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On Borromean links and related structures.

Michael O'Keeffe1, Michael M J Treacy2

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Researchers describe new molecular structures based on Borromean rings, expanding the family of linked components. These n-Borromean structures offer templates for designing complex polycatenanes and chain mail with novel linking patterns.

Keywords:
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Area of Science:

  • Supramolecular Chemistry
  • Synthetic Chemistry
  • Topology

Background:

  • The field of creating knotted, woven, and linked molecular structures is rapidly advancing.
  • Borromean rings, where no two rings are directly linked, represent a foundational concept in this area.
  • Generalizations of Borromean rings to n-component links (n-Borromean) and periodic structures are being explored.

Purpose of the Study:

  • To describe an extended family of n-Borromean structures.
  • To provide templates for the designed synthesis of Borromean polycatenanes.
  • To explore the linking patterns and embeddings of these complex molecular architectures.

Main Methods:

  • Utilizing graph theory, specifically complete directed graphs (tournaments), to describe linking patterns.
  • Enumerating vertex-transitive tournaments up to 13 vertices.
  • Determining optimal piecewise-linear embeddings in highest-symmetry point groups.

Main Results:

  • Description of an extended family of n-Borromean structures, including rings, periodic objects, and nets.
  • Enumeration of vertex-transitive linking patterns up to 13 components.
  • Provision of isonemal embeddings with rotoinversion symmetry for various numbers of rings (3, 5-7, 9-11, 13-14).
  • Piecewise-linear embeddings for 1- and 2-periodic polycatenanes (chains and chain mail).
  • Description of the linking of n-Borromean sets of interleaved honeycomb nets.

Conclusions:

  • The study expands the understanding of n-Borromean topology beyond classical rings.
  • The described structures and embeddings serve as valuable blueprints for future synthetic endeavors in supramolecular chemistry.
  • This work provides a framework for designing and synthesizing complex, non-covalently linked molecular architectures.