Reformulation of the Nosé-Hoover thermostat for heat conduction simulation at nanoscale

This paper investigates the heat conduction phenomena at nanoscale by reformulating the Nosé-Hoover thermostat for nonequilibrium molecular dynamics simulation. Inspired by the Nosé-Hoover mechanics, the feedback temperature force caused by the temperature control is reformulated to a more general level, aiming at (1) controlling the temperature locally at several distinct spots and (2) eliminating the rigid-body translation and rotation which are unexpectedly introduced into the system due to the feedback temperature force, so that accurate trajectories of atoms can be generated and the heat conduction simulation at nanoscale can be performed successfully. Correspondingly, the definition of temperature is modified; the expression of the Hamiltonian is generalized. To demonstrate the capability and feasibility of this newly formulated algorithm, we studied heat conduction phenomenon in a beam-like finite size specimen via our in-house developed computer code. The results, temperature distributions across the specimen, are shown to reach steady state after a period of time which cannot be achieved by the original Nosé-Hoover thermostat. Also, it is concluded that the heat conduction at nanoscale exhibits the same feature of Fourier's law at macroscopic scale, namely that the heat flux is linearly proportional to the temperature gradient, if the temperature is averaged over a sufficiently large time interval and large spatial region. The thermal conductivity can thereafter be calculated based on the linear relation between the heat flux and the temperature gradient. It is found that the obtained numerical value of thermal conductivity matches the experimental result very well.