Approximate Solutions for a Self-Folding Problem of Carbon Nanotubes

Mikata, Y.

Knolls Atomic Power Laboratory

关键词: Mathematical Models;    42 Engineering;    Nanotubes;    Carbon;    Aspect Ratio;   

DOI  :  10.2172/896369
RP-ID  :  LM-06K090
RP-ID  :  DE-AC12-00SN39357
RP-ID  :  896369

美国|英语

来源: UNT Digital Library

【 摘 要 】

This paper treats approximate solutions for a self-folding problem of carbon nanotubes. It has been observed in the molecular dynamics calculations [1] that a carbon nanotube with a large aspect ratio can self-fold due to van der Waals force between the parts of the same carbon nanotube. The main issue in the self-folding problem is to determine the minimum threshold length of the carbon nanotube at which it becomes possible for the carbon nanotube to self-fold due to the van der Waals force. An approximate mathematical model based on the force method is constructed for the self-folding problem of carbon nanotubes, and it is solved exactly as an elastica problem using elliptic functions. Additionally, three other mathematical models are constructed based on the energy method. As a particular example, the lower and upper estimates for the critical threshold (minimum) length are determined based on both methods for the (5,5) armchair carbon nanotube.