Comparison of Green–Kubo and NEMD heat flux formulations for thermal conductivity prediction using the Tersoff potential

The phonon-based thermal conductivity of graphene sheets is estimated using equilibrium and non-equilibrium molecular dynamics simulations. Different possible heat flux formulations, as a result of using the three-body Tersoff potential, have been examined to calculate the thermal conductivity by using equilibrium molecular dynamics (EMD) with Green–Kubo relations. Non-equilibrium molecular dynamics (NEMD) simulations are also performed to compare the heat flux formulations. We have found that the selected heat flux formulation has a prominent impact on the calculated thermal conductivity. A heat flux formulation choice is recommended that best maintains consistency between applied and calculated heat flux values in NEMD simulations.

• Different possible heat flux formulations were compared when the Tersoff potential is used. • Non-equilibrium molecular dynamics were performed to test each formulation and examine their consistency and accuracy. • Thermal conductivity of graphene in both zigzag and armchair directions were calculated using each formulation. • The best heat flux formulation was specified by comparing the steady state heat flux values with that of NEMD simulation.