Studies of Thermal Conductivity in Carbon Nanotubes Using Simulation

 

Sunil H. Ganatra*, Sneha D. Khobragade, Anushree S. Ujjankar, Chudaman D. Pourkar

Department of Chemistry, Institute of Science, R. T. Road, Nagpur – 440001, M.S. India

*Corresponding Author E-mail: sunilganatra@gmail.com

 

 

 

1. INTRODUCTION:

Carbon nanotubes were discovered in 1991 by Iijima of NEC Corporation.[1] Since then, efforts in synthesis, characterization and theoretical investigation on nanotubes has grown exponentially. This is due to their novel mechanical, electronic properties and tremendous potential for future technological applications. In 1993, the simplest kind of carbon nanotube i.e. single walled carbon nanotubes (SWNTs) were discovered independently by Iijima group and an IBM team headed by Bethune [2].  These SWNTs can be regarded as a rolled-up graphite sheet in the cylindrical form. Some specific defect-free forms of these SWNT show remarkable mechanical properties and metallic behaviour [1,2].

 

The Nano Heat Flow Tool [3] allows users to explore the time evolution of kinetic and potential energy among the vibrational modes of a carbon nanotube over the course of a molecular dynamics (MD) simulation. It is possible to observe the drop of vibrational energy through the modes of the system as a non-equilibrium population of phonons is dissipated towards thermal equilibrium, and thus gives insight into the basic sources of damping and dissipation within nanoscale objects.

 

 Figure 1: Nano Vibrational Modes in Swnts.

 

Material and Methods:

Molecular Dynamics calculations were performed using Large-scale atomic/molecular massively parallel simulator  LAMMPS on carbon nanotubes using online parallel processing computers (nanohub.org) [3] to understand the heat flow in C(6,0), C(6,3) and C(6,6). The nanotube coordinates were generated by Tube Gen Online software [4,5]. Micro canonical ensemble used to perform classical MD simulation of selected nanotubes. The initial conditions for the experiment restricted to the excitation of single vibrational modes of low frequency [6,7,8].

 

The simulations were performed on NanoHub [3] with Nano Heat Flow Tools. All tubes were tested for heat flow along the tube using LAMMPS. Simulations for all three tubes were performed separately with same basic parameters. [9,10,11] as listed in Table 1.

Table 1. : MD simulation Input Parameters

Parameter Name	Value	Remark
Type of Nanotube	C(6,0) : Zigzag C(6,6) : Armchair  C(6,3) : Chiral	One type at a time. In total three simulations performed for each type of tube.
Nanotube Unit Cells	2
Temperature	298.15 K
Number of Steps	20000	Number of steps of MD simulation.
Step Size	0.2 fs	Time period for each step size.
Vibrational Mode	First Longitudinal

 

 

Table 2 : The peak of energy / frequency graph for C(6,0) type Carbon Nanotube

Sr.No.	Energy	Frequency (THz)
1	0.060919	22.39164
2	0.080844	22.72093
3	0.11228	23.05022
4	0.165961	23.37951
5	0.268303	23.7088
6	0.497221	24.03809
7	1.139402	24.36738
8	3.062294	24.69667
9	2.794253	25.02596
10	1.0292	25.35524
11	0.461296	25.68453
12	0.253395	26.01382
13	0.158543	26.34311
14	0.108098	26.6724
15	0.078267	27.00169
16	0.059224	27.33098
17	0.046348	27.66027
18	0.037245	27.98956

 

Table 3 : The peak of energy / frequency graph for C(6,6) type Carbon Nanotube

Sr.No.	Energy	Frequency (THz)
1	0.05045	36.27509
2	0.06663058	36.63073
3	0.09196963	36.98637
4	0.1348236	37.34201
5	0.2155027	37.69765
6	0.3932584	38.05328
7	0.8891345	38.40892
8	2.591741	38.76456
9	3.064494	39.1202
10	1.056946	39.47584
11	0.4453835	39.83148
12	0.2367583	40.18711
13	0.1453171	40.54275
14	0.09786072	40.89839
15	0.070249	41.25403
16	0.052824	41.60967
17	0.041143	41.9653
18	0.032938	42.32094

 

