146
7 Carbon Allotropes
lower (larger value) to higher binding energies, to the contributions from the GNR
edge, the mono-layer GNR or the surface of the triple-layered graphene, and the
bulk graphite in multi-layered graphene. The C 1s spectrum of the multilayered
graphene is dominated by the surface and the bulk components while the spectra
for the mono- and the triple-layers are dominated by the surface and edge components. It has been found [89] from the epitaxial few-layer graphene that the work
function decreases from 4.6 to 4.3 eV and that the C 1s core level shifts positively
from 284.42 to 284.83 eV simultaneously when the number of graphene layers
is decreased from ten to one, which is consistent with the reported thickness
dependence of the Dirac point energy. The same thickness trend has also been
observed from the C 60 [90]. Unfortunately, few theoretical models are available
to account for the origin and interdependence of the coordination-resolved C 1s
binding energy shift and the associated work function reduction.
6. When the number-of-layer, strain, temperature, and pressure change, the vibration frequencies of the GNR and carbon alltorpes shift abnormally. Formulation
of the lattice dynamics is necessary.
7. The common origin of these anomalies and their interdependence need to be
established. The difference between the graphite and the GNRs or the CNTs
is nothing more than atomic undercoordination that could be the point of starting. From the observation of the atomic dynamics of carbon at the edge of a
hole in a suspended, single atomic layer of graphene, Girit et al. [49] found
the rearrangement of bonds and the electron beam-induced ejection of carbon
atoms as the vacancy hole grows in their high-resolution in situ TEM studies.
They observed the edge reconstruction and the stability of the “zigzag” edge
configuration, revealing the complex behavior of atoms preferentially occurring
at the boundary. Therefore, atomic undercoordination and its consequences on
the bond length, bond energy, and the associated electronic dynamics should be
the origin for the anomalies and their interdependence.
In order to harness the GNRs and CNTs, one has to get these concerns be understood. It should be clear what the advantages are and what the limitations would be,
and how to make use of the advantages and to overcome the limitations in practical
applications. In fact, properties of a substance are determined by the process and consequences of bond and nonbond formation, dissociation, relaxation and vibration,
and the associated energetics and dynamics of charge repopulation, polarization,
densification, and localization—the theme of bonding and electronic dynamics [91].
From this perspective, this section addresses the above challenging issues with a
focus on the fundamentals behind the fascinations and their interdependence. It is
demonstrated that the atomic-undercoordination-induced local bond contraction and
quantum entrapment, the polarization of the unpaired dangling σ-bond sp
2 electrons
by the entrapped core and bond charges at the atomic vacancy and the ZGNR edges,
and the formation of the pseudo-π-bond between the nearest dangling σ-bond electrons along the AGNR and the rec-ZGNR edges result in the fascinations. Theoretical
reproduction of the experimentally observed elastic modulus enhancement, melting
7 Carbon Allotropes
lower (larger value) to higher binding energies, to the contributions from the GNR
edge, the mono-layer GNR or the surface of the triple-layered graphene, and the
bulk graphite in multi-layered graphene. The C 1s spectrum of the multilayered
graphene is dominated by the surface and the bulk components while the spectra
for the mono- and the triple-layers are dominated by the surface and edge components. It has been found [89] from the epitaxial few-layer graphene that the work
function decreases from 4.6 to 4.3 eV and that the C 1s core level shifts positively
from 284.42 to 284.83 eV simultaneously when the number of graphene layers
is decreased from ten to one, which is consistent with the reported thickness
dependence of the Dirac point energy. The same thickness trend has also been
observed from the C 60 [90]. Unfortunately, few theoretical models are available
to account for the origin and interdependence of the coordination-resolved C 1s
binding energy shift and the associated work function reduction.
6. When the number-of-layer, strain, temperature, and pressure change, the vibration frequencies of the GNR and carbon alltorpes shift abnormally. Formulation
of the lattice dynamics is necessary.
7. The common origin of these anomalies and their interdependence need to be
established. The difference between the graphite and the GNRs or the CNTs
is nothing more than atomic undercoordination that could be the point of starting. From the observation of the atomic dynamics of carbon at the edge of a
hole in a suspended, single atomic layer of graphene, Girit et al. [49] found
the rearrangement of bonds and the electron beam-induced ejection of carbon
atoms as the vacancy hole grows in their high-resolution in situ TEM studies.
They observed the edge reconstruction and the stability of the “zigzag” edge
configuration, revealing the complex behavior of atoms preferentially occurring
at the boundary. Therefore, atomic undercoordination and its consequences on
the bond length, bond energy, and the associated electronic dynamics should be
the origin for the anomalies and their interdependence.
In order to harness the GNRs and CNTs, one has to get these concerns be understood. It should be clear what the advantages are and what the limitations would be,
and how to make use of the advantages and to overcome the limitations in practical
applications. In fact, properties of a substance are determined by the process and consequences of bond and nonbond formation, dissociation, relaxation and vibration,
and the associated energetics and dynamics of charge repopulation, polarization,
densification, and localization—the theme of bonding and electronic dynamics [91].
From this perspective, this section addresses the above challenging issues with a
focus on the fundamentals behind the fascinations and their interdependence. It is
demonstrated that the atomic-undercoordination-induced local bond contraction and
quantum entrapment, the polarization of the unpaired dangling σ-bond sp
2 electrons
by the entrapped core and bond charges at the atomic vacancy and the ZGNR edges,
and the formation of the pseudo-π-bond between the nearest dangling σ-bond electrons along the AGNR and the rec-ZGNR edges result in the fascinations. Theoretical
reproduction of the experimentally observed elastic modulus enhancement, melting