Superlattice Formation in a Binary Mixture of Block Copolymer Micelles

Abbas, Sayeed; Lodge, Timothy P.

doi:10.1103/physrevlett.97.097803

Cited by 26 publications

(28 citation statements)

References 29 publications

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“…Small-angle diffraction data have been obtained and analysed in many ways (Matsuoka et al, 1987(Matsuoka et al, , 1990Abbas & Lodge, 2006;Korgel & Fitzmaurice, 1999;Turner & Gruner, 1992;Lee et al, 2005;Toombes et al, 2007;Vonk, 1973). For a one-dimensional scattering profile from a three-dimensionally randomly oriented sample, or so-called powder diffraction, analysis can be categorized into the following: indexing and peak broadening analysis (Senesi et al, 2014), correlation function analysis (Vonk, 1973;Smarsly et al, 2005), liquid-like structure factor analysis (Smarsly et al, 2005;Korgel & Fitzmaurice, 1999), Fourier synthesis (Turner & Gruner, 1992;Wang et al, 2006;Lee et al, 2007;Zeng et al, 2011;Pan et al, 2006), and direct modeling (Toombes et al, 2007;Fö rster et al, 2005;Matsuoka et al, 1987;Jones et al, 2010;Macfarlane et al, 2011Macfarlane et al, , 2013Young et al, 2013;Yager et al, 2014;Perroni & Mahanthappa, 2013;Jin et al, 2007;Heo et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

Small-angle scattering of particle assemblies

Senesi

Lee

2015

J Appl Cryst

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Small‐angle scattering formulae for crystalline assemblies of arbitrary particles are derived from powder diffraction theory using the decoupling approximation. To do so, the pseudo‐lattice factor is defined, and methods to overcome the limitations of the decoupling approximation are investigated. Further, approximated equations are suggested for the diffuse scattering from various defects of the first kind due to non‐ideal particles, including size polydispersity, orientational disorder and positional fluctuation about their ideal positions. Calculated curves using the formalism developed herein are compared with numerical simulations computed without any approximation. For a finite‐sized assembly, the scattering from the whole domain of the assembly must also be included, and this is derived using the correlation function approach.

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Section: Introductionmentioning

confidence: 99%

Small-angle scattering of particle assemblies

Senesi

Lee

2015

J Appl Cryst

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“…A15, one of the Frank-Kasper phases, was also located in the phase space of block copolymer micelle systems (4,5). A superlattice micellar structure was shown to develop in a binary mixture of block copolymer micelles of different sizes (6). Furthermore, shearing the micelles on fcc lattices can result in a 12-or 18-fold aperiodic quasicrystalline order (7).…”

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confidence: 98%

Close-packed block copolymer micelles induced by temperature quenching

Chen

Lee

2018

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

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Close-packed structures of uniformly sized spheres are ubiquitous across diverse material systems including elements, micelles, and colloidal assemblies. However, the controlled access to a specific symmetry of self-assembled close-packed spherical particles has not been well established. We investigated the ordering of spherical block copolymer micelles in aqueous solutions that was induced by rapid temperature changes referred to as quenching. As a function of quench depth, the quenched self-assembled block copolymer micelles formed three different close-packed structures: face-centered cubic (fcc), random stacking of hexagonal-close-packed layers (rhcp), and hexagonal-close-packed (hcp). The induced hcp and rhcp structures were stable for at least a few weeks when maintained at their quench temperatures, but heating or cooling these hcp and rhcp structures transformed both structures to fcc crystallites with coarsening of the crystal grains, which suggests that these noncubic close-packed structures are intermediate states. Time-resolved scattering experiments prove that the micellar rhcp structures do not originate from the rapid growth of competing close-packed structures. We speculate that the long-lived metastable hcp and rhcp structures originate from the small size of crystal grains, which introduces a nonnegligible Laplace pressure to the crystal domains. The reported transitions from the less stable hcp to the more stable rhcp and fcc are experimental observations of Ostwald's rule manifesting the transition order of the key close-packed structures in the crystallization of close-packed uniform spheres.

