Kevin Chiu
Over the past few decades, the discovery of carbon nanotubes derived from fullerenes have sparked vast research efforts. Their surprising strength, along with many other novel properties, have put carbon nanotubes on the radar for widespread applications, from ice hockey sticks to maritime vessels. This paper discusses both the discovery and synthesis of carbon nanotubes, exploring the chemistry behind the structure of these materials and why certain properties are manifested. It explores the possibility of constructing a space elevator, a type of transportation system consisting of a cable tether extending into space, and how carbon nanotubes make it a much more realistic goal.
Tags: carbon nanotubes, fullerenes, graphite, graphene, space elevator, space, tensile strength
Multimedia suggestions: http://www.youtube.com/watch?v=_2M73aXuORI
Kevin Chiu is currently a sophomore studying Chemical Engineering at the University of
Southern California. He is fascinated by the properties of materials, from those found in objects such as his tennis racquet or his pair of skis to materials used in aerospace applications.
With its unique chemical versatility, it is no surprise that the carbon atom makes up some of the most important materials in the world. In recent decades, a new type of material, also derived from carbon has emerged. Carbon nanotubes, structures on the microscopic scale, have been successfully created from other special derivatives of carbon. These materials have novel strength properties that can be explained through their chemical bonding structure, and in turn these materials allow once unimaginable constructions to become a true possibility. Most notably, the thin walled carbon nanotubes will have the potential to create the space elevator, a gigantic cable structure that can carry payloads up into space. Carbon nanotubes are the only materials in existence today that exhibit the necessary strength suitable for an elevator to space, a structure that can bring humanity limitless possibilities.

The properties of the carbon atom are important in understanding the structures of materials derived from carbon, such as diamond and nanotubes. A carbon atom is characterized by having four empty orbitals that can each be filled with an electron, which is why carbon can form up to four bonds. In the ground state of carbon, the orbitals consist of one “s” orbital and then three “p” orbitals contained at a different energy level. However, what truly happens when carbon forms four single bonds is that one “s” valence orbital and three “p” valence orbitals mix together. This property is named sp 3 hybridization, creating four equally energized sp 3 orbitals arranged in a tetrahedral structure. Carbon also has the ability to form double and even triple bonds, using different forms of hybridization. In sp
2
hybridization, as the name implies, one “s” and two “p” orbitals are hybridized together to form three sp
2
orbitals, arranged in a trigonal structure. The ground state configuration, followed by the sp
2
and sp
3
hybridization configurations, are illustrated below in Figure 1.
Figure 1: sp
2
hybridization in graphite and sp
3 in diamond. Source: ruby.colorado.edu
In sp 2 hybridization, a double bond is possible because the one p orbital that remains unhybridized has the ability to form an additional bond alongside the existing sp
2
bond between carbon atoms. Both sp
3
and sp
2
hybridization appear in many structures with repeating patterns of carbon atoms, of which diamond and graphene are common examples of [1]. Diamond has sp
3

characterization with a repetition of cyclohexane chairs that form a three-dimensional network structure, while graphene is composed of a single planar sheet of graphite with a repeating hexagon theme that exhibits sp
2
characterization [1]. Fullerenes, molecules composed of carbon atoms that form a spherical shape, also exhibit sp
2
hybridization, but are not hybridized in a completely planar structure like graphene. Fullerenes are slightly pyramidalized, giving the planar sheet a degree of curvature that allows for the well-known, spherically shaped buckyballs to form. [1]. Both graphite and fullerenes are materials from which nanotubes are derived from.
In Figure 2, a carbon nanotube is shown with its detached cap made of fullerene.
Figure 2: Carbon nanotube with detached hemisphere of fullerene. Source: www.phys.ttu.edu
These fullerenes, which exhibit sp
2
hybridization but with some slight sp
3 character, were first discovered in 1985 [1]. Six years later, Sumio Iijimia was attempting to prepare fullerenes by electrically charging graphite soot, when he also discovered that cylindrical graphite structures had been deposited on the electrodes [1]. Carbon nanotubes can be imagined as rolled up, cylindrical sheets of perfect graphene, with the tips of the tubes sealed by two hemi-fullerene caps of the appropriate size [2]. Nanotubes may consist of a single wall of graphene or they may be multi-walled structures with concentric cylinders. The spherical caps are essential in multiwalled nanotubes in order to prevent concentric tubes from gliding relative to each other and inducing high strain [2].

