5 Enabling Materials By Dimensionality: From 0D to 3D Carbon-Based. . .
155
atoms, n = 3 are the internal degrees of freedom per atom and k B is the Boltzmann
constant. Since in the SuMBE approach the rotational and vibrational degrees of
freedom of C 60 result frozen, the second term in the left-hand side of Eq. 5.3 can be
neglected. Assuming σ f of the order of the mechanical strength of carbon nanotubes
[58] (50 GPa), the threshold kinetic energy of C 60 breakup would be estimated
40 eV. This value is in good agreement with our ab initio nonadiabatic simulations.
5.3 2D Carbon-Based Materials: Graphene and Its
Low-Density Allotropes
The large interest expressed over the last decade in graphene, the bi-dimensional
allotropic form of carbon, is largely determined by the honeycomb-shaped sp 2
carbon net from which it derives its unique electronic and mechanical properties
[11, 12, 18, 47, 48, 59–65], such as unexpectedly high opacity for a thin atomic
monolayer, high electron mobility at room temperature, with reported values in
excess of 15,000 cm 2 V −1 s −1 , and breaking strength over 100 times bigger than
a hypothetical steel film of the same thickness [4]. Furthermore, pristine graphene
differs from most three-dimensional materials being a semimetal or a zero-gap
semiconductor, in which electrons and holes behave like Dirac fermions due to
the linear dispersion in the vicinity of the six corners of the Brillouin zone, where
valence and conduction bands touch upon.
Despite some concern raised about the stability of suspended monolayers owing
to the theoretical prediction that a 2D lattice is unstable upon thermal fluctuations
[66, 67], graphene was synthesized in 2004 by K. Novoselov and A. Geim [68],
who managed to cleave out single-atom-thick crystallites from bulk graphite. Due
to its properties, graphene finds application in a variety of fields, including electronic
devices (transistors, sensors, batteries, transparent conductive coatings for solar
cells, OLEDs, high frequency devices), nanocomposites (to make lighter aircraft,
or embedded in plastics to conduct electricity, or again in sports equipment) or
in medicine (such as in artificial cell membranes). Thus, despite the difficulties in
synthesizing high-quality large-area graphene sheets [46, 49, 50], its great promises
and achievements in the fields of materials science motivate the large scientific and
technological efforts that the scientific community is pursuing.
Nevertheless, the importance of graphene goes beyond its own specific characteristics, as it represents the paradigm of a new class of bi-dimensional materials
obtained from layered structures, such as transition metal dichalcogenides (TMDs)
[69], silicene [70], germanene, the monolayer form of black phosphorous [71, 72]
and boron nitride.
In this section, due to the large amount of reviews [4] and books [73] on the
physics of graphene, we will only use graphene as a fundamental texture to deal
with some novel carbon allotropes at lower density. In particular, we discuss the
possibility to introduce interesting features in bi-dimensional all-carbon materials,
keeping the planar structure and the sp 2 -net of graphene. In this regard, one of the
155
atoms, n = 3 are the internal degrees of freedom per atom and k B is the Boltzmann
constant. Since in the SuMBE approach the rotational and vibrational degrees of
freedom of C 60 result frozen, the second term in the left-hand side of Eq. 5.3 can be
neglected. Assuming σ f of the order of the mechanical strength of carbon nanotubes
[58] (50 GPa), the threshold kinetic energy of C 60 breakup would be estimated
40 eV. This value is in good agreement with our ab initio nonadiabatic simulations.
5.3 2D Carbon-Based Materials: Graphene and Its
Low-Density Allotropes
The large interest expressed over the last decade in graphene, the bi-dimensional
allotropic form of carbon, is largely determined by the honeycomb-shaped sp 2
carbon net from which it derives its unique electronic and mechanical properties
[11, 12, 18, 47, 48, 59–65], such as unexpectedly high opacity for a thin atomic
monolayer, high electron mobility at room temperature, with reported values in
excess of 15,000 cm 2 V −1 s −1 , and breaking strength over 100 times bigger than
a hypothetical steel film of the same thickness [4]. Furthermore, pristine graphene
differs from most three-dimensional materials being a semimetal or a zero-gap
semiconductor, in which electrons and holes behave like Dirac fermions due to
the linear dispersion in the vicinity of the six corners of the Brillouin zone, where
valence and conduction bands touch upon.
Despite some concern raised about the stability of suspended monolayers owing
to the theoretical prediction that a 2D lattice is unstable upon thermal fluctuations
[66, 67], graphene was synthesized in 2004 by K. Novoselov and A. Geim [68],
who managed to cleave out single-atom-thick crystallites from bulk graphite. Due
to its properties, graphene finds application in a variety of fields, including electronic
devices (transistors, sensors, batteries, transparent conductive coatings for solar
cells, OLEDs, high frequency devices), nanocomposites (to make lighter aircraft,
or embedded in plastics to conduct electricity, or again in sports equipment) or
in medicine (such as in artificial cell membranes). Thus, despite the difficulties in
synthesizing high-quality large-area graphene sheets [46, 49, 50], its great promises
and achievements in the fields of materials science motivate the large scientific and
technological efforts that the scientific community is pursuing.
Nevertheless, the importance of graphene goes beyond its own specific characteristics, as it represents the paradigm of a new class of bi-dimensional materials
obtained from layered structures, such as transition metal dichalcogenides (TMDs)
[69], silicene [70], germanene, the monolayer form of black phosphorous [71, 72]
and boron nitride.
In this section, due to the large amount of reviews [4] and books [73] on the
physics of graphene, we will only use graphene as a fundamental texture to deal
with some novel carbon allotropes at lower density. In particular, we discuss the
possibility to introduce interesting features in bi-dimensional all-carbon materials,
keeping the planar structure and the sp 2 -net of graphene. In this regard, one of the