The first synthesis of carbon nanotubes is usually credited to Sumio Ijima in 1991. A single sheet of carbon atoms arranged in a hexagonal lattice is known as graphene. Graphite consists of a stack of graphene sheets held together by van der Waals forces. A single-walled nanotube (SWNT) is, in concept, the result of rolling a graphene sheet into a cylindrical tube with a diameter of several nanometers. The length of the nanotube can be of the order of millimeters, giving a length to diameter ratio of up to 20 million. Nanotubes have tensile strengths per unit weight some 10-100 times greater than that of steel. They possess other unique mechanical, electrical, and optical properties that show promise in the development of new nanotechnology and electronics, including, possibly, quantum computers.
Points on the graphene lattice can be described by vectors of the form
are integers (
are nonorthogonal unit vectors that can be taken as
, respectively. The chiral indices
determine the alignment of carbon hexagons around the circumference of the cylinder. Three different geometrical classifications or "flavors" of nanotubes can be distinguished. "Armchair" configurations are characterized by indices
while "zigzag" configurations are described by
. Chiral nanotubes have indices
) and can occur in two mirror-image forms. Armchair nanotubes show metallic electric conductivity, while the other flavors are semiconductors with varying characteristics.
In this Demonstration, you can view a nanotube structure with indices
or its conceptual graphene precursor. Pink cylinders are drawn as visual aids.