MORE ABOUT CARBON NANOTUBES

Carbon nanotubes (fullerene nanotubes) are part of the fullerene family of carbon materials discovered by Dr. Richard E. Smalley and colleagues in 1985. They include single-wall carbon nanotubes (SWNTs), and nested (endohedral or endotopic) SWNTs, i.e., one, two or more tubular fullerenes nested inside another tubular fullerene. Each tubular fullerene is a huge carbon molecule, often having millions of carbon atoms bonded together to form a tiny tube. Carbon nanotube diameters range from about 0.5 to about 10 nanometers (one nanometer = 10^-9 meter) and their lengths are typically between a few nanometers and tens of microns (one micron = 10^-6 meter).


Carbon is a truly remarkable atom. It readily bonds with itself into extended sheets of atoms comprising linked hexagonal rings shown below. Each carbon atom is covalently bonded to its three nearest neighbors.


This unique sheet structure is called graphene. Solid graphite is made up of layers of graphene stacked as shown above. No other element in the periodic table bonds to itself in an extended network with the strength of the carbon-carbon bond, which is among the strongest of chemical bonds. Some of the electrons in the carbon-carbon bonds are free to move about the entire graphene sheet, rather than stay home with their donor atoms, giving the structure good electrical conductivity. The tight coupling between atoms in the carbon-carbon bond provides an intrinsic thermal conductivity that exceeds almost all other materials. As suggested by the carbon nanotube figure above, the structure of a fullerene nanotube is that of a sheet of graphene, wrapped into a tube and bonded seamlessly to itself. This is a true molecule with every atom in its place and very few defects: an example of molecular perfection on a relatively large scale.

The special nature of the bonded carbon sheet, the molecular perfection of carbon nanotubes, and their long tubular shape endow them with physical and chemical properties that are unlike those of any other material. These properties include high surface area, excellent electrical and thermal conductivity, and tremendous tensile strength, stiffness, and toughness.

In a single tube, every atom is on two surfaces - the inside and the outside, and a single gram of nanotubes has over 2400 m² of surface area! The nature of the carbon bonding gives the tubes their great tensile strength and electrical and thermal conductivity. The carbon nanotubes' stiffness and toughness derives from their molecular perfection. In most materials the actual observed stiffness and toughness are degraded very substantially by the occurrence of defects in their structure. For example, high strength steel typically fails at about 1% of its theoretical breaking strength. Carbon nanotubes, however, achieve values very close to their theoretical limits because of their perfection of structure - there are no structural defects where mechanical failures can begin! It is, however, the tubular geometry of carbon nanotubes that gives them their most exotic properties. Depending on the orientation of the graphene sheet forming the tube's wall, the tube can be either metallic or semiconducting. The metallic tubes conduct electricity just as metals do and the semiconducting ones have great promise as the basic elements of a new paradigm for electronic circuitry at the molecular level.

Basic Structure
There are literally hundreds of different carbon nanotube structures. One can identify these structures by thinking of the carbon nanotube as a sheet of graphene wrapped into a seamless cylinder. As one might imagine, there are many ways to wrap a graphene cylinder, and the cylinder can have a wide range of dimensions. Soon after fullerene nanotubes were discovered, a classification scheme was devised to describe the different conformations of graphene cylinders. This classification scheme uses an ordered pair of numbers, (n,m), and is based upon the diagram of graphene shown below. Each carbon atom in the graphene sheet is bonded to three other carbon atoms, forming a Y-shaped vertex of carbon-carbon bonds. In order to make a seamless graphene tube of a uniform diameter, one must wrap the graphene sheet in a way that permits every carbon atom in the cylinder to be bonded to three other carbon atoms where the sheet joins to itself. The number of ways this wrapping can be achieved is countable according to the numbering scheme given in the figure below. The unit vectors of the 2-dimensional graphene lattice are shown as a1 and a2 below. Each vertex that could possibly join to the origin during a wrapping operation is labeled with an ordered pair wherein the first number of the pair is the distance (in lattice repeat units) of the vertex from the origin along a1, and the second number is the distance of the vertex from the origin along a₂.


AAs an example of the classification scheme, the (10,5) tube is shown below, and would result when graphene sheet is wrapped so that the vertex labeled (10,5) lands on top of the origin.


