Hard-to-Soft Transition in Radial Buckling of Multi-Concentric Nanocylinders

Sung-Jin Park, Motohiro Sato, Tetsuro Ikeda, Hiroyuki Shima

Department of Urban and Environment Engineering, University of Incheon, Incheon, Korea.
Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, Japan.
Division of Engineering and Policy for Sustainable Environment, Faculty of Engineering, Hokkaido University, Sapporo, Japan.
Division of Engineering and Policy for Sustainable Environment, Graduate School of Engineering, Hokkaido University, Sapporo, Japan.

DOI: 10.4236/wjm.2012.21006                

Abstract

We investigate the cross-sectional buckling of multi-concentric tubular nanomaterials, which are called multiwalled carbon nanotubes (MWNTs), using an analysis based on thin-shell theory. MWNTs under hydrostatic pressure experience radial buckling. As a result of this, different buckling modes are obtained depending on the inter-tube separation d as well as the number of constituent tubes N and the innermost tube diameter. All of the buckling modes are classified into two deformation phases. In the first phase, which corresponds to an elliptic deformation, the radial stiffness increases rapidly with increasing N. In contrast, the second phase yields wavy, corrugated structures along the circumference for which the radial stiffness declines with increasing N. The hard-to-soft phase transition in radial buckling is a direct consequence of the core-shell structure of MWNTs. Special attention is devoted to how the variation in d affects the critical tube number Nc, which separates the two deformation phases observed in N -walled nanotubes, i.e., the elliptic phase for N < Nc and the corrugated phase for N > Nc. We demonstrate that a larger d tends to result in a smaller Nc, which is attributed to the primary role of the interatomic forces between concentric tubes in the hard-to-soft transition during the radial buckling of MWNTs.

Keywords

Carbon Nanotube; Buckling; Radial Corrugation; High Pressure Phenomenon; Van der Waals Coupling; Multiple Core-Shell Structure; Thin Shell Theory

Conflicts of Interest

The authors declare no conflicts of interest.

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