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

Vertically aligned carbon nanotubes (VACNT) have been a recent subject of intense investigation due to the numerous potential applications of VACNTs ranging from 9eld emission and vacuum microelectronic devices to the creation of super-hydrophobic surfaces and as a source of well de9ned 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 e;ective bending sti;ness (EI)e; 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)e; in terms of an e;ective bending modulus E t , an e;ective axial modulus E t , and a wall modulus E w t of a nanotube. Nanoindentation tests on three VACNT forest samples reveal the e;ective bending modulus of multiwall carbon nanotubes to be E t = 0:91 ∼ 1:24 TPa, and e;ective axial modulus to be E t = 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 =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 ∗Corresponding author. Tel.: +1-617-253-2342; fax: +1-617-258-8742. E-mail address: mcboyce@mit.edu (M.C. Boyce). 0022-5096/$ see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jmps.2003.09.015 2214 H.J. Qi et al. / J. Mech. Phys. Solids 51 (2003) 2213–2237 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 sti;ness 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. ? 2003 Elsevier Ltd. All rights reserved.