Orthorhombic <i>Fddd</i> Network in Diblock Copolymer Melts

Takenaka, Mikihito; Wakada, Tsutomu; Akasaka, Satoshi; Nishitsuji, Shotaro; Saijo, Kenji; Shimizu, Hirofumi; Kim, Myung Im; Hasegawa, Hirokazu

doi:10.1021/ma070739u

Cited by 171 publications

(196 citation statements)

References 17 publications

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“…I, experiments in triblock 39 and diblock 40 copolymers as well as theoretical SCFT calculations 34 have shown the occurrence of an orthorhombic Fddd phase similar to that of the fco helices I region discussed here; although for diblock copolymers, it is predicted to be stable only in a very small domain of the phase diagram. 34 The possibility of a stable tetragonal I4 1 /amd phase like that predicted in the helices II region has also been suggested.…”

Section: B Discussion Of the Phase Diagramsupporting

confidence: 58%

“…Actually, except for the lamellar, one-dimensionally modulated phase that is always superseded by others, the phase diagram reported here contains all the phases commonly predicted in block copolymer melts 25,26,38 including tubular and bicontinuous structures such as the gyroid and the double diamond. In addition, we have obtained an orthorhombic phase which was found experimentally 39,40 and predicted 34 much later than the aforementioned ones, as well as a tetragonal phase which, to our knowledge, has not been predicted theoretically before. In both of them, one species forms a rather loose lattice with wide channels and the other is preferentially located inside these channels, where it forms helices of alternating chirality.…”

Section: Introductionsupporting

confidence: 51%

“…Choosing a specific realization of this model with, admittedly, no insight other than the fact that its ability to form microphases had already been established in a former study 20 uncovered all the phases commonly predicted and observed in block copolymer melts, namely, the primitive bcc Im3m, the equilateral triangular or hexagonal, and the gyroid I4 1 32 (double gyroid Ia3d if the two species are regarded as equivalent), except for the lamellar phase, which was always superseded by other, more stable structures. In addition, we obtained the diamond Fd3m phase (double diamond Pn3m for equivalent species) and two noncubic phases, namely, an orthorhombic Fddd phase which has been predicted 34 and observed in diblock 40 and triblock 39 copolymers not long ago, as well as a tetragonal I4 1 /amd phase whose existence has been conjectured, 64 but to our knowledge has not been reported so far in block copolymers, either theoretically or experimentally. In the latter phases, neither species can be considered localized, since each of them percolates in the voids left available by the other.…”

Section: A Overview Of the Resultsmentioning

confidence: 78%

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An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures

Pini

Parola

Reatto³

2015

The Journal of Chemical Physics

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Phase behavior and structure of star-polymer-colloid mixtures J. Chem. Phys. 116, 9518 (2002) The formation of microphases in systems of particles interacting by repulsive, bounded potentials is studied by means of density-functional theory (DFT) using a simple, mean-field-like form for the free energy which has already been proven accurate for this class of soft interactions. In an effort not to constrain the configurations available to the system, we do not make any assumption on the functional form of the density profile ρ(r), save for its being periodic. We sample ρ(r) at a large number of points in the unit cell and minimize the free energy with respect to both the values assumed by ρ(r) at these points and the lattice vectors which identify the Bravais lattice. After checking the accuracy of the method by applying it to a one-component generalized exponential model (GEM) fluid with pair potential ϵ exp[−(r/R) 4 ], for which extensive DFT and simulation results are already available, we turn to a binary mixture of Gaussian particles which some time ago was shown to support microphase formation [A. J. Archer, C. N. Likos, and R. Evans, J. Phys.: Condens. Matter 16, L297 (2004)], but has not yet been investigated in detail. The phase diagram which we obtain, that supersedes the tentative one proposed by us in a former study [M. Carta, D. Pini, A. Parola, and L. Reatto, J. Phys.: Condens. Matter 24, 284106 (2012)], displays cluster, tubular, and bicontinuous phases similar to those observed in block copolymers or oil/water/surfactant mixtures. Remarkably, bicontinuous phases occupy a rather large portion of the phase diagram. We also find two non-cubic phases, in both of which one species is preferentially located inside the channels left available by the other, forming helices of alternating chirality. The features of cluster formation in this mixture and in GEM potentials are also compared. C 2015 AIP Publishing LLC. [http://dx

