Author ORCID Identifier

Roger H. French

Document Type


Publication Date



The van der Waals-London dispersion (vdW-Ld) spectra are calculated for the [9,3,m] metallic and [6,5,s] semiconducting single wall carbon nanotubes (SWCNTs), graphite, and graphene (a single carbon sheet of the graphite structure) using uniaxial optical properties determined from ab initio band structure calculations. The [9,3,m]⁠, exhibiting metallic optical properties in the axial direction versus semiconducting optical properties in the radial direction, highlights the strong anisotropic nature of metallic SWCNTs. Availability of both efficient ab initio local density band structure codes and sufficient computational power has allowed us to calculate the imaginary parts of the frequency dependent dielectric spectra, which are then easily converted to the required vdW-Ld spectra for Hamaker coefficient calculations. The resulting Hamaker coefficients, calculated from the Lifshitz quantum electrodynamic theory, show that neither graphite nor graphene are accurate model materials for estimating the Hamaker coefficients of SWCNTs. Additionally, Hamaker coefficients were calculated between pure radial-radial, radial-axial, and axial-axial components of both SWCNTs. Analysis of these coefficients reveals that the vdW-Ld interactions will depend on both chirality and the particular orientation between neighboring SWCNTs. The minimization of energy, with respect to orientation, predicts that vdW-Ld alignment forces will arise as a result of the anisotropic optical properties of SWCNTs.


graphene, optical properties, dielectric spectroscopy, viscoelastic materials, carbon based materials, nanotubes, geometrical optics, intermolecular forces, chirality

Publication Title

Journal of Applied Physics






© 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in R. F. Rajter, R. H. French, W. Y. Ching, W. C. Carter, Y. M. Chiang; Calculating van der Waals-London dispersion spectra and Hamaker coefficients of carbon nanotubes in water from ab initio optical properties. J. Appl. Phys. 1 March 2007; 101 (5): 054303. and may be found at

Included in

Physics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.