Approximate Solutions for a Self-Folding Problem of Carbon Nanotubes
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.
- Research Organization:
- Knolls Atomic Power Lab. (KAPL), Niskayuna, NY (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- DE-AC12-00SN39357
- OSTI ID:
- 896369
- Report Number(s):
- LM-06K090; TRN: US200703%%694
- Country of Publication:
- United States
- Language:
- English
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