Molecular Dynamics Simulations of Heat Transfer Issues in Carbon Nanotubes

Several heat transfer problems related to singlewalled carbon nanotubes (SWNTs) are considered through molecular dynamics (MD) simulations. MD simulations of thermal conductivity along a nanotube, isotope effect in longitudinal thermal conductivity, and thermal boundary resistance in a junction of nanotubes are reviewed. Then, the heat transfer from an SWNT to various surrounding materials is simulated by MD simulations. Heat transfer between nanotubes in a bundle of nanotubes and between a nanotube and water are considered. The heat transfer rate can be well expressed by employing the thermal boundary resistance (TBR). The value of thermal boundary resistance is compared for nanotube-junction, bundle, and water-nanotubes cases. INTRODUCTION Single-walled carbon nanotubes (SWNTs) [1] have remarkable electrical, optical, mechanical, and thermal properties [2, 3]. In this paper, the thermal properties and heat transfer issues are considered from molecular dynamics (MD) simulations. We have been studying the heat conduction along a SWNT by MD method [4-7] with the simplified form [8] of Tersoff-Brenner bond order potential [9]. Our preliminary results showed that thermal conductivity was strongly dependent on the nanotube length for realistic length scale for device applications [5, 6]. Furthermore, we have reported the direct calculation of phonon dispersion relations and phonon density of states from molecular dynamics trajectories [5, 6]. For more practical situations, the isotope effect on thermal conductivity and thermal boundary resistance in a nanotube junction were discussed from MD simulation results [7]. In addition to the thermal conductivity along a SWNT, heat transfer from a nanotube to the surrounding material is quite important for the practical applications using carbon nanotubes as electrical devices and composite materials [7]. In this paper, in addition to a review of simulations of thermal conductivity, isotope effect, and thermal boundary resistance of a junction, the heat transfer from an SWNT to various surrounding materials is simulated by MD simulations. Heat transfer between nanotubes in a bundle of nanotubes and between water and a nanotube are considered. The heat transfer rate can be well expressed by the thermal boundary resistance (TBR). The value of thermal boundary resistance is compared for nanotube-junction, bundle, and water-nanotubes cases. SIMULATION TECHNIQUE The Brenner potential [9] with the simplified form [8] is employed as the potential function between carbon and carbon within a nanotube. This potential can describe variety of small hydrocarbons, graphite and diamond lattices. The basic formulation of the potential is based on the covalent-bonding treatment developed by Tersoff [10]. The total potential energy of the system Eb is expressed as the sum of the bonding energy of each bond between carbon atoms i and j.