Nucleation and growth of fullerenes and nanotubes having three-fold T-symmetry

A. Melker, M. Krupina, A. N. Matvienko
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Abstract

According to the periodic system of fullerenes, all the fullerenes can be classified into the groups having different symmetry. It is supposed that the fullerenes of one and the same symmetry have similar properties. Before the appearance of the periodic system in 2017 the fullerenes were chosen for study at a random way that instead of ordering the results only increased information entropy. We have studied possible ways of generation and growing the fullerenes, which refer to the group having three-fold T-symmetry. Beginning with cyclopropane C3H6 producing clusters C6, we have obtained elementary fullerenes C6 as well as mini-fullerenes C12, which in their turn have produced the fullerenes from C18 to C48, perfect and imperfect, as well as nanotubes. The basic perfect fullerenes C18, C24, C30, C36, C42 and C48 have the ordinary three-fold symmetry, the intermediate ones having no such symmetry. Their imperfection is connected with extra ‘interstitial’ or carbon dimers, the dimers playing the role of defects. One can define the imperfect fullerenes with defects as the fullerenes having topological three-fold symmetry. We have calculated their shape and energies using Avogadro package and discussed possible reasons of their dependence on a fullerene size and shape. We have found that the fullerenes can be divided into two groups, alive that can grow, and dead which are impotent. Taking into account the results obtained early, allows us to make predictions that the dead fullerenes C24R, C32R, C40R and C48R of three-, four-, five- and six-fold symmetry have the most chance to be found experimentally with comparison of their isomers.
具有三重t对称的富勒烯和纳米管的成核和生长
根据富勒烯的周期体系,可以将所有的富勒烯划分为具有不同对称性的基团。假设相同对称的富勒烯具有相似的性质。在2017年周期系统出现之前,富勒烯以随机方式被选择进行研究,而不是排序结果,只会增加信息熵。我们研究了产生和生长富勒烯的可能方法,富勒烯指的是具有三重t对称的基团。从环丙烷C3H6开始,我们得到了基本富勒烯C6和迷你富勒烯C12,它们依次得到了从C18到C48,完美和不完美的富勒烯,以及纳米管。基本完美富勒烯C18、C24、C30、C36、C42和C48具有普通的三重对称,中间富勒烯不具有这种对称。它们的缺陷与额外的“间隙”或碳二聚体有关,二聚体起缺陷的作用。有缺陷的不完美富勒烯可以定义为具有拓扑三重对称的富勒烯。我们用阿伏伽德罗包计算了它们的形状和能量,并讨论了它们依赖于富勒烯尺寸和形状的可能原因。我们发现富勒烯可以分为两类,活的可以生长,死的不能生长。考虑到早期得到的结果,我们可以预测三、四、五、六重对称的死富勒烯C24R、C32R、C40R和C48R的同分异构体最有可能在实验中被发现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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