As one can see from the illustration of the (10,5) tube above, the carbon hexagons appear to "spiral" around the tube's axis. This spiraling is sometimes referred to as the chirality of the tube, and the chirality is uniquely specified by the ordered pair (n,m). As do all chiral structures (such as wood screws, for example), the tubes have a "handedness". An (i,j) tube is the mirror image of a (j,i) tube, but is otherwise identical. There are two classes of nanotube conformations that are sometimes called "achiral" because their structure is completely symmetric, and the carbon hexagons do not spiral about the tube axis, but lie in lines exactly parallel to the axis. These two highly-symmetric conformations are the (n,0) (which are exactly the same as (0,n) tubes) and the (n,n) tubes, examples of which are shown below.


The (n, 0) tubes are often called "zig-zag" tubes since, if the tube is cut as shown above, the open end has carbon atoms in a regular zig-zag pattern. Likewise the (n,n) tubes are sometimes referred to as ˇ§armchairˇ¨ tubes because the carbon atoms at the cut end are in a pattern with two up, two down, and then two up again, which is reminiscent of the seat and arms of an armchair.

In production of nanotubes, there is a minimum size for the graphene sheet cylinder, which is believed to be a (4,4) tube, which is approximately 0.5 nanometers in diameter. Just to get an idea of how many different conformations of tubes there are, lets consider a maximum tube diameter of 3.5 nm, as isolated one-wall carbon nanotubes tubes tend to collapse above this diameter. A 3.5 nm diameter (n,n) tube would be a (26,26) tube. So we need to count the tubes with n and m in the range between 4 and 26, inclusive, where n and m can take on any values within that range. The number of different ordered pairs of two numbers between 0 and 26 is the number of permutations of 27 objects taken two at a time, which is 27!/(27-2)!, where y! is the product of y and all smaller numbers down to 1 (i.e. 4! = 4 x 3 x 2 x 1 =24). So then 27!/25! = 27 x 26 = 702. We estimate that the tubes for which both n and m are less than 4 do not exist, so we subtract the number of permutations of 4 objects (i.e. the numbers 0, 1, 2, and 3) taken 2 at a time, which is 4!/2! = 12. Thus a reasonable estimate of the number of relevant conformations for single-wall carbon nanotubes is 702-12 = 690. From this number, one should subtract the number of (0,n) conformations since they are indistinguishable from the (n,0) conformations, yielding 690-(27-4) = 667 different conformations of carbon nanotubes smaller than 3.5 nanometers in diameter.

Another structural aspect of tubes is their self-organization into "ropes," which consist of many (typically, 10-100) tubes running together along their length in contact with one another. Such a structure is shown graphically in the image below.
The sides of the tubes are very smooth, and the carbon bonds on one tube can get relatively close to those on an adjacent tube. When adjacent tubes are so close to one another, the electrons in one tube actually influence the motion of some electrons in its neighbor, giving rise to a short-range attractive force between the tubes called the van der Waals force. The binding energy between adjacent tubes due to this force is approximately 0.5eV per nanometer of contact length, which means that once the tubes stick together, it is very difficult to separate them! Ropes can be far longer than any individual tube within them: individual tubes are typically about 100-2000 nm in length, but ropes are virtually endless, branching off from one another, then joining others. A transmission electron microscope image of a nanotube rope is shown below. Here the rope is looping up toward the viewer, and passes through the focal plane of the microscope. Thus what we see appears to be a cross section of the rope that shows dozens of individual nanotubes stacked together in a fairly regular pattern. These ropes are useful in providing very long electrically conductive pathways in nanotube films and composite materials.


Carbon nanotubes include the one-wall tubes shown above as well as nested or endotopic (from the Greek endo for inside and topic for place or position) tubular fullerenes. That is to say that carbon nanotubes can be one, two or more tubular fullerenes nested inside one another as depicted in the image below. Because of the perfection of their sidewalls, these endotopic structures also form ropes, as shown in the figure below.


The endotopic carbon nanotubes are themselves very interesting in that the individual concentric tubes are mechanically independent from one another. Recent research has shown that one can actually make the inner tube slide within the outer ones. This research has suggested that endotopic carbon nanotubes have potential as elements of nanoscale machines.