Mapping hyperbolic order in curved materials

Martin Cramer Pedersen*, Stephen T. Hyde, Stuart Ramsden, Jacob J. K. Kirkensgaard

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

2 Citations (Scopus)

Abstract

Nature employs an impressive range of topologically complex ordered nanostructures that occur in various forms in both natural and synthetic materials. A particular class of these exhibits negative curvature and forms periodic saddle-shaped surfaces in three dimensions. Unlike pattern formation on flat or positively curved surfaces like spherical systems, the understanding of patterning on such surfaces is highly complicated due to the structures being intrinsically intertwined in three dimensions. We present a new method for visualisation and analysis of patterns on triply periodic negatively curved surfaces by mapping to two-dimensional hyperbolic space analogous to spherical projections in cartography thus effectively creating a more accessible "hyperbolic map" of the pattern. Specifically, we exemplify the method via the simplest triply periodic minimal surfaces: the Primitive, Diamond, and Gyroid in their universal cover along with decorations from a soft materials, whose structures involve decorations of soft matter on negatively curved surfaces, not necessarily minimal.

Original languageEnglish
JournalSoft Matter
Volume2023
Issue number19
Pages (from-to)1586-1595
Number of pages10
ISSN1744-683X
DOIs
Publication statusPublished - 2023

Keywords

  • PERIODIC MINIMAL-SURFACES
  • MOLECULAR-DYNAMICS SIMULATIONS
  • CRYSTALS
  • CRYSTALLOGRAPHY
  • PARAMETRIZATION
  • NETWORKS
  • PATTERNS
  • DIAMOND
  • SYSTEMS
  • TILINGS

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