Optimizing the thermoelectric performance of zigzag and chiral carbon nanotubes
© Tan et al; licensee Springer. 2012
Received: 5 November 2011
Accepted: 11 February 2012
Published: 11 February 2012
Using nonequilibrium molecular dynamics simulations and nonequilibrium Green's function method, we investigate the thermoelectric properties of a series of zigzag and chiral carbon nanotubes which exhibit interesting diameter and chirality dependence. Our calculated results indicate that these carbon nanotubes could have higher ZT values at appropriate carrier concentration and operating temperature. Moreover, their thermoelectric performance can be significantly enhanced via isotope substitution, isoelectronic impurities, and hydrogen adsorption. It is thus reasonable to expect that carbon nanotubes may be promising candidates for high-performance thermoelectric materials.
As it can directly convert waste heat into electric power, thermoelectric material is expected to be one of the promising candidates to meet the challenge of energy crisis. The performance of a thermoelectric material is quantified by the dimensionless figure of merit , where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature, and κe and κp are the electron- and phonon-derived thermal conductivities, respectively. An ideal thermoelectric material requires glass-like thermal transport and crystal-like electronic properties , i.e., one should try to improve the ZT value by increasing the power factor [S2σ] and/or decreasing the thermal conductivity (κ = κe + κp) at an appropriate temperature. Such a task is usually very difficult since there is a strong correlation of those transport coefficients according to the Wiedemann-Franz law . Low-dimensional or nanostructure approaches [3, 4], however, offer new ways to effectively manipulate electron and phonon transports and thus can significantly improve the ZT value.
As an interesting quasi-one-dimensional nanostructure with many unusual properties, carbon nanotubes [CNTs] have attracted a lot of attention from the science community since their discovery . However, few people believe that CNTs could be promising thermoelectric materials. This is probably due to the fact that although CNTs can have much higher electrical conductivities, their thermal conductivities are also found to be very high [6–11]. As a result, the ZT values of CNTs predicated from previous works [10, 12] are rather small (approximately 0.0047). Prasheret al.  found the so-called 'CNT bed' structure could reduce the thermal conductivity of CNTs. However, the random network of the samples may weaken the electronic transport, and the room temperature ZT value is estimated to be 0.2. Jiang et al.  investigated the thermoelectric properties of single-walled CNTs using a nonequilibrium Green's function approach [NEGF]. They found that CNTs exhibit very favorable electronic transport properties, but the maximum ZT value is only 0.2 at 300 K. The possible reason is the neglect of nonlinear effect  in the phonon transport, and the corresponding thermal conductivity was overestimated. If the thermal conductivity can be significantly reduced without many changes to their electronic transport, CNTs may have very favorable thermoelectric properties. In this work, we use a combination of nonequilibrium molecular dynamics simulations and NEGF method to study the thermoelectric properties of a serial of CNTs with different diameters and chiralities. They are the zigzag (7,0), (8,0), (10,0), (11,0), (13,0), (14,0) and the chiral (4,2),(5,1), (6,2), (6,4), (8,4), (10,5), and all are semiconductors in their pristine form. By cooperatively manipulating the electronic and phonon transports, we shall see that these CNTs could be optimized to exhibit much higher ZT values by isotope substitution, isoelectronic impurities, and hydrogen adsorption. It is thus reasonable to expect that CNTs may be promising candidates for high-performance thermoelectric materials.
The phonon transport is studied using the nonequilibrium molecular dynamics [NEMD] simulations as implemented in the LAMMPS software package (Sandia National Laboratories, Livermore, CA, USA). The Tersoff potential  is adopted to solve Newtonian equations of motion according to the Müller-Plathe algorithm  with a fixed time step of 0.5 fs. We carry out a 300-ps constant temperature simulation and a 200-ps constant energy simulation to make sure that the system has reached a steady state. The nanotubes are then divided into 40 equal segments with periodic boundary condition, and the first and twenty-first segments are defined as the hot and cold regions, respectively. The coldest atom in the hot region and the hottest one in the cold region swap their kinetic energies every hundreds of time steps, and then temperature gradient responses and thermal flux maintain via atom interactions in neighboring segments [19, 20]. The electronic transport is calculated using the NEGF method as implemented in the AtomistixToolKit code (Quantum Wise A/S, Copenhagen, Denmark) [21, 22]. The nanotube is modeled by a central part connected by the left and right semi-infinite one. We use the Troullier-Martins nonlocal pseudopotentials  to describe the electron-ion interactions. The exchange-correlation energy is in the form of PW-91 , and the cutoff energy is set to be 150 Ry. We use a double ζ basis set plus polarization for the carbon atoms, and the Brillouin zone is sampled with 1 × 1 × 100 Monkhorst-Pack meshes. The mixing rate of the electronic Hamiltonian is set as 0.1, and the convergent criterion for the total energy is 4 × 10-5eV.
