Morphology of model three-component three-arm star-shaped copolymers

Shigeru, Okamoto; Hasegawa, Hirokazu; Hashimoto, Takeji; Fujimoto, Teruo; Zhang, Hongmin; Kazama, Tomohiko; Takano, Atsushi; Isono, Yoshinobu

doi:10.1016/s0032-3861(97)00089-x

Cited by 88 publications

(83 citation statements)

References 18 publications

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“…1(b)]. Both structures have been previously hypothesized for ABC star triblock copolymers [16], although they have yet to be obtained experimentally.…”

Section: (Received 30 March 2000)mentioning

confidence: 79%

Discovering New Ordered Phases of Block Copolymers

2000

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We propose a new and general method for discovering novel ordered phases of block copolymer melts. The method involves minimizing a free energy functional in an arbitrary unit cell with respect to the composition profile and the dimensions of the unit cell, without any prior assumption of the microphase symmetry. Varying the initial conditions allows to search for different stable and metastable structures. Application of this method to ABC star and linear triblock copolymers using an approximate free energy reveals new morphologies not yet observed in experiment. PACS numbers: 61.25.Hq, 61.41.+e, 64.75.+g Block copolymers serve as a fertile source of "soft materials" exhibiting fascinating periodically ordered microphases such as the "knitting pattern" (KP) [1] and the core-shell bicontinuous gyroid phase [2]. The spontaneous microphase ordering of block copolymers is driven by repulsive interactions acting between distinct blocks, delicately balanced by the configurational entropy which reflects the elasticity of the polymer chain. The chemical bonds connecting different types of blocks keep the segregation on a molecular scale leading to domains of the order of 10-100 nm. The morphology formed in the ordered state depends on composition, the interaction energies between distinct blocks, as well as the particular molecular architecture. These facts are responsible for the rich and complex phase diagrams characterizing block copolymer melts [3].Different levels of mean field theory have proven to capture the essential features characterizing microphase ordering of block copolymers [3,4]. Among those, the most accurate calculation requires a full self-consistent field (SCF) approach [5]. However, in spite of the theoretical successes, novel morphologies have almost always been discovered first in experiments. The reason is that theoretical approaches are all based upon calculating and comparing free energies of predetermined symmetries. This limitation is especially accentuated when exploring the large parameter space and various molecular designs of multiblock copolymers. On the other hand, Monte Carlo simulation methods, though free of assumptions about the symmetry of the phases, are computationally expensive and limited by finite size effects [6,7].In this paper we propose an alternative approach for studying the morphology of multiblock copolymers without the need to assume the symmetry of the ordered phase. Drolet and Fredrickson [8] have recently proposed a numerical implementation of SCF theory that, similarly, does not require the assumption of the microphase symmetry. Unlike Matsen and Schick [5] they search for low free energy solutions by solving the self-consistent equations in real space. In contrast to their optimization procedure, our approach involves minimizing an approximate free energy functional in an arbitrary unit cell, with respect to both the density profile and the dimensions of the unit cell. Obviously, the same idea can be implemented using a SCF free energy; however, consideratio...

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“…1(b)]. Both structures have been previously hypothesized for ABC star triblock copolymers [16], although they have yet to be obtained experimentally.…”

Section: (Received 30 March 2000)mentioning

confidence: 79%

Discovering New Ordered Phases of Block Copolymers

2000

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“…Experimental or simulated realisations of polycontinuous geometries are being explored in a few distinct systems with important differences: Hyde et al have proposed tricontinuous surfaces as a natural candidate for the self-assembly of star-shaped molecules with three mutually immiscible arms in a radial arrangement, 29 such as mikto-arm star copolymers [34][35][36] and star polyphiles. 37 By microphase separation, the three immiscible components self-assemble into three distinct nanodomains.…”

Section: 3233mentioning

confidence: 99%

“…of tricontinuous structures, in which each of the domains forms a single connected network. 34,41 Importantly, in these instances, the existence of three distinct compartments or domains directly reflects the molecular architecture with three immiscible parts. While the three domains may be geometrically the same, each of them represents a chemically distinct molecular component.…”

Section: 3233mentioning

confidence: 99%

Polycontinuous geometries for inverse lipid phases with more than two aqueous network domains

et al. 2013

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Inverse bicontinuous cubic phases with two aqueous network domains separated by a smooth bilayer are firmly established as equilibrium phases in lipid/water systems. The purpose of this article is to highlight the generalisations of these bicontinuous geometries to polycontinuous geometries, which could be realised as lipid mesophases with three or more network-like aqueous domains separated by a branched bilayer. An analysis of structural homogeneity in terms of bilayer width variations reveals that ordered polycontinuous geometries are likely candidates for lipid mesophase structures, with similar chain packing characteristics to the inverse micellar phases (that once were believed not to exist due to high packing frustration). The average molecular shape required by global geometry to form these multi-network phases is quantified by the surfactant shape parameter, v/(al); we find that it adopts values close to those of the known lipid phases. We specifically analyse the 3etc(187 193) structure of hexagonal symmetry P6 3 /mcm with three aqueous domains, the 3dia(24 220) structure of cubic symmetry I 43d composed of three distorted diamond networks, the cubic chiral 4srs(24 208) with cubic symmetry P4 2 32 and the achiral 4srs(5 133) structure of symmetry P4 2 /nbc, each consisting of four intergrown undistorted copies of the srs net (the same net as in the Q G II gyroid phase). Structural homogeneity is analysed by a medial surface approach assuming that the headgroup interfaces are constant mean curvature surfaces. To facilitate future experimental identification, we provide simulated SAXS scattering patterns that, for the 4srs(24 208) and 3dia(24 220) structures, bear remarkable similarity to those of bicontinuous Q G II -gyroid and Q D II -diamond phases, with comparable lattice parameters and only a single peak that cannot be indexed to the wellestablished structures. While polycontinuous lipid phases have, to date, not been reported, the likelihood of their formation is further indicated by the reported observation of a solid tricontinuous mesoporous silicate structure, termed IBN-9, which formed in the presence of surfactants [Han et al

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“…Our interest in polyphilic systems was piqued by early studies of complex copolymer molecules, which suggested very complex mesostructures, possibly with three interwoven 3D domains. 7 Copolymer science has now moved beyond just two immiscible domains: so-called 'mikto-arm' copolymers have been investigated, containing three and four mutually immiscible domains, joined to a common central node, forming a star architecture. The problem of self-assembly in these systems is more challenging than that of two-phase systems, since all three (or more) moieties share a common molecular centre from which the immiscible moieties radiate.…”

Section: 2mentioning

confidence: 99%

Tricontinuous mesophases of balanced three-arm ‘star polyphiles’

Hyde

Campo

Oguey³

2009

Soft Matter

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We construct simple models to compare ordered tricontinuous patterns that are topologically consistent with the constraints imposed by three-arm star polyphile self-assembly, analogous to steric packing and elastic bending models used to analyse bicontinuous mesophases in amphiphilic assemblies. We find a number of competing low-energy ordered structures, composed of threading of three identical labyrinths, with three-fold infinite branch lines, that are likely to be of comparable energy for polyphile shapes with moderately splayed arms. These patterns are triply-periodic analogues of the hexagonal honeycomb, which is most favoured for unsplayed three-arm polyphile architectures.

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Morphology of model three-component three-arm star-shaped copolymers

Cited by 88 publications

References 18 publications

Discovering New Ordered Phases of Block Copolymers

Discovering New Ordered Phases of Block Copolymers

Polycontinuous geometries for inverse lipid phases with more than two aqueous network domains

Tricontinuous mesophases of balanced three-arm ‘star polyphiles’

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