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

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.