ELEG 867 Nanotechnology
Homework #8 - due Wednesday, 21 November 2001

1. For C nanotubes, derive the correct equation for the chiral angle, q, between the circumference direction and the nearest zigzag axis. Note that Eq. (2) on p. 311 of the text by G. Timp is slightly incorrect. Hint: use vector algebra with the definitions of the circumference vector C, and the unit vectors a₁ and a₂.

2. For zigzag-cap type C nanotubes (Text Fig. 11 b, p. 311), use simple two dimensional geometry and bond counting to derive an equation for the diameter of a single nanotube in terms of the number of hexagons N_h along the circumference. Assume that the C atoms are points, with average bond length a_C-C = 0.144 nm, that lie on a 2D sheet that can be rolled into a tube. Give an equation and plot a few discrete point of diameter versus number of hexagons (or C atoms) on the circumference.

3. Search the scientific literature to find an experimental value for the resistance of a single C nanotube for the two cases of metallic and semiconducting. Feel free to start from the reviews and references in the review paper by Tseng and Ellenbogen at: http://www.sciencemag.org/cgi/content/full/294/5545/1293.

For full credit, find the tubule resistance that does not include the contact resistance. Provide the numerical values, and cite the reference that you used.

For proper credit, you must include the course number, assignment number, and due date on your submission.