Evolution of local motifs and topological proximity in self-assembled quasi-crystalline phases: Evolution of local motifs

Martin Cramer Pedersen*, Vanessa Robins, Kell Mortensen, Jacob J.K. Kirkensgaard

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    Abstract

    Using methods from the field of topological data analysis, we investigate the self-assembly and emergence of three-dimensional quasi-crystalline structures in a single-component colloidal system. Combining molecular dynamics and persistent homology, we analyse the time evolution of persistence diagrams and particular local structural motifs. Our analysis reveals the formation and dissipation of specific particle constellations in these trajectories, and shows that the persistence diagrams are sensitive to nucleation and convergence to a final structure. Identification of local motifs allows quantification of the similarities between the final structures in a topological sense. This analysis reveals a continuous variation with density between crystalline clathrate, quasi-crystalline, and disordered phases quantified by 'topological proximity', a visualization of the Wasserstein distances between persistence diagrams. From a topological perspective, there is a subtle, but direct connection between quasi-crystalline, crystalline and disordered states. Our results demonstrate that topological data analysis provides detailed insights into molecular self-assembly.

    Original languageEnglish
    Article number20200170
    JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    Volume476
    Issue number2241
    DOIs
    Publication statusPublished - 1 Sept 2020

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