Results and discussions
Summary of the NEMD-calculated room temperature κp of a series of zigzag and chiral nanotubes
It should be mentioned that we have used the term 'conductivity' for the phonon transport but 'conductance' for the electronic transport. To avoid arbitrary definition of cross-sectional area in low-dimensional system such as CNTs, we rewrite the figure of merit as , where the phonon-induced thermal conductance (λp) has been used to replace the original thermal conductivity(κp). Figure 3d shows the chemical potential dependent ZT value at 300 K for the (10,0) and (6,4) tubes. We see that both of them exhibit two peak values around the Fermi level, which suggest that by appropriate p-type and n-type doping, one can significantly enhance the thermoelectric performance of CNTs. For the (10,0) tube, the maximum ZT value is found to be 0.9, and it appears at μ = ± 0.40 eV. In the case of (6,4) tube, the ZT value can be optimized to 1.1 at μ = ± 0.44 eV. The same doping level for the p-type and n-type doping in the (10,0) or (6,4) tubes is very beneficial for their applications in real thermoelectric devices.
A similar improvement of the thermoelectric performance can be achieved by hydrogen adsorption on the (10,0) tube. As shown in Figure 6b, two hydrogen atoms are chemisorbed on top of a C-C bond along the tube axis, and the product has a concentration of C40H2. Our calculated results indicate that such hydrogen adsorption causes deformation of the (10,0) tube and reduces both the phonon- and electron-induced thermal conductance while keeping the S2G less affected. For example, the calculated λp at 600 K is 0.072 nW/K, which is much lower than that found for the pristine (10,0) tube (0.21 nW/K). The calculated λe also decreases from 0.089 to 0.062 nW/K. At the same time, we find that the S2G of the chemisorbed product (9.47 × 10-13 W/K2) is slightly lower than that of the pristine (10,0) tube (1.28 × 10-12 W/K2). As a result, the calculated ZT value at 600 K increases significantly from 2.6 to 4.2 which is even higher than the highest value of the pristine (10,0) tube. The chemisorptions of hydrogen also increase the ZT value at other temperatures, as indicated in Figure 6c. It is interesting to note that the temperature-dependent behavior almost coincides with that from Si doping, especially in the temperature region from 400 to 700 K.
In summary, our theoretical calculations indicate that by appropriate n-type and p-type doping, one can obtain much higher ZT values for both the zigzag and armchair CNTs, and those tubes with an intermediate diameter (0.7 to 0.8 nm) seems to have better thermoelectric properties than others. With the zigzag (10,0) as an example, we show that the phonon-induced thermal conductance can be effectively reduced by isotope substitution, isoelectronic impurities, and hydrogen adsorption, while the electronic transport is less affected. As a result, the ZT value can be further enhanced and is very competitive with that of the best commercial materials. To experimentally realize this goal, one needs to fabricate CNTs with specific diameter and chirality, and the tube length should be at least 1 μm. This may be challenging but very possible, considering the fact that the (10,0) tube was successfully produced by many means, such as by direct laser vaporization , electric arc technique , and chemical vapor deposition , and can be selected from mixed or disordered samples using a DNA-based separation process .
This work was supported by the '973 Program' of China (grant no. 2007CB607501), the National Natural Science Foundation (grant no. 51172167), and the Program for New Century Excellent Talents in the University. We also acknowledge the financial support from the inter-discipline and postgraduate programs under the 'Fundamental Research Funds for the Central Universities'. All the calculations were performed in the PC Cluster from Sugon Company of China.
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