Table 4 : The peak of energy / frequency graph for C(6,3) type Carbon Nanotube

Sr.No.	Energy	Frequency (THz)	Frequency Range (THz)
1	3.606208	19.77989	16.6567 –22.9030
2	1.992325	9.716438	7.2872­ ­– 11.1045
3	1.305825	39.21277	36.7836 – 41.6418
4	1.136508	28.45528	26.7202 –30.5373
5	0.7431926	56.91056	55.5225 – 57.6047
6	0.7148732	58.29863	57.6046 – 60.3807
7	0.403017	49.27622	47.8881 – 50.6642
8	0.308775	12.1455	11.4515 – 13.1865
9	0.2553308	32.27245	31.2314 – 32.9664
10	0.2066284	66.627	65.5859 – 69.0561
11	0.1551181	54.82847	53.7874 – 55.5225
12	0.1447582	61.07475	60.0337 – 62.1158
13	0.1147414	64.19789	63.5038 – 65.2389
14	0.111506	52.39936	51.7053 – 53.4401

 

Results:

The MD simulations were executed and the heat flow values in the form of energy (on arbitrary scale) against the frequency were calculated. The reported values for C(6,0), C(6,6) and C(6,3) nanotubes are shown in Table 2,3 and 4 respectively. Table 5 shows the highest energy values at specific frequencies for C(6,0), C(6,6) and C(6,3)  types of Carbon nanotubes at 298.15 K.

 

The variations of Eigen value frequency in THz were studied for various vibration modes for all three types of carbon nanotubes.  Figure 3 shows the variation of Eigen value frequency in graphical form. It was clearly observed that C(6,0) and C(6,6) represents the uniform phenomenon, whereas C(6,3) shows highly diverse phenomenon.

 

Figure 4, 5 and 6 shows the 3D graphical representation of time scale variation of Energy Vs Frequency for C(6,0), C(6,6) and C(6,3) Carbon nanotube.

 

 

Table 5 : The Highest Energy Values at a specific frequency for various types of Carbon Nanotubes at 298.15 K.

Sr. No.	Nanotube Type	No. of Peaks	Highest Energy Peak	Frequency (THz)	Range of Frequency for peak energy
1	C(6,0)	1	3.062294	24.69667	22.39164– 27.98956
2	C(6,6)	1	3.064494	39.1202	36.27509– 42.32094
3	C(6,3)	14	3.606208	19.77989	16.6567 –22.9030

 

 

Figure 2 shows the variation of frequencies with energy for C(6,0), C(6,6) and C(6,3)  types of Carbon nanotubes at 298.15 K.

 

Figure 2 : Variation of frequencies with energy at 298.15 K.

 

 

fig. 3 : variation of Eigen value verses vibrational mode number.

 

fig. 4 :  3D Time scale variation of energy vs frequency for c(6,0)

 

Fig. 5 :  3D Time Scale Variation of Energy Verses Frequency For C(6,6)

 

Fig. 6 :  3D Time Scale Variation of Energy Verses Frequency For C(6,3)

 

 

Conclusion:

The selected nanotubes i.e. C(6,0), C(6,3) and C(6,6) show the thermal conductivity at various frequencies.  The surprise results for C(6,0) and C(6,6); where the frequency  is highly selective and having single peak. Whereas, in case of C(6,3) various frequency peaks are reported and spread in wide spectrum. 

 

The C(6,0) and C(6,6) shows heat energy at 25 THz and 38 THz respectively. Only single peak is observed in these types of nanotubes. This uniqueness is due to their structure arrangement. Whereas C(6,3) shows heat energy at various levels. There are number of peaks at 10, 20, 28, 38, 48 THz frequency with single peak and 58 THz with shoulder.  This is again due to the structure arrangement of carbon in  C(6,3) structure. The heat flow in this case of carbon tube is with multiple frequencies and spread widely on frequency band. 

 

The conclusion is also confirmed from the figure 4,5 and 6 showing the time scale variation of Energy Vs Frequency. In case of  C(6,0)  and  C(6,6) the frequency is uniformed whereas in C(6,3) the frequency is varied with energy.

REFERENCE:

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Received on 28.03.2012         Modified on 05.04.2012

Accepted on 15.04.2012         © AJRC All right reserved