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“…The very small difference between the two SAXS profiles is indicative of nearly random orientation of the grains. In these SAXS profiles, scattering peaks located at 3q/q 1 ) 3, 4, 8,11,12,19,20,35, and 36, where q 1 is the smallest q value for the observed peaks, are identified. This is consistent with the F j 43m space group symmetry of the ZnS structure.…”

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confidence: 99%

Giant Zincblende Structures Formed by an ABC Star-Shaped Terpolymer/Homopolymer Blend System

Hayashida¹,

Takano²,

Dotera³

et al. 2008

Macromolecules

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Much attention has been focused on construction of mesoscopic diamond and/or zincblende (ZnS) structures as a result of their most robust photonic band gaps. 1-4 Self-organizing systems of spherical particles such as nanocrystal superlattices 5-8 and colloidal crystals 9-11 are candidates for building blocks of the diamond and ZnS structures. Recently, a ZnS lattice with a 19 nm lattice constant has been reported which has been obtained by fine-tuning of sizes, charges, and surface layers of nanoparticles. 7 However, it is still very difficult to construct the diamond and ZnS structures by the sphere packing plus interaction approach mainly because such structures have non-close-packed lattices.On the other hand, it is well-known that the block copolymers exhibit a large variety of microphase-separated structures within the mesoscopic length scale in a manner that depends on the volume fractions and chain architectures of the molecules. 12-14 Among these materials, ABC star-shaped terpolymers adopt many unique microphase separations, which cannot be formed by linear-type block polymers such as AB, ABA, and ABC, in condensed 15-24 and solution 25-27 states because the three polymer chains are connected at one junction point and because the junction points must be aligned in a single dimension ( Figure 1a, left). We previously reported that cylindrical structures, whose cross sections reveal various periodic tiling patterns consisting of polygons, are predominantly formed by ISP starshaped terpolymers composed of polyisoprene (I), polystyrene (S), and poly(2-vinylpyridine) (P). [16][17][18][19] For example, the I 1 S 1.8 P 0.8 sample (Supporting Information) adopts a (6.6.6) Archimedean tiling pattern, consisting of three kinds of hexagons (Figure 1a, right). 18 This raises the question as to what morphology is adopted by the I 1 S 1.8 P 0.8 sample when the S chains are sufficiently extended. We can imagine that if a sufficient amount of the S component surrounds the I and P chains, the junction points of the ISP star molecules will be aligned annularly (Figure 1b, left). In the microphase-separated structure, the I and P chains are inclined to form spherical domains due to the requirement of minimizing the I/S and P/S interfacial energies (Figure 1b, right). If each spherical domain is packed periodically, mesoscopic CsCl, NaCl, and/or ZnS structures can be formed by proper placement of the I and P domains alternatively. Here we report that an ISP star-shaped terpolymer/homopolymer blend system can build up a giant zincblende structure. A 3K S-homopolymer has been added to the I 1 S 1.8 P 0.8 sample to increase the volume ratio of the S component instead of extending the S chains. The resulting I 1 S 2.3 P 0.8 and I 1 S 2.5 P 0.8 samples have been found to adopt the ZnS structure. In this structure, the I and P components form spherelike domains in mutual contact at the tetrahedral positions while component S covers the I and P components as matrix. Figure 2a illustrates the ZnS lattice for the I 1 S 2.3 P 0.8 sa...

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Superlattice Formation in a Binary Mixture of Block Copolymer Micelles

Cited by 26 publications

References 29 publications

Small-angle scattering of particle assemblies

Small-angle scattering of particle assemblies

Close-packed block copolymer micelles induced by temperature quenching

Giant Zincblende Structures Formed by an ABC Star-Shaped Terpolymer/Homopolymer Blend System

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