title: Geometric constant defining shape transitions of carbon nanotubes under pressure.
abstract: We demonstrate that when a single-walled carbon nanotube is under pressure it undergoes a series of shape transitions, first transforming from a circle to an oval and then from an oval to a peanut. Most remarkably, the ratio of the area of the tube cross sections at the second transition over that at the first transition appears as a constant, independent of the tube radius. Its accurate value is computed to be G=0.819 469, by formulating a variational geometry problem to represent single-walled carbon nanotubes with a family of closed plane curves of fixed length and minimum bending energy. The implications of such a geometric constant in designing nanotube electromechanical pressure sensors are discussed.
authors.affiliation: Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA.
authors.forename: Ji
authors.initials: J
authors.lastname: Zang
authors.forename: Andrejs
authors.initials: A
authors.lastname: Treibergs
authors.forename: Y
authors.initials: Y
authors.lastname: Han
authors.forename: Feng
authors.initials: F
authors.lastname: Liu