Determination of mechanical properties of carbon nanotubes and vertically aligned carbon nanotube forests using nanoindentation

Abstract

Vertically aligned carbon nanotubes (VACNT) have been a recent subject of intense investigation due to the numerous potential applications of VACNTs ranging from field emission and vacuum microelectronic devices to the creation of super-hydrophobic surfaces and as a source of well defined CNTs. In this paper, a new method to determine the mechanical properties of VACNT and constituent nanotubes using nanoindentation tests is proposed. The study of nanoindentation on a VACNT forest reveals a process whereby nanotubes are consecutively bent during the penetration of the indentor. Therefore, the resistance of a VACNT forest to penetration is due to successive bending of nanotubes as the indentor encounters nanotubes. Using a micro-mechanical model of the indentation process, the effective bending stiffness ( EI) eff of constituent nanotubes in the VACNT array is then deduced from nanoindentation force-penetration depth curves. A simple method accounting for the multiwalled structure of multiwall nanotubes is used to interpret the obtained ( EI) eff in terms of an effective bending modulus E t b, an effective axial modulus E t a, and a wall modulus E t w of a nanotube. Nanoindentation tests on three VACNT forest samples reveal the effective bending modulus of multiwall carbon nanotubes to be E t b =0.91∼1.24 TPa , and effective axial modulus to be E t a=0.90– 1.23 TPa . These values are in good agreement with tests conducted on isolated MWCNTs. Taking the mechanical wall thickness to be 0.075 nm , the nanotube wall modulus is found to be E t w=4.14– 5.61 TPa , which is in good agreement with predictions from atomic simulations. The use of nanoindentation together with the proposed micromechanical model of the successive bending of nanotubes as the indentor penetrates into the forest is hereby shown to result in a novel approach for determining not only the dependence of the indentation resistance on the key structural features of the forest (CNT diameter, length and areal density), but also provides a measure of the stiffness of the constituent carbon nanotubes. This new technique requires no special treatment of the samples, making it promising to apply this method to a large number of tests to determine the statistical properties of CNTs, and implying the potential use of this method as a quality control measurement in mass production.