Now, how exactly does this particular structure make carbon nanotubes a material with one of the highest strength to weight ratios in the world? The answer lies in the atomic structure of graphene sheets, which constitute the walls of the carbon nanotube. Unlike diamond, which is known to be one of the hardest materials on earth, graphite is commonly misconceived to be weak and brittle. Graphite is composed of individual, monoatomic graphene layers of carbon stacked one atop another. These layers are not held together by chemical bonds and so are indeed weak. However, this is not the case for the individual graphene sheets that constitute the layers of graphite. Whereas diamond has a repeating three-dimensional crystal lattice structure, graphene has a repeating planar honeycomb structure with bonds that are sp
2
hybridized. These sp
2
bonds between each carbon in the hexagonal network of graphene are stronger than their sp
3 counterparts in diamond, thus giving a single graphene sheet a higher tensile strength than diamond [3]. Each carbon in the honeycomb lattice makes three sp 2 bonds to neighboring carbons, each at an angle of 120° to each other. This creates the hexagon pattern in the planar sheet. Additionally, the remaining empty p orbital that was left unhybridized lies perpendicular to the planar lattice, and can interact with the p orbitals on any of the three neighboring carbon atoms. This interaction is a delocalized pi bond, because although a pi bond can be made between the carbon atom to one of the other neighboring carbons, this double bond has an equal opportunity of forming with the other two neighboring carbons as well. This is shown below in
Figure 3, where the p orbitals, colored orange, interact with each other in delocalized bonds.

Figure 3: Delocalized pi bonds in benzene. Souce: en.wikipedia.org
The additional delocalized pi bond interaction is the source of the impressive strength in these carbon to carbon bonds. The increased strength of these bonds is furthermore evidenced by the length of the carbon bonds, as shorter bond lengths correlate to stronger bonding. The carbon to carbon bond length in diamond is 0.154 nm whereas in graphene it is 0.142 nm, making nanotubes particularly stable against deformations [2].
In reality however, materials are measured by their tangible physical quantities, such as tensile strength. Tensile strength is a measure of the maximum stress that a material can withstand while a force is being applied to stretch it. The tensile strength of a simple singlewalled carbon nanotube is already 20 times that of steel, measuring at around 45 GPa [2]. Ropes composed of carbon nanotubes are expected to have an ideal tensile strength of 100 GPa, which can be achieved once defects in the nanotubes are eliminated [4]. More recently, values of tensile strength as high as 150 GPa have been recorded for perfect multi-walled nanotubes, but it is unknown why such a large increase in strength from single-walled nanotubes arises [2]. These values of tensile strength indicate the amount of weight that can be held per unit of cross sectional area, meaning that a nanotube of 130 GPa would be able to hold 1,300,000 kg on a cable with a cross sectional area of one square centimeter [5]. The incredible strength of cables

made from carbon nanotubes has made an old concept feasible for the first time – the space elevator.
A space elevator consists of a cable attached to the Earth’s surface that extends all the way into outer space. This cable would extend far enough so that its center of mass would reach the geostationary orbit, an orbit with a rotational period equal to Earth’s [6]. In this way, the entire structure would stay fixed in geosynchronous orbit as the Earth revolved. The downward force of the space elevator’s weight would be supported by centrifugal forces caused by Earth’s rotation [4]. Payloads would be carried into space by climbers on the cable, much like a train on a railroad track. The earth’s rotational energy would also assist these climbers in accelerating to the top. In this structure, the maximum stress placed on the cable would be located at the geostationary orbit. Thus, the cable design would need to exceed a certain taper ratio: the ratio between the cable’s maximum cross sectional area, located at geostationary orbit, to the cable’s minimum cross sectional area, located at the Earth’s surface [4]. Carbon nanotubes only require a taper ratio of 1.9 as opposed to the much higher ratios required of materials such as steel and
Kevlar, which would be impossible to construct the space elevator with. More importantly, the maximum tensile stress experienced at the geostationary point is equal to 63 GPa [4]. Therefore, the carbon nanotubes of today can already withstand this, and perfecting its flaws can provide an additional factor of safety for using the material. The other quality of nanotube material that makes it feasible in the space elevator is its weight. The use of any material for the ribbon besides carbon nanotubes would require the cable to be extremely thick and heavy, and only possible to construct with thousands of rocket launches [5]. This is because construction involves launching rockets to hoist up the cable tether into space. Not only are most materials not strong

