Qualitatively graph-theoretical study on stability and formation of fullerenes and nanotubes

Kekule structures of different carbon species have been determined. On the basis of Kekule structure and C-C bond counts as well as the surface curvature, stability of diverse carbon species, driving force for curling of graphite fragments and formation of fullerenes and nanotubes, have been discussed. Curling of graphite flat fragments, end-capping of nanotubes, and closure of curved structures are driven by a tremendous increase in Kekule structures as terminal carbon atoms couple their dangling bonds into C-C o bonds. The increasing tendency becomes particularly striking for large cages and nanotubes. Resonance among numerous Kekule structures will stabilize the curved structure and dominate formation of closed carbon species. For similar carbon cages with comparable Kekule structure counts in magnitude, the surface curvature of carbon cages, as a measure for the strain energy, also plays an important role in determining their most stable forms.     

富勒烯和碳纳米管稳定性与形成机理的图形理论定性研究

应用图形理论对不同种类碳簇体系的Kekulé结构数进行了计算, 并在半经验方法(AM1)和密度泛函理论(DFT)水平上，讨论了不同种类碳簇的结构与稳定性. 基于Kekulé结构计数, C-Cσ键数, 富勒烯的表面曲率和能量, 对石墨碎片的卷曲行为以及富勒烯的形成机理进行了讨论. 研究结果表明石墨碎片的卷曲, 一端闭合, 到完全封闭, 可以减少结构中的悬键; 随着新的C-Cσ键生成, Kekulé结构数将急剧地增加, 特别是大的富勒烯和碳纳米管, 这种增加更为显著. 大量Kekulé结构间的共振使体系获得显著的共振稳定化能, 稳定具有张力的富勒烯和碳纳米管, 并驱动平面碳簇结构向闭合结构的转化. 对于Kekulé结构数相近的碳笼, 表面曲率对曲面结构的稳定性有重要的影响. 把Kekulé结构计数和表面曲率结合起来, 可以合理地理解球形笼状富勒烯、闭合纳米管和类“洋葱”型结构等高碳簇在热力学上的稳定性.