Persistent Homology to Quantify the Quality of Surface‐Supported Covalent Networks

Gutiérrez, Abraham; Buchet, Mickaël; Clair, Sylvain

doi:10.1002/cphc.201900257

Cited by 2 publications

(3 citation statements)

References 60 publications

(84 reference statements)

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“…To further quantify the degree of order of the molecular networks, we resort to a persistent homology (PH) method. 47 The persistent diagrams are created from STM topographic images to track the evolution of the pores in the molecular networks. The PH scores were computed depending on how concentrated the persistent diagrams are, providing a numerical score to evaluate the regularity of the network.…”

Section: Resultsmentioning

confidence: 99%

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Order–Disorder Transition of Two-Dimensional Molecular Networks through a Stoichiometric Design

Lu,

Nieckarz,

Jiang

et al. 2023

ACS Nano

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Materials with disordered structures may exhibit interesting properties. Metal−organic frameworks (MOFs) are a class of hybrid materials composed of metal nodes and coordinating organic linkers. Recently, there has been growing interest in MOFs with structural disorder and the investigations of amorphous structures on surfaces. Herein, we demonstrate a bottom-up method to construct disordered molecular networks on metal surfaces by selecting two organic molecule linkers with the same symmetry but different sizes for preparing twocomponent samples with different stoichiometric ratios. The amorphous networks are directly imaged by scanning tunneling microscopy under ultrahigh vacuum with a submolecular resolution, allowing us to quantify its degree of disorder and other structural properties. Furthermore, we resort to molecular dynamics simulations to understand the formation of the amorphous metal−organic networks. The results may advance our understanding of the mechanism of formation of monolayer molecular networks with structural disorders, facilitating the design and exploration of amorphous MOF materials with intriguing properties.

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Section: Resultsmentioning

confidence: 99%

“…To further quantify the degree of order of the molecular networks, we resort to a persistent homology (PH) method . The persistent diagrams are created from STM topographic images to track the evolution of the pores in the molecular networks.…”

Section: Resultsmentioning

confidence: 99%

Order–Disorder Transition of Two-Dimensional Molecular Networks through a Stoichiometric Design

Lu,

Nieckarz,

Jiang

et al. 2023

ACS Nano

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show abstract

“…Any process that can elucidate as yet hidden structure in materials, or improve its description, naturally has potential to be extremely useful. In this vein, persistent homology has already been applied to diverse topics such as granular matter [3], porous media [4], water networks [5], fullerenes [6] and, of particular importance to this work, amorphous materials [7][8][9][10][11]. The latter studies claim to highlight structures that are not available using more conventional techniques, quantify the medium range order in glass, and explain phenom-ena such as the origin of the first sharp diffraction peak 39 in disordered materials.…”

Section: Introductionmentioning

confidence: 99%

Persistent homology in two-dimensional atomic networks

Morley

Salmon

Wilson

2021

The Journal of Chemical Physics

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The topology of two-dimensional network materials is investigated by persistent homology analysis. The constraint of two dimensions allows for a direct comparison of key persistent homology metrics (persistence diagrams, cycles, Betti numbers) with more traditional metrics such as the ring-size distributions. Two different types of networks are employed in which the topology is manipulated systematically. In the first, comparatively rigid networks are generated for a triangle-raft model, which are representative of materials such as silica bilayers. In the second, more flexible networks are generated using a bond-switching algorithm, which are representative of materials such as graphene. Bands are identified in the persistence diagrams by reference to the length-scales associated with distorted polygons. The triangle-raft models with the largest ordering allow specific bands Bn (n = 1, 2, 3,. . . ) to be allocated to configurations of atoms separated by n bonds. The persistence diagrams for the more disordered network models also display bands albeit less pronounced. The persistent homology method thereby provides information on n-body correlations that is not accessible from structure factors or radial distribution functions. An analysis of the persistent cycles gives the primitive ring statistics, provided the level of disorder is not too large. The method also gives information on the regularity of rings that is unavailable from a ring-statistics analysis. The utility of the persistent homology method is demonstrated by its application to experimentally-obtained configurations of silica bilayers and graphene. 42In this paper the utility of persistent homology will 43 be assessed using two-dimensional amorphous materials. 44The interpretation of the properties of these reduced di-45 mensional systems is simpler compared to three dimen-46 sional networks, and should bring insight to the analysis 47 of the latter. The paper begins by outlining the relevant 48 theory to persistent homology, with the aid of small ex-49 ample systems. Persistent homology is then calculated 50 for triangle rafts (a proxy for amorphous bilayers of, e.g., 51 silica), systematically generated with increasing levels of 52 disorder. The results are contrasted with those obtained 53 from generic random-networks as produced from bond 54 switching. In addition, the persistence diagrams are dis-55 cussed for configurations obtained directly from experi-56 ments on silica bilayers and graphene. Finally, the con-57 clusions of these investigations are assessed in the con-58 text of more complex systems, and the potential utility 59 of persistent homology as an analytic tool for materials 60 characterisation is examined. 61 II. OVERVIEW OF TRADITIONAL METHODS 62 Amorphous network-forming materials are usually 63 built from simple local-structural-units such as the SiO 4 64 tetrahedron in amorphous silica. Bond-length and bond-65 bending flexibility leads, however, to structural complex-66 ity as these units connect to form configurations on lon...

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Persistent Homology to Quantify the Quality of Surface‐Supported Covalent Networks

Cited by 2 publications

References 60 publications

Order–Disorder Transition of Two-Dimensional Molecular Networks through a Stoichiometric Design

Order–Disorder Transition of Two-Dimensional Molecular Networks through a Stoichiometric Design

Persistent homology in two-dimensional atomic networks

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