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.