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Vibrational properties of carbon nanotubes

Vibrational properties of carbon nanotubes
Vibrational properties of carbon nanotubes
This work investigates the limits of Continuum Theory when describing the normal modes of vibration of free single-walled carbon nanotubes (CNTs). Quantitative and qualitative differences are systematically studied between molecular dynamics (MD) simulation results and their corresponding calculations using continuum theory on a set of free CNTs. A comparison of the frequencies calculated using classical continuum theories such as Euler-Bernoulli, Timoshenko beams or Thin Shell Theory shows good agreement for long waves and progressive failure of the continuum theories as the effective wavelength becomes of the order of the interatomic distance. The physical basis of the differences in frequency between the models are brought out with novel methods. A scaling expression of the deviation is inferred from the comparative analysis. It is found that the assumption underlying in the Euler-Bernoulli model that normals to the neutral axis remain normal is the main cause for the frequency deviation. For the Timoshenko and Thin Shell models, the cause is attributed to the shape mismatch between the quantisized MD-modelled CNTs and their corresponding continuum counterparts. From the novel MD data, it has also been shown that the temperature at which the specific heat capacity changes from cubic to linear is lower than the transition temperature suggested by other authors. Finally, the wall thickness of a CNT is calculated from its fundamental MD frequency.
Fernandez, Ignacio Rodriguez
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Fernandez, Ignacio Rodriguez
f27f1ded-93b7-4661-9ad8-8b0eeb649cec
Fanghor, Hans
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Bhaskar, Atul
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Fernandez, Ignacio Rodriguez (2009) Vibrational properties of carbon nanotubes. University of Southampton, School of Engineering Sciences, Masters Thesis, 100pp.

Record type: Thesis (Masters)

Abstract

This work investigates the limits of Continuum Theory when describing the normal modes of vibration of free single-walled carbon nanotubes (CNTs). Quantitative and qualitative differences are systematically studied between molecular dynamics (MD) simulation results and their corresponding calculations using continuum theory on a set of free CNTs. A comparison of the frequencies calculated using classical continuum theories such as Euler-Bernoulli, Timoshenko beams or Thin Shell Theory shows good agreement for long waves and progressive failure of the continuum theories as the effective wavelength becomes of the order of the interatomic distance. The physical basis of the differences in frequency between the models are brought out with novel methods. A scaling expression of the deviation is inferred from the comparative analysis. It is found that the assumption underlying in the Euler-Bernoulli model that normals to the neutral axis remain normal is the main cause for the frequency deviation. For the Timoshenko and Thin Shell models, the cause is attributed to the shape mismatch between the quantisized MD-modelled CNTs and their corresponding continuum counterparts. From the novel MD data, it has also been shown that the temperature at which the specific heat capacity changes from cubic to linear is lower than the transition temperature suggested by other authors. Finally, the wall thickness of a CNT is calculated from its fundamental MD frequency.

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Published date: 12 November 2009
Organisations: University of Southampton

Identifiers

Local EPrints ID: 156973
URI: http://eprints.soton.ac.uk/id/eprint/156973
PURE UUID: 2f2bbc82-4748-461c-b167-7a8daf52a6ec

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Date deposited: 11 Jun 2010 11:09
Last modified: 14 Mar 2024 01:45

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Contributors

Author: Ignacio Rodriguez Fernandez
Thesis advisor: Hans Fanghor
Thesis advisor: Atul Bhaskar

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