Elsevier

Computational Materials Science

Volume 54, March 2012, Pages 249-254
Computational Materials Science

Prediction of thermal expansion properties of carbon nanotubes using molecular dynamics simulations

https://doi.org/10.1016/j.commatsci.2011.10.015Get rights and content

Abstract

The axial coefficients of thermal expansion (CTE) of various carbon nanotubes (CNTs), i.e., single-wall carbon nanotubes (SWCNTs), and some multi-wall carbon nanotubes (MWCNTs), were predicted using molecular dynamics (MDs) simulations. The effects of two parameters, i.e., temperature and the CNT diameter, on CTE were investigated extensively. For all SWCNTs and MWCNTs, the obtained results clearly revealed that within a wide low temperature range, their axial CTEs are negative. As the diameter of CNTs decreases, this temperature range for negative axial CTEs becomes narrow, and positive axial CTEs appear in high temperature range. It was found that the axial CTEs vary nonlinearly with the temperature, however, they decrease linearly as the CNT diameter increases. Moreover, within a wide temperature range, a set of empirical formulations was proposed for evaluating the axial CTEs of armchair and zigzag SWCNTs using the above two parameters. Finally, it was found that the absolute value of the negative axial CTE of any MWCNT is much smaller than those of its constituent SWCNTs, and the average value of the CTEs of its constituent SWCNTs. The present fundamental study is very important for understanding the thermal behaviors of CNTs in such as nanocomposite temperature sensors, or nanoelectronics devices using CNTs.

Highlights

► Based on MM, we explore the influences of temperature and diameter on CTEs of CNTs. ► We provide a set of empirical formulations to predict CTEs of SWCNTs. ► We find that the CTEs of CNTs depend on temperature nonlinearly, but on diameter linearly. ► We find that a MWCNT is more insensitive to the temperature change compared with its constituent SWCNTs. ► We find that the CTEs of a MWCNT converge with the increase of wall number.

Introduction

Due to their superior mechanical, electrical and thermal properties, carbon nanotubes (CNTs) have many potential applications such as nanoscale sensors, nanocomposites sensors, and nanoelectronics [1], [2], [3], [4], [5], [6], [7]. For instance, for the application of nanocomposite temperature sensors [1], [2] or strain sensors [6], [7], [8], it is necessary to understand the thermal properties of CNTs for developing highly efficient sensors under the different temperature environments. For some other examples of nanoelectronics including the next-generation computers, e.g., [9] and nanotube transistors [10], these CNT-based nanoelectronic devices may experience high temperature during manufacture and operation. This leads to thermal expansion and residual stress in devices, and affects the device reliability. Therefore, the coefficient of thermal expansion (CTE) of CNTs is a key property for CNT-based nanoelectronics. At present, accurately evaluating CTE using experimental methods still suffers from size restrictions and measurement limitations. Therefore, computational methods, e.g., molecular dynamics (MD) simulations, prove to be an ideal tool to evaluate the CTEs. Up to date, there have been some limited theoretical or numerical predictions on the CTE of single-wall carbon nanotubes (SWCNTs). For instance, an analytic method [11] to determine the CTE of SWCNTs directly from the inter-atomic potential and the local harmonic model was developed to evaluate the CTE of SWCNTs. Based on MD simulations, in [12], [13], the CTE of SWCNTs was also studied. The influence of temperature has been mainly investigated in the above stated previous studies [11], [12], [13]. Both the axial and radial CTEs of SWCNTs have been explored. It was found that similar to Si, the axial CTE of SWCNTs displays an unusual and intriguing temperature dependence, namely being negative (i.e., thermal contraction) at low temperature, and positive (i.e., thermal expansion) at high temperature. However, due to the limitation of computational cost, only some representative SWCNTs of very small diameters have been studied, and the influence of the diameter of CNTs on the CTE of CNTs has not been studied extensively. Moreover, for the case of multi-wall carbon nanotubes (MWCNTs), the influence of the number of walls on the CTEs has not been explored to the present authors’ best knowledge although MWCNTs are much more widely used in the various applications compared with SWCNTs.

In this work, the CTE of CNTs was studied by using MD. We focused on the axial CTE of CNTs since the aspect ratios of CNTs are usually very high which leads to the much higher importance of the axial CTE of CNTs compared with the radial CTE of CNTs. In this paper, besides the influence of temperature on the CTE of CNTs, we also extensively explored the influence of the diameter and the number of walls of CNTs on the axial CTE.

Section snippets

MD simulations

To investigate the axial CTE of various CNTs, the direct MD simulations were carried out using the Materials Studio (Accelrys). For the case of MWCNTs, the wall spacing of any MWCNT model was given by 0.34 nm, which is close to the interlayer distance in graphite. The Lennard–Jones potential with a cut-off distance of 0.95 nm was used to describe the van der Waals (vdW) interaction among walls as used in our previous studies [14], [15], [16], [17], [18] and the electrostatic Coulombic interaction

Verification

Firstly, to verify the effectiveness of our approach for predicting the CTE of CNTs, a zigzag SWCNT(9, 0) used in some previous studies [11], [13] was employed as an example. The obtained results are demonstrated in Fig. 2 compared with other two results [11], [13]. From this figure, it can be found that the present result is just located between the previous two results, and possesses the similar variation trend with temperature. There is a negative CTE for the present and previous results [11]

Summary

In this work, we investigated the axial CTEs of various CNTs, e.g., SWCNTs and MWCNTs, by using MD simulations. It was found that the axial CTEs of CNTs are negative in a wide low temperature range, and vary nonlinearly with the temperature. These axial CTEs may become positive as the temperature increases, especially for those SWCNTs and MWCNTs of small diameters of the innermost wall. However, the axial CTEs of SWCNTs and MWCNTs vary linearly with the diameter of the innermost wall. With the

Acknowledgements

This work is partly supported by two Grand-in-Aids for Scientific Research (Nos. 22360044 and 21226004) from the Japanese Ministry of Education, Culture, Sports, Science and Technology. The authors acknowledge Prof. C.B. Fan (Beijing Institute of Technology, China) for kindly providing the computational resources.

References (20)

  • R.S. Ruoff et al.

    Carbon

    (1995)
  • N. Hu et al.

    Acta Mater.

    (2008)
  • N. Hu et al.

    Carbon

    (2010)
  • N. Hu et al.

    Int. J. Solids Struct.

    (2007)
  • Y. Li et al.

    Carbon

    (2010)
  • Y. Li et al.

    Comput. Mater. Sci.

    (2011)
  • M.G. Martin

    Fluid Phase Equilibr.

    (2006)
  • A. Saraiya et al.

    Met.-Org. Nano-Met. Chem.

    (2006)
  • H.C. Neitzert, A. Sorrentino and L. Vertuccio, Epoxy/MWCNT Composite Based Temperature Sensor with Linear...
  • D. Srivastava et al.

    Comput. Sci. Eng.

    (2001)
There are more references available in the full text version of this article.

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