Volume 13 Issue 7 - April 23, 2010 PDF
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Molecular Dynamics Study of Thermal Conductivity of Carbon Nanotubes
C. H. Wu1 and Jang-Yu Hsu*1,2,3
  1. Department of Physics, National Cheng Kung University, Tainan, Taiwan
  2. Institute of Space, Astrophysical and Plasma Sciences, National Cheng Kung University, Tainan, Taiwan
  3. Department of Engineering and System Sciences, National Tsing Hua University, Hsinchu, Taiwan
 
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Scientific computing, especially modeling and simulation, can be an important part of knowledge creation. Observation - to see is to believe, enables scientists to make scientific discovery and to understand nature more deeply. The visualization in computation can help uncover the underlying physical principles which otherwise could be difficult or expensive to do in nature or in the lab, but can be carried out in the computer. Due to the nature of multi-scales and multi-sciences of nanobio research, computer simulation is becoming increasingly important, as evidenced from these biomedical terms: the in-vivo (inside the biological system), the in-vitro (inside the lab) and the in-silico (inside the silicon chip).

After the discovery of carbon nanotube (CNT) in 1991, the race to develop products of nanotechnology has begun. CNT belongs to the carbon family that can be large, complex, and diverse with the famous members such as the fullerene, the graphene and the diamond. Carbon atoms are the most versatile building blocks of molecules, and their molecular diversity has made possible the diversity of living beings that have evolved on Earth for 3.5 billion years.

Figure 1. The armchair CNT of chiral vector (10, 10) and the model of measuring the thermal conductivity. The red atoms on the left hand side are kept at a high temperature and the blue on the right at a low temperature.
In this work, we primarily focus on the single walled carbon nanotube (SWNT) and apply the molecular dynamics (MD) simulation to study its thermal conductivity. The single-walled carbon nanotube is basically constructed from a rolled-up graphene sheet. How the graphene sheet is rolled up would make different chiral types such as the armchair (cf. Figure 1), or zigzag CNTs. The physical and chemical properties of CNTS are of great interest to scientists for their many potential applications, such as the space ladder proposed by NASA and to be attempted by Japan as well, the field emission transistor (FET), and the cantilever of the atomic force microscopy, not to mention the tennis racket that is supposed to make the tennis player all mighty powerful.

Thermal conductivity of CNT was studied by experiments and MD simulations. The subject is still an open question in that there appears to have two camps of results. One camp has the thermal conductivity on the order of thousands of W/mK, the other at hundreds of W/mK, almost one order of magnitude smaller. Both camps have experimental observations, MD simulations, and theoretical calculations. As it is not an easy task to identify or to select the tube chirality in experiments, to compare the experimental results with simulations to a greater quantitative precision is out of the question. While in the MD simulation, it is easier to select a CNT to measure its characteristics, the tube length is, however, restricted by the computing capability. Many MD simulations have the tube length much shorter than those in experiments. Therefore, they simulate in the ballistic regime with the thermal transport limited by the boundary effect of its length.

Figure 2. The phonon density of states of SWNT (10, 10) at temperature 300 K.
When carrying out the molecular dynamics simulation, we need the interaction potential among the bonding carbon atoms. The exact description would be a quantum mechanical approach. It can, however, be rather expensive and time consuming. Therefore, an empirical Tersoff potential is applied which has been tested and shown time and again to be amazingly agreeable with the experimental data. For nonbonding interactions between carbon atoms, Lennard-Jones potential can be used. We also need to control the temperature by a thermal reservoir. It is, in principle, an easy task to do as any physics undergraduate would understand the underlying mechanism. It is to equilibrate with a huge number of particles with the energy distribution in a canonical ensemble at a specific temperature. It turns out that the Monte Carlo method is applicable and no need to keep reservoir particles in the computer memory but to sample them as needed on the fly. There is, however, the real challenge to define the precise temperature from the absolute zero Kelvin and up. For this, we have to include the quantum mechanical effect by applying the phonon (Boson) statistics to the specific heat. The phonon density of states (cf. Figure 2) must be calculated to take the measure of the internal energy so to determine the specific heat accordingly. Moreover, we need to exact the heat source and heat sink in order to obtain the heat transfer coefficient. This is achieved by carefully monitoring the energy exchange between the reservoir particles and the atoms of the CNT at the two ends (Figure 1).

At low temperature, the CNT thermal conductivity increases with increasing temperature. After reaching its peak that is limited by the length of CNT, it decreases with temperature due to the phonon-phonon interactions. The scaling law of thermal conductivity as function of temperature and length is inferred from the simulation results, allowing predictions for CNTs of much longer length beyond what MD could simulate.

About the authorThe research team is the First Principle Group ( http://fpg.phys.ncku.edu.tw/~jyhsu/FPG/fpg.html ) working on nanoscience and plasma physics from the first principles. Michael Wu finished his undergraduate study of physics at NCKU and is right now serving in the military. He plans to continue his higher education abroad. James Hsu has just published his book: Nanocomputing – Computational Physics for Nanoscience and Nanotechnology ( http://www.panstanford.com/books/nanosci/v014.html ). He chairs the Conference on Computational Physics 2009 ( http://www.ccp2009.tw/Invitation.asp ), which will be held on December 16-19 in Kaohsiung, Taiwan, and welcomes computational scientists to attend.
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