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Addressing the isomer cataloguing problem for nanopores in two-dimensional materials

Nature Materialsvolume 18pages129135 (2019) | Download Citation


The presence of extended defects or nanopores in two-dimensional (2D) materials can change the electronic, magnetic and barrier membrane properties of the materials. However, the large number of possible lattice isomers of nanopores makes their quantitative study a seemingly intractable problem, confounding the interpretation of experimental and simulated data. Here we formulate a solution to this isomer cataloguing problem (ICP), combining electronic-structure calculations, kinetic Monte Carlo simulations, and chemical graph theory, to generate a catalogue of unique, most-probable isomers of 2D lattice nanopores. The results demonstrate remarkable agreement with precise nanopore shapes observed experimentally in graphene and show that the thermodynamic stability of a nanopore is distinct from its kinetic stability. Triangular nanopores prevalent in hexagonal boron nitride are also predicted, extending this approach to other 2D lattices. The proposed method should accelerate the application of nanoporous 2D materials by establishing specific links between experiment and theory/simulations, and by providing a much-needed connection between molecular design and fabrication.

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The datasets generated during and/or analysed during the current study, including the XYZ files of the MPIs, are available online at, under the directory ‘catalog’.

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We acknowledge the Army Research Office (grant 64655-CH-ISN to M.S.S. via the Institute for Soldier Nanotechnologies) for the work on graphene, US Department of Energy (DOE), Office of Science, Basic Energy Sciences (grant DE-FG02-08ER46488 Mod 0008, to M.S.S. and A.G.R.) for the work on hBN, the National Science Foundation (NSF) (grant CBET-1511526, to D.B. and A.G.R.) for modelling the interactions of etchant atoms with 2D materials and the DOE CSGF (grant DE-FG02-97ER25308, to K.S.S.). This work used the XSEDE supercomputing resources, which are supported using NSF grant ACI-1053575. Sample preparation/imaging (Fig. 3c) was conducted at the Center for Nanophase Materials Sciences, by P. Bedworth, S. Heise and D. Cullen. We thank Z. Yuan, R. P. Misra, A. Cardellini and D. Kozawa for discussions.

Author information


  1. Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    • Ananth Govind Rajan
    • , Kevin S. Silmore
    • , Daniel Blankschtein
    •  & Michael S. Strano
  2. Lockheed Martin Space, Palo Alto, CA, USA

    • Jacob Swett
  3. Department of Materials, University of Oxford, Oxford, UK

    • Alex W. Robertson
    •  & Jamie H. Warner


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A.G.R., D.B. and M.S.S. formulated the solution to the ICP, including the isomer-distinguishing methodology. A.G.R. carried out ab initio and KMC simulations and performed data analysis. K.S.S. assisted in formulating the isomer distinguishing methodology. J.S. prepared the graphene nanopore sample depicted in Fig. 3c. A.W.R. and J.H.W. contributed to understanding the kinetics of silicon-catalysed etching of graphene nanopores and provided TEM images of graphene nanopores depicted as Fig. 3b. A.G.R., D.B. and M.S.S. wrote the manuscript. All authors commented on the final version of the manuscript.

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The authors declare no competing interests.

Corresponding author

Correspondence to Michael S. Strano.

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