Single- to multiple-layer transitions of flat and curved graphite sheets

A model previously developed by the authors in order to describe the energetics of single graphitic sheets (Int. J. Mod. Phys. B9, in press 1995)(1) is extended to include interlayer Mn der Waals forces. It is shown that above a critical size two-layer structures are energetically more favourable than single sheets. When the dangling bond energy is high this crossover size is found to be relatively large, especially for layers with free edges. This suggests the existence of a regime where single sheets are the dominant structures, the majority of which are expected to be closed in order to minimise the dangling bond energy. Partly closed structures may also occur in a slightly out-of-equilibrium environment. This theoretical result is shown to be in good agreement with high resolution transmission electron microscope observations of the sp(2)-microporous carbon found in conjunction with fullerene-related material. The relevance of this model in understanding the growth of single- and many-layer sp(2)-carbon structures of nanometric size is also discussed.