By Hiroyuki Shima, Motohiro Sato
Carbon nanotubes provide large capability in such a lot of fields due partly to their major mechanical homes, together with outstanding stress, resilience, durability, and suppleness. Mechanical deformation of carbon nanotubes is understood to reason substantial alterations of their actual and chemical houses during the nontrivial structure-property correlation. a robust realizing in their deformation mechanism and on hand geometry is, hence, an important to constructing nanotube-based functions. This publication concentrates at the notable mechanical homes of carbon nanotubes, masking theoretical and experimental progresses from the final decade.
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Extra resources for Elastic and plastic deformation of carbon nanotubes
11]. 3 Left: Schematic of beam bending with the tip of an atomic force microscope (AFM). Right: Schematic of a pinned beam with a free end. The beam of length L is subjected to a point load P at x = a and to a distributed friction force f . Adapted from Ref. . corresponding linear increase in the lateral force with deﬂection. The right panel shows the system after the tip has passed over the beam. The lateral force drops to its initial value (left), and the beam snaps back to its undeﬂected, equilibrium position.
The reason for this disagreement can be ultimately traced to the simplicity of the model used by Lu, which included only harmonic springs to represent C–C bonds and pairwise Lennard–Jones type potentials to model the interlayer interaction in MWNTs. In the case of bundles of SWNTs, it was found that Young’s modulus decreases as the diameter of the nanotubes forming the bundle is increased. However, this does not reﬂect a weakening of the C–C bonds in these bundles but simply is a consequence of the fact that unit-cell volume grows more rapidly than the number of atoms.
97 TPa for isolated SWNTs. Cornwell and Wille obtained Young’s modulus of SWNTs under axial compression by the MD calculation . 24[GPa]. ˚ r [A] The values obtained from this formulation agree reasonably well with a methods for approximating Young’s modulus developed by Ruoﬀ and Lorents . 1 Dependence on Diameter and Chirality The hexagonal symmetry of a graphene sheet ensures a perfect isotropy of its in-plane elastic behavior. As the sheet is rolled seamlessly into a tube, the bending strain induces a slight outof-plane distortion of the C–C bonds, resulting in a hybridization of the σ bonds, which increases as the diameter decreases.