enough to be suitable for the cable, but they would be too heavy to be transported in the first place.
Construction begins with a single satellite launch that carries a spool of the paper thin nanotube cable [5]. Because of the high tension force that would be experienced at geostationary orbit, this cable would be tapered at a width of a meter where this maximum stress would occur, to about 14 cm where minimal stress would occur. Once the satellite reaches geostationary altitude, it will begin to unwind the spool of cable tether [5]. As the cable is spooled downward, conservation of momentum will ensure that the system’s center of mass remains the same. Thus the lowering of the cable will cause a momentum exchange that moves the satellite further away, in order to extend the cable past the geostationary orbit [5]. Figure 4 depicts this process, beginning with the satellite at geostationary altitude and then unwinding its cable tether.
Figure 4: Deployment of initial space elevator cable by satellite. Source: [7]
Once the cable is completely unwound, the satellite will remain as the initial countermass needed to keep the cable taut. Then, a small mechanical climber will begin to ascend the newly formed

cable, while deploying a second cable tether alongside the first. This process of mechanical climbers that attach parallel cable strings during their ascension is repeated over and over again until the cable is sufficiently strong enough to hold much heavier payloads [5]. Although seemingly tedious, this would be an effective method that could pay for itself in time.
The completion of this tether capable of transporting heavy cargo into space would bring immense advantages to humanity to justify its cost. In fact, its biggest ability would be to lower the expense of getting objects into space. Currently, it costs about $40,000 per pound to send payloads into orbit by rocket launch. The space elevator would bring this cost down to an estimated $100 per pound, opening up the door to many opportunities in space that were previously too expensive to pursue [7]. For one, human tourism could be achieved more easily.
Space exploration would probably be able to expand greatly in quantity and capability [6].
Factories producing products in the weightless space environment would be able to manufacture effective pharmaceuticals, exotic chemicals, and special materials. Solar energy obtained directly from space could be easily relied on to power our ever growing world. The estimated cost of building the space elevator structure will be about $7 billion, well worth the advantages it can old in the future [7]. The concept of a space elevator may seem slightly far-fetched to nearing impossible, but upon closer inspection, the strength of a cable made from carbon nanotubes can make this dream a reality. That carbon nanotubes have made such an influential impact in the concept of the space elevator truly demonstrates how advances in technology can bring old ideas back to life.

Works Cited
[1] C.N.R. Rao, B.C. Satishkumar, A.Govindaraj and M. Nath, "Nanotubes," Chemphyschem , vol. 2, pp. 78–105, Feb. 2001.
[2] M. Monthioux, P. Serp, E. Flahaut, M. Razafinimanana, C. Laurent, A. Peigney, W. Bacsa, and J.M. Broto, “Introduction to Nanotubes,” in Springer Handbook of Nanotechnology ,
Springer Berlin Heidelberg, 2010, ch. 3, pp. 47–118.
[3]K.D. Sattler, “Raman Spectroscopy of sp
2
Nano-Carbons,” in Handbook of Nanophysics ,
Boca Raton: Taylor and Francis Group LLC, 2011, ch. 7.
[4] N.M. Pugno, “On the strength of the carbon nanotube-based space elevator cable: from nanomechanics to megamechanics,”
Journal of Physics: Condensed Matter, vol. 18, no. 33, pp.
1971-1989, 2006.
[5] M. Van Pelt, “Space Elevators,” in Space Tethers and Space Elevators , New York: Springer
NY, 2009, ch. 6, pp. 143-178.
[6] B.E. Laubscher, “The Space Elevator,” Electronic Properties of Novel Nanostructures, vol.
786, pp. 602-606, 2005.
[7] P. Johnson, “Stairway to heaven: building a real elevator to space using paper-thin, carbon nanotubes,”
Canadian Chemical News , vol. 56, no. 10, pp. 18, 2004.