Structural rigidity and low frequency vibrational modes of long carbon tubules

Abstract

Abstract.We have studied the low frequency vibrational modes and the structural rigidity of long graphitic carbon tubules consisting of 100, 200, and 400 atoms. Our calculations have been performed using an empirical Keating Hamiltonian with parameters determined from first principles. We have found the "beam bending" mode to be one of the softest modes in these structures. The corresponding beam rigity of a " b u c k y tube" is compared to an found to exceed the highest values found in presently available materials. PACS: 36.40. +d; 81.20.Sh The successful synthesis [ 1] of macroscopic quantities of C60 clusters with a fascinating hollow "buckyball" structure [2] has ignited the interest of the scientific community in these and similar structures to an unprecedented degree. More recently, successful synthesis and identification of helical microtubules of graphitic carbon has been reported [3]. These graphite whiskers or "bucky tubes" are topological relatives of the "buckyball" [4] and might have been synthesized in direct current arc in inert gas already in the lat 50's [5]. Most interest in "bucky tubes" has concentrated on their electronic properties which can range from metallic to insulating [6]. In this paper, we present the first study of the mechanical properties of these structures. We show that these structures may be the finest and toughest fibers presently available, as was suggested recently [7].We focus our study on the low frequency vibrational eigen :modes of "bucky tubes" consisting of 100, 200, and 400 carbon atoms which reflect the rigidity of these structures. Among the man3, possible isomers [8], we consider those which can be generated by splitting the C60 "buckyball" into equal halves, and connecting the two "bucky caps" by a graphitic cylinder of variable length. All carbon atoms in the structure are three-fold coordinated. The "bucky tubes", like all members of the fullerene family, consist of a varying number of hexagonal carbon rings (distributed across the caps and the cylinder) and of twelve pentagons (on the caps). The equilibrium structure of a "bucky tube" consisting of 200 atoms is shown in Fig. la.In order to determine the structural rigidity and the vibrational eigen modes of such a complex structure, we use an elastic model with central and angular forces for the nearest neighbor bonds. Such models are currently widely used to describe properties of covalently bonded solids with directional bonding [9][10][11]. In the present study, we will use the Keating potential [9] which is attractive due to its simple form and its successful application to complex structures such as the C60 solid [12] and amorphous silicon [ 13].The Keating potential V x describes potential energy changes with respect to a relaxed reference state, and consists of a bond stretching and a bond bending term. The bond stretching term is a central nearest-neighbor two-body potential. The bond bending part of the potential is a three-body interaction term which is sensitive to changes of the angle between n...

Fullerenes

“…240 These calculations show that the lowest bending mode decreases as the length of the fullerene tube increases, saturating at a cluster size of about 200 carbon atoms. The magnitude of the beam rigidity of these tubules is found to exceed that of presently available materials, 240 so that graphene tubules are expected to offer outstanding mechanical properties. Kosakovskaya et al have also reported extreme hardness for tows of carbon tubules, exceeding that of the toughest alloys which they used as substrates.…”

“…The special geometry of C 6 o and C 60 -related tubules should make these structures relatively incompressible to hydrostatic stress, when compared to other materials. 240 From a theoretical standpoint, fullerene tubules are interesting as examples of a one-dimensional periodic structure along the tubule axis. Confinement in the radial direction is provided by the monolayer thickness of the tubule.…”

Equivalent‐Continuum Modeling of Nanostructured Materials

“…Due to the aspect ratio and tube-like geometry of SWNT, many studies have been conducted concerning the buckling and bending response of nanotubes using both theoretical [12,15,[17][18][19][20] and experimental [21,22] approaches. In particular, Overney et al [17] conducted a computational study and calculated a bending parameter of a graphene sheet based on the vibrational modes of a nanotube.…”

Scalable nanotemplate assisted directed assembly of single walled carbon nanotubes for nanoscale devices

“…Various CNT based devices including scanning probes, 1 field emitters, 2 field effect transistors, 3 biological sensors, 4 chemical sensors, 5 and memory devices 6 have been fabricated and studied. For realization of large scale production of single walled nanotube ͑SWNT͒ based devices, controlled assembly and precise alignment of SWNTs on prefabricated structures over large areas have been proposed.…”