利用六边形晶格组合学枚举石墨烯中稳定纳米孔及其几何性质
Enumerating Stable Nanopores in Graphene and their Geometrical Properties Using the Combinatorics of Hexagonal Lattices
AI总结：
本研究利用二维三角格点动物理论改进Redelmeier算法，枚举石墨烯中所有稳定纳米孔形状，通过几何规则剔除不稳定结构，大幅降低稳定纳米孔数量，还可按尺寸和形状因子筛选纳米孔。
摘要：
二维（2D）材料（包括石墨烯）中的纳米孔可用于多种应用，例如气体分离、海水淡化和DNA测序。然而到目前为止，石墨烯纳米孔所有可能的同分异构体形状尚未被完全枚举。由于空位尺寸增大时纳米孔的数量会呈指数级增长，以往研究采用概率方法来预测二维材料中的纳米孔形状。例如，当移除N=6个原子时，存在12种可能的同分异构体；而当从石墨烯晶格中移除N=20个原子时，该数量理论上会增至1170万。构建一个规模更小、涵盖所有稳定纳米孔形状的详尽数据集，能够为未来聚焦于将纳米多孔二维材料应用于各类场景的实验和理论研究提供助力。在本研究中，我们利用二维三角“格点动物”理论，对多形体数学组合学中著名的Redelmeier算法进行改进，构建了包含所有稳定石墨烯纳米孔形状的库。我们证明了石墨烯纳米孔与三角多形体（称为polyiamond（三角多格形））以及六边形多形体（称为polyhex（六边多格形））之间存在对应关系。我们提出了polyiamond ID的概念，用于识别独特的纳米孔同分异构体。我们还利用三角多格形和六边多格形的几何概念，剔除了含有悬挂原子、悬挂键和悬挂基团的不稳定纳米孔。排除这类不稳定纳米孔后，可能的纳米孔数量从N=20时的1170万大幅减少至仅18.4万，这表明稳定纳米孔的数量几乎低了两个数量级，更易于处理。不仅如此，通过提取六边多格形轮廓，我们的算法还能够搜索尺寸和形状因子处于指定范围内的纳米孔。
英文摘要：
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 N=6 atoms are removed, a number that theoretically increases to 11.7 million when N=20 atoms are removed from the graphene lattice. The development of a smaller, exhaustive dataset of stable 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 geometry to eliminate unstable nanopores containing dangling atoms, bonds, and moieties. The exclusion of such unstable nanopores leads to a remarkable reduction in the possible nanopores from 11.7 million for N=20 to only 0.184 million nanopores, thereby indicating that the number of stable nanopores is almost two 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.
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