(135e) Addressing the Isomer Cataloging Problem for Nanopores in Graphene and Other 2D Materials

Extended defects or nanopores in graphene and other 2D materials, such as hexagonal boron nitride (hBN), can be used to tailor their electronic, magnetic, electrochemical, and barrier membrane properties. However, the existence of a large number of possible lattice isomers of nanopores makes their quantitative study a seemingly intractable problem, while confounding the interpretation of experimental and simulated data. Herein, we formulate an ab initio solution to this Isomer Cataloging Problem (ICP), which combines extensive electronic-structure calculations, kinetic Monte Carlo simulations, and chemical graph theory, consistent with the underlying symmetries of 2D materials, to generate a catalog of unique, most-probable isomers of 2D lattice nanopores. The calculated first-principles data set provides precise, experimentally consistent rates for transitions between nanopore shapes in the graphene lattice. Further, the results demonstrate remarkable agreement of our model with precise nanopore shapes observed in graphene using transmission electron microscopy, and show that the thermodynamic stability of a nanopore in graphene is distinct from its kinetic stability. The methodology also predicts the experimentally observed prevalence of triangular nanopores in hBN, supporting the assertion that it can solve a wide range of ICPs for other 2D membranes and lattices, thereby providing a much-needed connection between molecular design and fabrication. The methodology developed herein should accelerate the application of nanoporous graphene and other 2D materials for optoelectronics, magnetism, gas separations, desalination, and biological applications, by establishing specific links between experiment and theory/simulations through the solutions of ICPs.