Delivered by Ingenta to: UNIVERSIDAD AUTONOMA DE SAN LUIS POTOSI, MEDICINA IP : 148.224.113.19 Thu, 25 Oct 2012 18:50:35 ARTICLE Copyright © 2013 by American Scientific Publishers All rights reserved. Printed in the United States of America Advanced Science, Engineering and Medicine Vol. 5, pp. 262–265, 2013 (www.aspbs.com/asem) Allometric Pressure versus Volume Behavior of Single-Walled Carbon Nanotubes Under High Pressure L. I. Espinosa-Vega, A. G. Rodríguez * , H. Navarro-Contreras, and M. A. Vidal Coordinación para la Innovación y la Aplicación de la Ciencia y la Tecnología (CIACYT), Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, San Luis Potosí, S. L. P. 78000, México Single-walled carbon nanotubes (SWCNT) under high pressure have been studied by Raman spectroscopy. Considering cylindrical nanotubes with circular cross sections at all pressures the experimental data show an allometric pressure versus volume (PV) behavior under non-hydrostatic and quasi-hydrostatic conditions. We show that there is no need to consider a structural phase transition to explain the dependence of the radial breathing mode (RBM) phonon frequency with pressure. The bulk modulus (B o ) of the bundled nanotubes obtained from the PV data increases with pressure following a fit given by B o = 2.38 + 10.77P GPa. KEYWORDS: Single-Walled Carbon Nanotubes, High Pressure, Bulk Modulus, Raman Spectroscopy. 1. INTRODUCTION Interest in one-dimensional nanostructures such as wires and tubes has continuously grown in recent years. The potential applications of carbon nanotubes (CNT) in diverse areas such as electronics, material science, optics, etc. are widely known. In some of these applications the physical properties of CNT could be intentionally or unin- tentionally modified because of an elastic deformation. 1–4 Therefore, it is important to know how CNT are affected under different strain conditions such as the volumetric deformation and collapsing of single-walled carbon nano- tubes (SWCNT) under high hydrostatic pressure. CNT under high hydrostatic pressure have been widely stud- ied both theoretically and experimentally. 1–11 In particular, Raman spectroscopy has proven to be a very useful characterization tool to obtain important parameters of the nanotubes. 12–16 Information about crystallinity, diam- eter and even chirality of SWNT can be revealed by Raman spectroscopy. Under hydrostatic pressure the CNT phonons shift to higher frequency because of the car- bon structure stiffness. A few authors have noted that the intensity of the tangential mode phonon decreases lin- early within two orders of magnitude when pressure is increased up to a critical pressure P c of approximately 2 GPa. 2 Other studies also report a different increase rate ∗ Author to whom correspondence should be addressed. Email: angel.rodriguez@uaslp.mx Received: 18 June 2012 Revised/Accepted: 28 June 2012 with pressure or vanishing of the radial breathing mode (RBM) around this pressure P c . 5 It has been proposed that a structural phase transition occurs at this pressure P c , but the nature of the transition has been controversial because its reversibility. 1–11 For some authors the nanotubes cross section suffers an hexagonal deformation due to a change to a close-packed structure at P c . On the other hand, there are authors that propose a complete flattening of the nanotubes at a critical collapse pressure that is diameter dependent. 1–11 In this report, we show that the experimental data of the Raman shifts are consistent with an allometric behavior of the volume change with pressure considering that the nanotubes keep a circular cross section at all pressures. We also obtain from the experimental data, the dependence with pressure of the bulk modulus of bundled nanotubes. 2. MATERIALS AND METHODS The SWCNT bundles under study were purchased from Nano-Lab. The nanotubes diameter is 1–1.5 nm with an average length of 1 m. Raman scattering measurements were carried out in single-walled carbon nanotubes under high hydrostatic pressure. The Raman scattering measure- ments were done at room temperature using a Jobin-Yvon T64000 spectrometer operating in the triple configuration. A multichannel charge-coupled device cooled to 140 K using liquid nitrogen was used as the detector. The samples were analyzed in the backscattering zxy ¯ z geometry using the 5145 Å line of an Ar laser. The CNTs were loaded in 262 Adv. Sci. Eng. Med. 2013, Vol. 5, No. 3 2164-6627/2013/5/262/004 doi:10.1166/asem.2013.1246