The elastic buckling of super-graphene and super-square carbon nanotube networks

doi:10.1016/j.physleta.2010.02.033

Physics Letters A

Volume 374, Issues 15–16, 5 April 2010, Pages 1773-1778

https://doi.org/10.1016/j.physleta.2010.02.033 Get rights and content

Abstract

The super-graphene (SG) and super-square (SS) carbon nanotube network are built by the straight single-walled carbon nanotubes and corresponding junctions. The elastic buckling behaviors of these carbon nanotube networks under different boundary conditions are explored through the molecular structural mechanics method. The following results are obtained: (a) The critical buckling forces of the SG and SS networks decrease as the side lengths or aspect ratios of the networks increase. The continuum plate theory could give good predictions to the buckling of the SS network but not the SG network with non-uniform buckling modes. (b) The carbon nanotube networks are more stable structures than the graphene structures with less carbon atoms.

Introduction

Carbon nanotubes (CNTs) have attracted extensive interests for their exceptional mechanical properties, low density and high conductivity of thermal expansion, etc. Therefore, the CNTs are also widely envisioned as ideal building blocks for high performance engineering materials such as nanoelectronics and other nanodevices. However, the assembly of single-walled carbon nanotubes (SWNTs) with well ordered positions and orientations is a big challenge, which has received many attentions [1], [2], [3], [4], [5], [6]. Fan and his coworkers [7] have used the super-aligned CNT arrays to fabricate a super-aligned CNT grid, which could be used for high resolution transmission electron microscopy of nanomaterials. Besides, these CNT thin films could also be applied for flexible, stretchable, transparent loudspeakers and fast high-temperature incandescent displays [8], [9]. Thus the CNT networks will be good candidates for advanced engineering materials.

However, little is known about the influences of architectures of CNT networks on the mechanical, electronic and thermal properties. Romo-Herrara et al. [10], [11], [12] have theoretically studied the generation and characterization of 2D and 3D well ordered CNT networks, which are connected by the 1D block (SWNT) covalently. Fig. 1 show two planar, well ordered 2D CNT networks: (a) the super-graphene (SG) and (b) the super-square (SS). These 2D CNT networks could be generated by SWNTs with corresponding CNT junctions. These CNT networks are found much more stable than the fullerene (C₆₀) [10]. The charges in these CNT networks also follow specific paths through the nodes of their CNT junctions, which indicate that these CNT network could be used as complex integrated nanoelectronic circuits [11], [12]. Coluci et al. [13] have used the molecular mechanics and impact molecular dynamics method to study the static and dynamic properties of the SG and SS CNT networks. A transition from high to moderate flexibility is found in the dynamic deformation stages of these CNT networks [13]. Li et al. [14] have studied the deformation mechanisms of SG and SS CNT networks under uniaxial tension. The SG and SS CNT networks are bending-dominated and stretching-dominated structures [14], respectively. The specific heat of these CNT networks is also predicted by quantized molecular structural mechanics method and is found to be only dependent on their building blocks [15]. The SG and SS CNT networks are also found to have ultra-low specific heat per unit area and could be used for fabricating novel loudspeakers with a wide frequency response range and a high sound pressure level [15]. Besides, the Super Carbon Nanotube (ST), which could be generated by rolling SG network up, is found to have many excellent mechanical and thermal properties [16], [17], [18], [19], [20], [21], [22], [23].

In the recent work by Jiang et al. [24], the different CNT junctions as well as the CNT networks could be synthesized by the self-assembling of corresponding two tailored graphene nanoribbons under the high temperature (about 3000 K). Therefore, a controllable self-assemble approach of these SG and SS CNT networks has been proposed and verified by the molecular dynamics (MD) simulations [24]. Besides, these 2D CNT networks as well as some 3D CNT networks have also been simulated by Romo-Herrara et al. [10], [11], [12] with the first principle method. Although many works have been done on the mechanical, electronic and thermal properties of SG and SS CNT networks, the elastic buckling of these networks has not been considered. As the buckling of CNTs is critical to the applications of CNTs [25], [26], [27], [28], [29], the buckling of the SG and SS CNT networks could be an important issue in the application of these CNT networks. In this work, the elastic buckling behaviors of SG and SS CNT networks are explored through the molecular structural mechanics (MSM) method [30], which are found quite similar to that of continuum plates. The effects of geometry and topology on the critical buckling forces of these CNT network are also discussed.

Section snippets

Method and model

The MSM method proposed by Li and Chow [30] is employed to study the elastic buckling of SG and SS CNT networks. The key idea of MSM method is to use beam element with circular cross section to characterize the C single bond C covalent bond of these carbon structures. The numerical results of MSM method agree reasonable well with both the experimental and MD results, not only in the simulations of SWNTs [28], [30], but also in the simulations of SG, SS and ST CNT networks [14], [15], [18], [20], [21], [22],

Result and discussions

Fig. 3 shows the buckling modes of the SG@ $(6, 0)$ and SS@ $(6, 0)$ CNT networks under the fully-clamped boundary condition. The buckling modes of these CNT networks are quite similar to that of the continuum plate [31] and the graphene [32]. However, the buckling mode of the SG@ $(6, 0)$ CNT network is not as uniform as that of the SS@ $(6, 0)$ CNT network, which could be induced by the different orientations of the straight SWNTs in the SG@ $(6, 0)$ : the straight SWNTs parallel to the loading direction are

Conclusions

The elastic buckling behaviors of the SG and SS CNT networks under uniform compression are studied by the MSM method, the following conclusions are obtained:

(1)
The buckling modes of SG and SS CNT networks are quite similar to that of a continuum plate. However, the buckling deformation of SG CNT network is not as uniform as that of SS network.
(2)
The critical buckling force per unit length of SG CNT network decreases as the aspect ratio or side length increases and has some unchanged stages when the

Acknowledgements

Supports by the Chinese NSFC (Grant No. 10872114) are gratefully acknowledged. X.M. Qiu would like to thank the Chinese NSFC (Grant No. 10972111) and the National Basic Research Program of China through Grant No. 2006CB601202. Q. Fan and Y. Yin would like to thank the financial support from Natural Science Foundation of Jiangsu Province (BK2008370).

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The elastic buckling of super-graphene and super-square carbon nanotube networks

Abstract

Introduction

Section snippets

Method and model

Result and discussions

Conclusions

Acknowledgements

Chem. Phys. Lett.

Carbon

Solid State Commun.

Phys. Lett. A

J. Mech. Phys. Solids

Mech. Mater.

Int. J. Solids Struct.

Comput. Mater. Sci.

Angew. Chem.

J. Am. Chem. Soc.

Nanoletters

Nanoletters

Small

Nanoletters

Nanoletters

Adv. Mater.