ArticleProceedings of the National Academy of Sciences of the United States of America2018
Stable Frank-Kasper phases of self-assembled, soft matter spheres.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 31 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
31 citing papers in PubMed.
- Ionic liquid as a structure-directing agent for Frank-Kasper phase formation in block copolymers.Nature communications · 2026Article
- On and Off Deformability of Supramolecular Micelles in the Soft Frank-Kasper σ Phase.The journal of physical chemistry letters · 2026Article
- Learning nature's assembly language with polymers.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Emergence of Frank-Kasper Phases from Chemically Simple Block Copolymer: Poly(ethylene oxide)-Macromolecules · 2026Article
- Accessing Frank-Kasper Phases via Blending of Architecturally Distinct and Sustainable Sugar-Based Block Co-Oligomers.Macromolecules · 2025Article
- Designing the Self-Assembly of Disordered Materials Via Color Frustration.Advanced materials (Deerfield Beach, Fla.) · 2025Article
- Discovery of the final primitive Frank-Kasper phase of clathrate hydrates.Science advances · 2024Article
- Frank-Kasper-like network phase from self-assembly of high-χ star-block copolymers.Science advances · 2024Article
- Self-assembled soft alloy with Frank-Kasper phases beyond metals.Nature materials · 2024Article
- Frank-Kasper Phases of Diblock Copolymer Melts: Self-Consistent Field Results of Two Commonly Used Models.Polymers · 2024Article
- Discrete Miktoarm Star Block Copolymers with Tailored Molecular Architecture.ACS polymers Au · 2023Article
- Atomistic-geometry inspired structure-composition-property relations of hydrogen sII hydrates.Scientific reports · 2023Article
- Topological dual and extended relations between networks of clathrate hydrates and Frank-Kasper phases.Nature communications · 2023Article
- The first space-filling polyhedrons of polymer cubic cells originated from Weaire-Phelan structure created by polymerization induced phase separation.Scientific reports · 2022Article
- Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers.Nature communications · 2022Article
- Enhancing ion transport in charged block copolymers by stabilizing low symmetry morphology: Electrostatic control of interfaces.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
- Dodecagonal quasicrystals of oil-swollen ionic surfactant micelles.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
- Article
- Implementation of organization and end-user computing-anti-money laundering monitoring and analysis system security control.PloS one · 2021Article
- Discrete Block Copolymers with Diverse Architectures: Resolving Complex Spherical Phases with One Monomer Resolution.ACS central science · 2020Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
6 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Single molecular species can self-assemble into Frank-Kasper (FK) phases, finite approximants of dodecagonal quasicrystals, defying intuitive notions that thermodynamic ground states are maximally symmetric. FK phases are speculated to emerge as the minimal-distortional packings of space-filling spherical domains, but a precise measure of this distortion and how it affects assembly thermodynamics remains ambiguous. We use two complementary approaches to demonstrate that the principles driving FK lattice formation in diblock copolymers emerge directly from the strong-stretching theory of spherical domains, in which a minimal interblock area competes with a minimal stretching of space-filling chains. The relative stability of FK lattices is studied first using a diblock foam model with unconstrained particle volumes and shapes, which correctly predicts not only the equilibrium σ lattice but also the unequal volumes of the equilibrium domains. We then provide a molecular interpretation for these results via self-consistent field theory, illuminating how molecular stiffness increases the sensitivity of the intradomain chain configurations and the asymmetry of local domain packing. These findings shed light on the role of volume exchange on the formation of distinct FK phases in copolymers and suggest a paradigm for formation of FK phases in soft matter systems in which unequal domain volumes are selected by the thermodynamic competition between distinct measures of shape asymmetry.
Indexed as
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.