase to be more stable than the perforated-lamellar (PL) phase as confirmed later by experiment.8 In a subsequent calculation by Matsen and Bates, 9 a narrow closed-packed spherical (S cp ) phase was predicted along the order−disorder transition (ODT), which has since been associated with a region of densely packed spherical micelles. 10,11 Most recently, the Fddd (O 70 ) phase was predicted by Tyler and Morse 12 and later observed in experiment.13−15 Figure 1 shows the current up-to-date SCFT phase diagram for AB diblock copolymer melts.The AB diblock is just the simplest block copolymer among an unlimited variety of different architectures. It is natural to ask how the phase behavior changes for other architectures, but this has proven to be a daunting task as soon as a third chemically distinct component is involved; in fact, even the simple linear ABC triblock exhibits so many morphologies that we might never catalogue them all. 16 Nevertheless, the phase behavior appears manageable for those architectures comprised of just two segment types. Among this class of architectures, the ABA triblock is the next most studied block copolymer, 17 mainly because of its commercial use as a thermoplastic elastomer. There were also a considerable number of early experiments on star block copolymers, formed by joining three or more diblocks together by their ends. The general conclusion from these studies is that all AB-type architectures have similar phase diagrams, but with significantly shifted phase boundaries. The reason for the similarity is fairly well understood. Although mechanical properties are completely altered by snipping the middle B blocks of an ABA triblock melt in half, the free energy is re...

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Section: ■ Discussionmentioning

confidence: 99%

Effect of Architecture on the Phase Behavior of AB-Type Block Copolymer Melts

2012

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“…In view of the centrosymmetry of these phases, we set l À;G m n k ¼ l À;Gmnk at the same time. In Landau theory of block copolymer [20,21], the reciprocal vectors of FCC phase are {1 1 1} (including ð1 1 1Þ; ð1 1 1Þ; ð1 11Þ; ð1 1 1Þ), whereas from our experience, the final structure would not be the FCC phase if only the vectors {1 1 1} are used as initial ones. So we use crystal structure factor of Fm 3m [22] to get the initial reciprocal vectors, as shown in Table 1.…”

Section: The Strategy To Estimating Good Initial Valuesmentioning

confidence: 96%

“…Leibler [19] has given these reciprocal lattice vectors of lamellar, hexagonal and body-centered cubic spheres (BCC) phases. The reciprocal lattice vectors of gyroid and face-centered cubic spheres (FCC) phases were given by Erukhimovich [20] and Fddd phase has been studied by Ranjan and Morse [21]. An alterative approach is directly using the crystal structure factor to obtain the reciprocal lattice vectors.…”

Section: The Strategy To Estimating Good Initial Valuesmentioning

confidence: 99%

“…Fortunately, the microscopic equilibrium state structures of the diblock copolymer melt demonstrate certain crystal symmetry. Based on the fact that the initial reciprocal lattice vectors can be obtained from Landau theory of block copolymers [19][20][21] or the crystal structure factor table [22]. The Landau theory of block copolymer is applied to weakly-segregated melts, and gives reciprocal lattice vectors that belong to different stable phases.…”

Section: The Strategy To Estimating Good Initial Valuesmentioning

confidence: 99%

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Spectral method for exploring patterns of diblock copolymers

Jiang

Huang

Zhang

2010

Journal of Computational Physics

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“…Furthermore, the structure of metal nanofoam can be tuned by variation of the morphology of the starting block copolymer. Besides the gyroid phase, block copolymer morphologies such as plumber's nightmare 39 or the orthorhombic Fddd network [40][41][42] are interesting candidates for the metal nanofoam preparation. The field of metal nanofoams is still poorly examined and it is expected to bring the exciting discoveries in future.…”

Section: Discussionmentioning

confidence: 99%

Gyroid Nickel Nanostructures from Diblock Copolymer Supramolecules

Vuković

Punzhin

Voet

et al. 2014

JoVE

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Nanoporous metal foams possess a unique combination of properties -they are catalytically active, thermally and electrically conductive, and furthermore, have high porosity, high surface-to-volume and strength-to-weight ratio. Unfortunately, common approaches for preparation of metallic nanostructures render materials with highly disordered architecture, which might have an adverse effect on their mechanical properties. Block copolymers have the ability to self-assemble into ordered nanostructures and can be applied as templates for the preparation of wellordered metal nanofoams. Here we describe the application of a block copolymer-based supramolecular complex -polystyrene-block-poly(4-vinylpyridine)(pentadecylphenol) PS-b-P4VP(PDP) -as a precursor for well-ordered nickel nanofoam. The supramolecular complexes exhibit a phase behavior similar to conventional block copolymers and can self-assemble into the bicontinuous gyroid morphology with two PS networks placed in a P4VP(PDP) matrix. PDP can be dissolved in ethanol leading to the formation of a porous structure that can be backfilled with metal. Using electroless plating technique, nickel can be inserted into the template's channels. Finally, the remaining polymer can be removed via pyrolysis from the polymer/inorganic nanohybrid resulting in nanoporous nickel foam with inverse gyroid morphology. Video LinkThe video component of this article can be found at

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Landau theory of the orthorhombicFdddphase

Cited by 37 publications

References 8 publications

Effect of Architecture on the Phase Behavior of AB-Type Block Copolymer Melts

Effect of Architecture on the Phase Behavior of AB-Type Block Copolymer Melts

Spectral method for exploring patterns of diblock copolymers

Gyroid Nickel Nanostructures from Diblock Copolymer Supramolecules

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