Estimating the Thermal Conductivities and Elastic Stiffness of Carbon Nanotubes as a Function of Tube Geometry

Z H Zhang,N Yu,W H Chao

doi:10.1155/2012/939806

Abstract

The thermal conductivities and elastic properties of carbon nanotubes (CNTs) are estimated by using the double-inclusion model, which is based on rigorous elasticity approach. The model regards a CNT as one inclusion (the inner cylindrical void) embedded in the other (the outer coaxial single-crystal graphite shell). The concept of homogenization is employed, and vital microstructural parameters, such as CNT diameter, length, and aspect ratio, are included in the present model. The relationship between microstructure and thermal conductivities and elastic stiffness of CNTs is quantitatively characterized. Our analytical results, benchmarked by experimental data, show that the thermal conductivities and elastic stiffness of CNTs are strongly dependent on the diameter of CNT with little dependence on the length of CNT.

Highlights

The present work employs and modifies the double-inclusion model [1] to estimate, from a microstructural point of view, the thermal conductivities and elastic stiffness of carbon nanotubes (CNTs)
The predicted axial Young’s modulus increases with a decrease in CNT diameter, which is consistent with the available experimental data, yet is in contrast with what is predicted by Li and Chou [18]
The double-inclusion model [1], which is based on elasticity solutions [20, 21] and is originally presented in the context of linear elasticity, is employed and extended to predict the thermal conductivities and elastic constants of CNTs

Summary

Introduction

The present work employs and modifies the double-inclusion model [1] to estimate, from a microstructural point of view, the thermal conductivities and elastic stiffness of carbon nanotubes (CNTs). Chantrenne and Barrat [14] derive analytical expressions for the thermal conductivities of a single graphene and a CNT as a function of their characteristic lengths. Their analytical estimates show good agreement for single graphene but not for CNTs. The reported experimental data of thermal conductivities and Young’s and shear moduli of CNTs from literature are summarized in Tables 1 and 2, respectively.

The Model

Results

Conclusion