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Section: B Discussion Of the Phase Diagramsupporting

confidence: 58%

Section: Introductionsupporting

confidence: 51%

Section: A Overview Of the Resultsmentioning

confidence: 78%

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An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures

Pini

Parola

Reatto³

2015

The Journal of Chemical Physics

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“…38 Consequently, for pure block copolymers only 3-fold networks have been predicted [39][40][41] or observed. 5,[42][43][44] Chain stretching in a 4-fold or 6-fold node can be reduced by the presence of a second component that occupies the center of the node. For example, adding homopolymer to the minority phase of a diblock copolymer is predicted to stabilize the double diamond morphology.…”

Section: Discussionmentioning

confidence: 99%

A Re-Evaluation of the Morphology of a Bicontinuous Block Copolymer−Ceramic Material

et al. 2007

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The structures of a poly(isoprene-block-ethylene oxide) (PI-b-PEO) block copolymer-directed aluminosilicate mesostructure and the resulting ceramic material obtained from calcination were studied via smallangle X-ray scattering (SAXS) and transmission electron microscopy (TEM). The PI minority phase (volume fraction 0.36) formed a continuous network of channels, previously reported 1,2 to be consistent with the plumber's nightmare 3 morphology. The solvent casting process used to form the material caused it to shrink uniaxially by ∼30%, deforming the network structure within it. Calculated structure factors for constant-curvature and constantthickness models of a distorted double gyroid structure are consistent with SAXS from the material, while [100] and [111] projections of the distorted double gyroid structure match the TEM data. Because the structural data from the material is most consistent with a distorted version of the double gyroid morphology, the previous assignment of the plumber's nightmare morphology must be reconsidered. Approaches for structural assignment are also discussed.

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“…1,2 By adjusting the relative sizes of the two blocks 1,3 in pure diblock copolymer (DBC) melts, different morphologies of specific geometry can be rationally obtained; i.e., spheres with bcc packing (S), cylinders hexagonally packed (C), the lamellar phase (L), the bicontinuous gyroid phase 3,4 (G), and the recently-observed co-continuous O 70 phase. 5,6 Since nanoparticles can be designed to have preference for one of the copolymer blocks, bicontinuous phases can be used as templates for ordering nanoparticles. These nanocomposites can find new attractive applications, as it can be envisioned if the particles had high electrical conductivity or catalytic activity.…”

Section: Introductionmentioning

confidence: 99%

Final Report: Grant DE-FG02-05ER15682. Simulation of Complex Microphase Formation in Pure and Nanoparticle-filled Diblock Copolymers

Escobedo¹

2009

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SummaryThe goal of this project was to use molecular simulation to quantify the impact of additives on the onset and structure of bicontinuous phases in linear diblock copolymers (DBC). The focus was on understanding how additives with selective affinity for a given block will distribute and perturb the structure of complex bicontinuous phases (like gyroid, double diamond, and plumbers nightmare whose minority component block forms two interweaving 3D networks) in DBCs; it was hypothesized that a suitable choice of additive type, size, affinity, and concentration may suppress or stabilize a particular bicontinuous phase. The ultimate goal in this line of investigation is to elucidate the rational design of the optimal additive for which the composition range of stability of a particular bicontinuous phase is maximized. Ours are the first published simulation studies to report on the formation of the gyroid phase in DBC melts and of other bicontinuous phases in DBC-modified by homopolymer.The following tasks were carried out: (i) simulation of bicontinuous phases of pure DBCs via both on-lattice Monte Carlo simulations and continuum-space Monte Carlo and molecular dynamics simulations, (ii) determination of the effect of selective additives (homopolymer) of different sizes on such bicontinuous phases, and (iii) development of novel Monte Carlo methods to map out reliable phase diagrams and improve ergodic sampling; in particular, optimized expanded-ensemble techniques for measuring free-energies and for chemical potential equilibration.

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Orthorhombic Fddd Network in Diblock Copolymer Melts

Cited by 171 publications

References 17 publications

An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures

An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures

A Re-Evaluation of the Morphology of a Bicontinuous Block Copolymer−Ceramic Material

Final Report: Grant DE-FG02-05ER15682. Simulation of Complex Microphase Formation in Pure and Nanoparticle-filled Diblock Copolymers

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