Collapse of Single-Wall Carbon Nanotubes is Diameter Dependent James A. Elliott, 1 Jan K.W. Sandler, 1 Alan H. Windle, 1 Robert J. Young, 2 and Milo S. P. Shaffer 1, * 1 Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge, CB2 3QZ 2 Materials Science Centre, UMIST/University of Manchester, Grovesnor Street, Manchester, M1 7HS (Received 3 December 2002; published 2 March 2004) We present classical molecular dynamics simulations demonstrating that single-wall carbon nano- tube (SWNT) bundles collapse under hydrostatic pressure. The collapse pressures obtained as a function of nanotube diameter are in excellent quantitative agreement with new data presented here for small diameter (d  0:8 nm) SWNTs, and the majority of previously published results, although there remain some unreconciled contradictions in the literature. The collapse pressure is found to be independent of the nanotube chirality, and a lower limit on the largest SWNT that remains inflated at atmospheric pressure is established (d> 4:16 nm). DOI: 10.1103/PhysRevLett.92.095501 PACS numbers: 61.46.+w, 02.70.Ns, 62.50.+p, 78.30.Na Introduction.—Since their identification in 1991, inter- est in carbon nanotubes has continued to grow, focusing on both their intrinsic properties and potential applica- tions. The behavior of individual tubes has been explored via experiment [1–3] and computer simulation, e.g., [4–7], in both axial and bending geometries. Elastic properties have generally been found to be broadly con- sistent with the in-plane properties of graphite, but strengths have proved harder to assess, with simulation results consistently predicting higher values than have been observed experimentally, probably as a result of defects in the real materials. Carbon nanotubes have also been explored under hydrostatic pressure, using Raman spectroscopy [8–13], x-ray diffraction [14,15], and neutron diffraction techniques [16]. Raman spectros- copy, in particular, has proved to be a very useful tool in the characterization of single-wall carbon nanotubes (SWNTs), revealing information about crystallinity, di- ameter, and even chirality. Under increasing hydrostatic pressure, the Raman peaks shift to higher frequencies, corresponding to a stiffening of the carbon framework. Some authors have noticed that the peak position of the tangential mode, corresponding to in-plane vibrations of adjacent carbon atoms in the graphene sheet, shifts linearly over two regimes with a change in gradient at a critical pressure of approximately 2 GPa, depending on the type of nanotube material used. A number of studies also reported the disappearance of the radial breathing mode (RBM) from the spectrum above that critical pressure. Similarly, x-ray results demonstrate the disap- pearance of scattering associated with the hexagonally close-packed lattice into which the SWNT bundles are organized [14]. Clearly, a structural phase transition oc- curs at this critical pressure, but the exact nature of this change has proved controversial. Most authors seem to favor a transition to a close-packed structure of hexago- nally deformed nanotubes (‘‘polygonization’’), while others propose a complete flattening or ‘‘collapse’’ [17]. A previous TEM study of multiwall nanotubes (MWNT) found evidence for collapse to form ribbons, although the cause was unclear [18]. In a recent study [19], we used Raman spectroscopy to compare the behavior of bundles of single and a range of MWNTs to that of graphite, under hydrostatic pressure. The initial gradient of the peak shift could be explained entirely in geometric terms, using a continuum mechan- ics model and the relevant internal and external diame- ters. Above the critical pressure, the gradient was equal to that of the graphite, which exhibited no transition over the pressure range up to 10 GPa. We interpreted these results as evidence supporting the complete collapse of the hollow core of the nanostructures to produce materials resembling graphite in terms of density and hybridiza- tion. The peak shifts appeared to be completely reversible within experimental accuracy, as long as the maximum pressure was kept below 10 GPa. The SWNTs in this experiment were supplied by Tubes@Rice, and are gen- erally considered to be predominantly either (10,10) nanotubes or other chiralities with similar diameters. The critical pressure for these nanotubes to collapse was found to be 2:1  0:2 GPa. This Letter describes a series of molecular dynamics simulations intended to examine the proposed mecha- nism of collapse, and explore the response of other diameters and chiralities of nanotubes. In the light of these predictions, we then performed further Raman pressure experiments that proved to be in excel- lent agreement with our simulations, as described below. Simulation methodology.—A common approach to modeling the mechanical behavior of carbon nanotubes has been the use of ab initio quantum methods, e.g., [5–7,20,21]. However, such techniques are computation- ally expensive for large molecular systems. Although second-generation reactive empirical bond order (REBO) potentials [22] offer an improvement in this respect, for simulations in which there is no change in intramo- lecular bonding, and where intermolecular forces play a PHYSICAL REVIEW LETTERS week ending 5 MARCH 2004 VOLUME 92, NUMBER 9 095501-1 0031-9007= 04=92(9)=095501(4)$22.50  2004 The American Physical Society 095501-1