Biomedical Engineering Reference
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not aromatic and the C-C-C bond angles are closer to the tetrahedral
109.5° than the planar hexagonal 120°. We can see from Fig. 7.5b
that even though this occurs spontaneously, so as to lower the cost
of dangling C-C bonds, this energetic barrier is significant. At around
30% hydrogenation the aromatic sheet/layer is strained, and the
stored elastic energy is sufficient to drive the rehybridization of
the entire structure. The second cascade is associated with the
reattachment of the sheet to the surface below. This is more efficient,
since there are already dangling bonds in both the sheet and the
surface beneath, and the barrier is low. The energy associated with
the dangling bonds goes to zero as the number of dangling bonds
goes to zero, and the C-H bond energy reaches equilibrium. Upon
conclusion all C atoms in the system are sp
3
hybridized.
We can see how using this technique the ambiguity associated
with the assignment of sp
3
2
bonds in carbon systems can be
addressed, and a clear picture of the bonding in nanocarbon systems
can also be constructed [12]. This situation is not dissimilar to the
conversion of carbon onions to nanodiamonds under irradiation
(as opposed to gas exposure). Both situations involve hybrid
materials with a combination of sp
to sp
2
3
bonds at the surface and sp
bonds beneath. The phase transition between nanodiamond and
onion-like structures has been modeled by Zaiser and Banhart
[54], who presented a thermodynamic quasi-equilibrium theory to
explain this irradiation-induced transformation of carbon-onions to
nanodiamond. The model was based on the premise that irradiation
of carbon-onions leading to the destabilization of the sp
2
structure
was due to the large difference in the cross-sections for irradiation-
induced displacements of carbon atoms in diamond and graphite. A
nonequilibrium phase diagram was calculated showing the stability
of graphite and diamond (as a function of the displacement rate
of atoms), and the results related to the experimentally observed
results [14]. In this approach the issue of nucleation was excluded
in favor of considering the phase transformation as the motion of a
phase boundary separating the two (solid) allotropes. The carbon-
onion to nanodiamond phase transition was attributed to ballistic
displacements causing interstitial C atoms (predominantly from
sp
2
2
3
lattice sites) causing a net flux of atoms from the sp
to the sp
allotrope. It was shown, however, that if the temperature exceeds
an (upper) critical temperature the sp
bonding may be stable, even
though phase transitions may still occur at lower temperatures
2
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