Joule heating in single-walled carbon nanotubes (CNTs) using a quantum mechanical approach is presented in this paper. The modeling is based on the energy transfer between the electrons and both acoustic and optical phonons. In this formulation, only the knowledge of the full energy dispersion relation, phonon dispersion relation, and the electron-phonon coupling potential is required for the calculations. For verification of the proposed model, the current-voltage relation for extremely long nanotubes is calculated and the results are compared with the experimental data. The electric field dependence of the amount of energy generated by Joule heating is plotted. Moreover the effect of the thermal environment on the behavior of Joule heating is studied. The formulation proposed in this paper can also be used for structures other than CNTs. Computations indicate that, contrary to popular opinion, metallic CNT does not follow Joule’s law of $P=IV$ . Joule heating in CNT is significantly less than what is predicted with Joule law $\left(P=IV\right)$ , which would make it a perfect candidate to replace copper as interconnect material in electronics.

Using molecular dynamics (MD) simulations, the frictional properties of the interface between graphene nanoflake and single crystalline diamond substrate have been investigated. The equilibrium distance between the graphene nanoflake and the diamond substrate has been evaluated at different temperatures. This study considered the effects of temperature and relative sliding angle between graphene and diamond. The equilibrium distance between graphene and the diamond substrate was between 3.34 Å at 0 K and 3.42 Å at 600 K, and it was close to the interlayer distance of graphite which was 3.35 Å. The friction force between graphene nanoflakes and the diamond substrate exhibited periodic stick-slip motion which is similar to the friction force within a graphene–Au interface. The friction coefficient of the graphene–single crystalline diamond interface was between 0.0042 and 0.0244, depending on the sliding direction and the temperature. Generally, the friction coefficient was lowest when a graphene flake was sliding along its armchair direction and the highest when it was sliding along its zigzag direction. The friction coefficient increased by up to 20% when the temperature rose from 300 K to 600 K, hence a contribution from temperature cannot be neglected. The findings in this study validate the super-lubricity between graphene and diamond and will shed light on understanding the mechanical behavior of graphene nanodevices when using single crystalline diamond as the substrate.