Conformational Asymmetry and Quasicrystal Approximants in Linear Diblock Copolymers

Schulze, Morgan W.; Lewis, Ronald M.; Lettow, James H.; Hickey, Robert J.; Gillard, Timothy M.; Hillmyer, Marc A.; Bates, Morgan W.

doi:10.1103/physrevlett.118.207801

Cited by 117 publications

(213 citation statements)

References 35 publications

(44 reference statements)

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“…decreased mean A) below the Weaire-Phelan structure if the equalvolume constraint for distinct cells is relaxed, as would occur for molecular exchange between distinct qSD [11]. Based on the Voronoi partitions, which have unequal volumes for FK lattices, σ was argued to have lower mean dimensionless area than A15, and thus should be stable over that lattice according to the sphericity argument, consistent with observations of a σ lattice in diblock copolymer melts [13] and self-consistent field theory of conformationally and architecturally asymmetric diblocks [28].…”

Section: Introductionsupporting

confidence: 63%

Stable Frank–Kasper phases of self-assembled, soft matter spheres

Reddy

Buckley

Arora

et al. 2018

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

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131

248

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SignificanceFormation of complex Frank–Kasper phases in soft matter systems confounds intuitive notions that equilibrium states achieve maximal symmetry, owing to an unavoidable conflict between shape and volume asymmetry in space-filling packings of spherical domains. Here we show the structure and thermodynamics of these complex phases can be understood from the generalization of two classic problems in discrete geometry: the Kelvin and Quantizer problems. We find that self-organized asymmetry of Frank–Kasper phases in diblock copolymers emerges from the optimal relaxation of cellular domains to unequal volumes to simultaneously minimize area and maximize compactness of cells, highlighting an important connection between crystal structures in condensed matter and optimal lattices in discrete geometry.

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Section: Introductionsupporting

confidence: 63%

Stable Frank–Kasper phases of self-assembled, soft matter spheres

Reddy

Buckley

Arora

et al. 2018

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

Self Cite

131

248

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“…Fig. 1 shows a 12-fold symmetry diffraction pattern whichwas frequently observed in many kinds of soft matter [30][31][32][33][34][35][36][37][38][39][40][41]. From the group theory point of view, the similar symmetry patterns with 5-, 8-and 10-fold are possible candidates for soft-matter quasicrystals as well.…”

Section: Symmetry Symmetry Breaking Elementary Excitations Of Soft-mentioning

confidence: 99%

“…The approximate solutions of dislocations of the first kind of soft-matter quasicrystals have beendiscussed in detail previously [20,21,55], it is not needed to 36 introduce any more. If we want to promote the research work of dislocation problems, some new techniques need to be developed, e.g.…”

Section: Fig21mentioning

confidence: 99%

Generalized Dynamics of Soft-Matter Quasicrystals

Tang¹

2017

Springer Series in Materials Science

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This article provides a detailed review on the generalized dynamics of soft-matter quasicrystals developed recent years. Comparing to solid quasicrystals consisted mainly with metallic alloys, soft-matter quasicrystals have been observed in liquid crystals, polymers, colloids, nanoparticles and surfactants, which indicates quite different formation mechanism. Based onLandau-Anderson theory and group representation theory, we have studied the symmetry, symmetry breaking and elementary excitations for the observed and possible soft-matter quasicrystals. We further proposed one more elementary excitation -fluid phonon additional to the phonon and phason for solid quasicrystals, to quantitatively describe the dynamics of soft-matter quasicrystals. The general governing equations and the solutions of the dynamics evolution on the distribution, deformation and motion of the new phase are studied, which reveal quite distinguishing dynamic behaviour with those of conventional fluids and solid quasicrystals. Someapplications are introduced, which show this is an important field of new materials and materials science. 9

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“…2,3 Further, there is evidence that conformational asymmetry can expand the window of accessibility for phases near the critical point such as the bicontinuous gyroid phase and Frank−Kaspar phases, in addition to related long-lived metastable phases. 2,4 Past work on conformational asymmetry has raised important questions: in particular, are the effects of conformational asymmetry on self-assembly primarily entropic or enthalpic in nature? 5 Theoretical work predicts an entropic conformational effect on self-assembly arising from how conformational asymmetry changes the space-filling nature of chains and therefore the relative penalties for chain stretching and deformation.…”

Section: ■ Introductionmentioning

confidence: 99%

Impact of Helical Chain Shape in Sequence-Defined Polymers on Polypeptoid Block Copolymer Self-Assembly

et al. 2018

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Controlling the self-assembly of block copolymers with variable chain shape and stiffness is important for driving the self-assembly of functional materials containing nonideal chains as well as for developing materials with new mesostructures and unique thermodynamic interactions. The polymer helix is a particularly important functional motif. In the helical chain, the traditional scaling relationships between local chain stiffness and space-filling properties are not applicable; this in turn impacts the scaling relationships critical for governing self-assembly. Polypeptoids, a class of sequence-defined peptidomimetic polymers with controlled helical secondary structure, were used to systematically investigate the impact of helical chain shape on block copolymer self-assembly in a series of poly(n-butyl acrylate)-b-polypeptoid block copolymers. Small-angle X-ray scattering (SAXS) of the bulk materials shows that block copolymers form hexagonally packed cylinder domains. By leveraging sequence control, the polypeptoid block was controlled to form a helix only at the part either adjacent to or distant from the block junction. Differences in domain size from SAXS reveal that chain stretching of the helix near the block junction is disfavored, while helical segments at the center of cylindrical domains contribute to unfavorable packing interactions, increasing domain size. Finally, temperature-dependent SAXS shows that helix-containing diblock copolymers disorder at lower temperatures than the equivalent unstructured diblock copolymers; we attribute this to the smaller effective N of the helical structure resulting in a larger entropic gain upon disordering. These results emphasize how current descriptions of rod/coil interactions and conformational asymmetry for coil polymers do not adequately address the behavior of chain secondary structures, where the scalings of space-filling and stiff−elastic properties relative to chain stiffness deviate from those of typical coil, semiflexible, and rodlike polymers.

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Conformational Asymmetry and Quasicrystal Approximants in Linear Diblock Copolymers

Cited by 117 publications

References 35 publications

Stable Frank–Kasper phases of self-assembled, soft matter spheres

Stable Frank–Kasper phases of self-assembled, soft matter spheres

Generalized Dynamics of Soft-Matter Quasicrystals

Impact of Helical Chain Shape in Sequence-Defined Polymers on Polypeptoid Block Copolymer Self-Assembly

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