The disappearance of dangling bonds in F and O
leads to significant drop of their total free energy GF
and GO because cGh
disappears, which stabilizes F and
O when the size of the nanocarbon is very small. This
is clearly shown in Fig. 2. The energetic increase caused
by the dangling bonds in D is greater than the energetic
decrease induced by Pin at very small size. Because these
different contributions of surface energy and surface
stress in different structures at different sizes on nanocarbons
are distinct, nanocarbons undergo transitions in a
series of G ! D ! O(F) or bonding of sp2 ! sp3 ! sp2
with reducing size.