Department of Chemical Engineering, Indian Institute of Science Education and Research Bhopal, Bhauri, Madhya Pradesh462066, India.
Department of Chemical Engineering, Indian Institute of Science, Bengaluru, Karnataka560012, India.
J Chem Inf Model. 2023 Feb 13;63(3):870-881. doi: 10.1021/acs.jcim.2c01306. Epub 2023 Jan 13.
Nanopores in two-dimensional (2D) materials, including graphene, can be used for a variety of applications, such as gas separations, water desalination, and DNA sequencing. So far, however, all plausible isomeric shapes of graphene nanopores have not been enumerated. Instead, a probabilistic approach has been followed to predict nanopore shapes in 2D materials, due to the exponential increase in the number of nanopores as the size of the vacancy increases. For example, there are 12 possible isomers when = 6 atoms are removed, a number that increases to 11.7 million when = 20 atoms are removed from the graphene lattice. In this regard, the development of a smaller, exhaustive data set of nanopore shapes can help future experimental and theoretical studies focused on using nanoporous 2D materials in various applications. In this work, we use the theory of 2D triangular "lattice animals" to create a library of all stable graphene nanopore shapes based on a modification of a well-known algorithm in the mathematical combinatorics of polyforms known as Redelmeier's algorithm. We show that there exists a correspondence between graphene nanopores and triangular polyforms (called polyiamonds) as well as hexagonal polyforms (called polyhexes). We develop the concept of a polyiamond ID to identify unique nanopore isomers. We also use concepts from polyiamond and polyhex geometries to eliminate unstable nanopores containing dangling atoms, bonds, and moieties. We verify using density functional theory calculations that such pores are indeed unstable. The exclusion of these unstable nanopores leads to a remarkable reduction in the possible nanopores from 11.7 million for = 20 to only 0.184 million nanopores, thereby indicating that the number of stable nanopores is almost 2 orders of magnitude lower and is much more tractable. Not only that, by extracting the polyhex outline, our algorithm allows searching for nanopores with dimensions and shape factors in a specified range, thus aiding the design of the geometrical properties of nanopores for specific applications. We also provide the coordinate files of the stable nanopores as a library to facilitate future theoretical studies of these nanopores.
二维（2D）材料中的纳米孔，包括石墨烯，可以用于各种应用，例如气体分离、海水淡化和 DNA 测序。然而，到目前为止，还没有枚举所有合理的石墨烯纳米孔的异构形状。相反，由于随着空位尺寸的增加，纳米孔的数量呈指数级增加，因此采用了概率方法来预测 2D 材料中的纳米孔形状。例如，当从石墨烯晶格中移除 6 个原子时，有 12 种可能的异构体，当移除 20 个原子时，这个数字增加到 1170 万。在这方面，开发一个更小的、详尽的纳米孔形状数据集，可以帮助未来的实验和理论研究集中在使用纳米多孔 2D 材料的各种应用上。在这项工作中，我们使用二维三角形“晶格动物”理论，根据众所周知的多形体数学组合学中的 Redelmeier 算法的修改，创建一个基于所有稳定石墨烯纳米孔形状的库。我们表明，石墨烯纳米孔与三角形多形体（称为多菱形）以及六边形多形体（称为多六边体）之间存在对应关系。我们开发了多菱形 ID 的概念来识别独特的纳米孔异构体。我们还使用多菱形和多六边体几何的概念来消除含有悬键、键和部分的不稳定纳米孔。我们使用密度泛函理论计算验证了这些孔确实是不稳定的。排除这些不稳定的纳米孔导致可能的纳米孔从 20 个原子时的 1170 万减少到只有 0.184 万个纳米孔，这表明稳定纳米孔的数量几乎低了 2 个数量级，并且更容易处理。不仅如此，通过提取多六边体的轮廓，我们的算法允许在指定范围内搜索具有尺寸和形状因子的纳米孔，从而有助于设计特定应用的纳米孔的几何特性。我们还提供了稳定纳米孔的坐标文件库，以方便未来对这些纳米孔的理论研究。
