Figure 3. Steady-state temperature profiles along the length of the
monolayer graphene nanoribbon with substantially smooth edges.
The thermal properties of the graphene nanoribbon with different lengths
are investigated to determine the structure factors limiting the heat
transfer process. The thermal conductivity can conveniently be
determined by the temperature gradient in the direction of heat flow.
The effect of nanoribbon length on the thermal conductivity of the
monolayer graphene nanoribbon is illustrated in Figure 4 with different
transverse edge termination states. The results obtained for both zigzag
edges and armchair edges are presented. Shortened graphene nanoribbons,
as defined herein, refers to, for example, graphene nanoribbons that
have had their aspect ratios reduced by a cutting technique through
their long axis. When not otherwise specified herein, the term shortened
graphene nanoribbons should be interpreted to encompass both oxidized
graphene nanoribbons and reduced graphene nanoribbons that have been
shortened by cutting. Non-limiting means through which cutting can occur
include, for example, mechanically, through application of high shear
forces, through high-energy sonication, or chemically. In some cases,
shortened graphene nanoribbons have aspect ratios of less than about 5.
In other cases, shortened graphene nanoribbons have aspect ratios of
less than about 3, or less than about 2. According to theoretical
predictions, single-atomic and multiple-atomic layer graphene
nanoribbons have a high surface energy that is thought to prevent their
growth directly from the gas phase, even with proper nucleation. The
failure to grow graphene nanoribbons directly from the gas phase is
thought to be due to their tendency either to stack into graphite
crystals or to fold into carbon nanotubes or similar closed structures.
Although a strain energy barrier results from the curvature of the
carbon nanotubes, the strain energy of the carbon nanotubes is less than
the surface energy of the graphene sheets. Hence, carbon nanotubes are a
preferred gas phase reaction product. The transverse edges of the
graphene nanoribbon are substantially smooth. The edge termination state
has little effect on the thermal conductivity, since there is little
difference in thermal conductivity between zigzag-edged and
armchair-edged graphene nanoribbons. However, the thermal conductivity
depends strongly upon the nanoribbon length. More specifically, the
thermal conductivity increases with increasing nanoribbon length due to
the reduced probability of phonon scattering from grain boundaries. This
is because the mean free path of phonons in graphene, which can be up to
700 nanometers at room temperature as noted above, is very large
compared to the dimensions of the graphene nanoribbon. As a result, the
length of the graphene nanoribbon is vital in determining the thermal
conductivity. Consequently, the length of the graphene nanoribbon is an
important factor affecting the thermal properties, and must be taken
into account so as to provide more accurate predictions about the
thermal conductivity.