arXiv:1409.5342v1 [cond-mat.mtrl-sci] 18 Sep 2014 Thermal rectification of a single-wall carbon nanotube: a molecular dynamics study Azadeh Saeedi 1 , Farrokh Yousefi 1 , Saeed Khadesadr 3 and M. Ebrahim Foulaadvand 1,2 1 Department of Physics, University of Zanjan, P. O. Box 313, Zanjan, Iran 2 School of Nano-science, Institute for Research in Fundamental Sciences (IPM) , P.O. Box 19395-5531, Teheran, Iran 3 Department of Physics, Tarbiyat Moddares University, P. O. Box 14115-111, Teheran, Iran (Dated: September 24, 2018) We have investigated the thermal rectification phenomenon in a single-wall mass graded carbon nanotube by molecular dynamics simulation. Second generation Brenner potential has been used to model the inter atomic carbon interaction. Fixed boundary condition has been taken into account. We compare our findings to a previous study by Alaghemandi et al [18] which has been done with a different potential and boundary condition. The dependence of the rectification factor R on temperature, nanotube diameter and length as well as mass gradient are obtained. It is shown that by increasing the temperature, the rectification decreases whereas by increasing the other parameters namely the mass gradient, diameter and the tube length it increases. PACS numbers: I. INTRODUCTION Rectifcation is a transport process that takes place faster in one direction than in the opposite one. This phenomenon has attracted much attention in recent years [1]. In electronics this phenomenon has been used exten- sively in ubiquitous devices such as diodes and electric rectifiers [2, 3]. The phenomenon of rectification is not restricted to electronic flow. In 1970 it was experimen- tally shown that rectification can occur in thermal cur- rent. For detailed review on thermal rectification in solid state physics see [4]. Recently the process of thermal rectification of heat flow has been detected in nano-sized materials. It has been empirically shown that exter- nally mass-loaded carbon and boron nitride nanotubes are capable of exhibiting thermal rectification [5]. The empirical findings of Chang et al have stimulated the interest of theoreticians on the issue of thermal rectifi- cation [5]. Thermal property of nanoscale materials is also important both for fundamental physical theory as well as as for applications [6]. In recent years, different carbon nanotubes (CNT) [5, 7–10] and Graphene Nano Ribbon (GNR) [11–13] structures have been proposed as candidates for thermal rectifers [14]. These nano-sized carbon-based materials would have deep implications in thermal energy control such as on-chip cooling, high ef- ficiency energy conversion and other phononics applica- tions. Li and co-workers could theoretically show that thermal rectification appears in a one-dimensional (1D) chain with non linear interaction among the masses [14] and also in a mass-graded monoatomic chain interacting through the Fermi-Pasta-Ulam (FPU) potential [15, 16]. The anharmonicity is the key feature which leads the thermal rectification in these one dimensional model sys- tems. In fact the overlap of the vibrational spectra at the two ends of the chain is the reason for the existence of the thermal rectification. Recently Alaghemandi et al have executed extensive simulation and have shown that mass graded single-walled carbon nanotubes (SWCNTs) exhibit thermal rectification [17–19]. They have stud- ied the dependence of rectification on the tube diame- ter, length, mass gradient and temperature. According to their results, rectification magnitude increases with increasing the CNT diameter as well as the mass gradi- ent. Moreover, they showed that the rectification magni- tude decreases when the temperature is enhanced. They have used reverse non-equilibrium molecular dynamics [20]. The interaction potential between carbon atoms is adopted from a mechanical viewpoint and includes ra- dial harmonic, angular and torsion terms [21]. In this paper we study the thermal rectification of a SWCNT with the reactive empirical bond order (REBO) interac- tion potential [22] between carbon atoms and find the differences/similarities of our results with those found by Alagemandi et el. II. METHODOLOGY We have used classical non equilibrium molecular dy- namics (NEMD) simulation to calculate the thermal con- ductivity of an armchair single-wall carbon nanotube (SWCNT). The interaction between two carbon atoms C- C is modelled by the second-generation reactive empirical bond order (REBO) potential [22]. Simulations were per- formed using the LAMMPS package [23]. The velocity Verlet method was employed to integrate the equations of motion with a time step of one femto second. First, the entire nanotube is coupled to a Nos´ e-Hoover thermostat at temperature T and MD is performed to equilibrate and relax the system for 1 ns. After equilibrium, we fix the atoms of one unit cell (two rings) of carbon atoms from each end of the CNT. The third unit cell from each end is coupled to a Nose-Hoover thermostat. The second unit cell is not connected to a thermostat in order to sup- press the phonon reflection from edges. The hot (cold) reserviour temperature is set to T +ΔT (T − ΔT ) re- spectively. In our simulations we have taken ΔT = 10 K . See figure (1) for illustration. We then perform a run for 10 ns. As a result of cou-