Elastic properties of single-wall nanotubes

Abstract

We report results of theoretical studies on the elastic properties of single-wall nanotubes of the following compositions: C, BN, BC3, BC2N and C3N4. These studies have been carried out using a total energy, non-orthogonal tight-binding parametrisation which is shown to provide results in good agreement both with calculations using higher levels of theory and the available experimental data. Our results predict that of all types of nanotubes considered, carbon nanotubes have the highest Young's modulus. We have considered tubes of different diameters, ranging from 0.5 to 2 nm, and find that in the limit of large diameters the mechanical properties of nanotubes approach those of the corresponding flat graphene-like sheets.The discovery of C 60 and fullerenes [1] in the mid 80's was soon followed by the observation of nanotubes [2], first reported by Iijima [3] in 1991. Since then nanotubes have been the focus of attention of a growing scientific community, attracted to them by their many interesting properties, such as their structure, electrical conductivity and mechanical properties, as well as by their large potential for practical applications. Two types of nanotubes exist: those originally observed by Iijima [3] were multi-wall nanotubes (MWNT's), formed by concentric shells of apparently seamless cylinders of graphene, having a separation between them similar to that in graphite. More recently, single-wall nanotubes (SWNT's) have also been synthesized. As their name indicates, these consist of a single seamless cylinder of graphene [2].Soon after the discovery of carbon nanotubes it was proposed that other compounds forming graphite-like structures, such as BN [4], BC 3 [5], BC 2 N [6], and CN [7], could also form nanotubular structures. Indeed BN [8][9][10], BC 3 and BC 2 N [11] have now been synthesized, though the actual structure of BC 2 N tubes seems to correspond to concentric shells of C and BN in a 'sandwich' structure [12]. Other tubular structures formed by heavier element compounds have been predicted, such as GaSe [13], and synthesized, like WS 2 and MoS 2 [14].In this paper we focus our attention on the structural, energetic and mechanical properties of single-wall carbon and composite nanotubes. We perform a systematic study of these systems using Tight-Binding total energy methods [15], as well as first-principles [16] calculations. Some of the results reported here have already appeared in published form [17], but we also provide previously unpublished results for the C 3 N 4 nanotubes.The structure of this paper is as follows. In Sec. I we review the available experimental data on the mechanical properties of nanotubes, while Sec. II is devoted to discussing previous theoretical work. In Sec. III we describe the models used in our work and the calculations carried out in order to address the issues discussed here. Then, in Sec. IV we discuss our results and conclusions.

Equivalent-continuum modeling of nano-structured materials

“…[43] 0.021 Sawada and Hamada [44] 0.017 Miyamoto et al [45] 0.020 Hernandez et al . (n,n) [46] 0.021 Hernandez et al (n,0) [46] 0.022 Average 0.018 …”

“…Values of the force constant, K ω , have been determined using computational chemistry data from several studies [36,[43][44][45][46] and equation (25). Even though the computational chemistry data was obtained for the specific case of bending of graphene sheets to form complete nanotubes or nanotube-like structures, the concepts of structural mechanics can be implemented such that these values could apply to any bending mode of graphene sheets.…”

Molar Binding Energy of Zigzag and Armchair Single-Walled Boron Nitride Nanotubes

“…The theoretical studies of the elastic properties of single-walled BN nanotubes, carried out using the total -energy non-orthogonal tight-binding parameterization, were reported in [99]. Tubes of different diameters, ranging from 0.5 to 2 nm, were examined.…”

Vibration analysis of single-walled carbon nanotubes using wave propagation approach

“…Shows the schematic variation of (5, 5), (7, 7) and (9, 9) armchairs nanotubes. Hernandez et al (1999), Tu and Ou-Yang (2002), Wang et al (2005). The value of K extension obtained in most of previous studies (see Yakobson et al, 1996;Lu, 1997;Jin and Yuan, 2003;Wang et al, 2005;Chen and Gao, 2006;Robertson et al, 1992) mainly falls in the range of 330 to 363 J m −2 and v varies from 0.14 to 0.34.…”