Carbon is a constituent element of DNA, proteins, fats, and carbohydrates and makes up approximately 20% of the human body. Carbon symbolizes love and commitment in some cultures and is scratched on paper to express ideas. It is a key ingredient in the fossil fuels used to power our cities and vehicles and is used in industry as coke in steel making, carbon black in printing, and activated charcoal in water treatment (Emsley 1998). Not surprisingly, carbon is also a key ingredient in the emerging field of nanotechnology. Aside from the long known allotropes of graphite and diamond, carbon is also found in the nanostructured forms of spherical fullerenes (buckyballs) and carbon nanotubes (CNTs).

The four main forms of carbon—diamond, graphite, buckyballs, and CNTs—are an excellent vehicle for teaching fundamental principles of chemical bonding, material structure, and properties. Carbon atoms form a variety of structures that are intrinsically connected to the properties they exhibit. Educators can take advantage of this striking relationship between atomic structure and material properties to address several Physical Science Standards (9–12), including Structure of Atoms and Structure and Properties of Matter (NRC 1996, p. 178). This article discusses two new allotropes of carbon that are important for nanotechnology—buckyballs and CNTs—and related activities for the classroom.

Figure 1. Atomic structure of diamond.

Atomic structure and forms of carbon

Even though diamond and graphite are made of the exact same element, carbon, the atoms can arrange in such a way as to make one of the hardest materials and one of the softest. In diamond, the hardest known natural material, each carbon atom is bonded to four other carbon atoms. Each bond is equal in strength and is oriented tetrahedrally to form a three-dimensional network.

Figure 2. Atomic structure of graphite. The top view highlights the layered nature of the structure, while the bottom view shows the hexagonal pattern that the atoms form in each sheet.

In contrast, each carbon atom in graphite is strongly bonded to three carbon atoms in the same plane and only weakly bonded to carbon atoms in other planes. The carbon atoms in the plane are arranged in the shape of hexagons, called graphene sheets, while the weak bonding out of plane allows the sheets to slide easily past each other. Graphite is used as a lubricant and in pencil “lead” because of the ease with which graphene layers slide past each other onto the paper when writing. The key to these two allotropes behaving very differently is at the nanoscale, in their atomic arrangement: diamond = tetrahedral network (Figure 1); graphite = hexagonal sheet (Figure 2).

More recently discovered forms of carbon are nanoscale materials. A buckyball looks like a nanometer-sized soccer ball and a CNT looks like a single graphene sheet rolled up into a cylinder. Given the dramatic differences between diamond and graphite, it is not surprising that buckyballs and CNTs exhibit very different properties as well.

A buckyball in its simplest form is a soccerball–shaped molecule that consists of 60 carbon atoms (C₆₀) arranged in pentagonal and hexagonal rings (Figure 3) and has a diameter of ~0.7 nm (7Å) (Kroto et al. 1985). To put the extremely small size of the buckyball into perspective, consider that the relative size of a soccer ball with respect to the planet Neptune is approximately the relative size of C₆₀ with respect to a soccer ball.

Figure 3. A C60 fullerene, or buckyball.

Since their discovery, buckyballs have been proposed for numerous applications, including possible HIV inhibitors and signal amplifiers for fiber optic communications. In 1996, Richard Smalley, Robert Curl, and Harold Kroto received the Nobel Prize in Chemistry for their discovery of fullerenes (Nobel Foundation 2005). While these tiny, spherical molecules are relatively new to science (first discovered in 1985), their structure is historically found in many different places, including sports, architecture, and art. In fact, buckyballs (fullerenes) were named after architect Buckminster Fuller, who was responsible for the design of the first geodomes.

CNTs, another recently discovered form of carbon, are tubular molecules (see “How are CNTs made?,” p. 38). They were first discovered—accidentally—by Sumio Iijima in 1991. Iijima was trying to make buckyballs when he noticed long, needlelike structures in addition to the round buckyballs he was expecting. The CNTs he observed can be classified as three different types—armchair, zigzag, and chiral—determined by the orientation of the carbon hexagons. CNTs can also be described as single-walled (SWNT), resembling a single graphene sheet rolled up, or multi-walled (MWNT), like several SWNT nested inside each other.

CNTs and buckyballs are good examples of how, like many things in nature, subtle differences in a material’s structure can change the behavior that it exhibits. Scientists have found that the armchair, zigzag, and chiral types of CNTs have very different properties.

The following CNT activities are great ways to build on student understanding of atoms and the elements and to incorporate cutting-edge science in the classroom by teaching students something new about nanotechnology. We have found that additional activities (see “Additional CNT Activities and Standards,” p. 41) may be needed.

Depending on the level and background of the class, activities may be aimed at understanding how small nano is and why it is exciting for scientists and engineers to create materials and devices at the nanoscale (see “Applications of CNTs”).

[Note: One such activity can be found at http://mrsec.wisc.edu/Edetc/IPSE/educators/nanotube.html.]

Activity I: Chicken wire nanotubes: CNT structures and properties

A sheet of plastic-coated chicken wire is a convenient model for a graphene sheet because both have the same hexagonal pattern. Each intersection on the sheet represents a single carbon atom and the lines between the intersections represent bonds. By rolling up the chicken wire so that the opposite edges touch, the sheet can demonstrate the structure of a CNT (Figure 4). [Safety note: Small sheets of plastic-coated chicken wire should be prepared for classroom use with a wire cutter while wearing safety glasses or goggles.] Rolling up the sheet in different ways produces different patterns along the circumference of the tube. [Note: Movies showing the different structures created by rolling the sheet can be viewed at http://mrsec.wisc.edu/Edetc/cineplex/nanotube/index.html.]

Figure 4. Chicken wire CNT models.
a) A graphene sheet can be rolled up to form an allotrope of carbon called a carbon nanotube. The graphene sheet can be rolled more than one way, producing the three different types of CNTs: b) armchair, c) zigzag, d) chiral.	b
	c
a	d

The structures of the nanotubes—armchair, zigzag, and chiral—determine their unique physical properties, such as:

• Electrical conductivity properties: One of the main things that distinguish CNTs from other nanomaterials is their electrical properties. They can have semiconducting properties (some zigzag, chiral) or metallic properties (armchair, some zigzag) depending on their structure.
• Mechanical properties (tensile strength): Based on small-scale experiments and theoretical calculations, a ~2.5 cm (1 in.) thick rope made of CNTs is predicted to be 100 times stronger and 1/6 the weight of steel.
• Thermal conductivity properties: CNTs conduct heat very well. A nanotube’s thermal conductivity is predicted to be 10 times higher than silver. Unlike metals, which conduct heat by moving electrons, CNTs conduct heat by wiggling the covalent bonds between the carbon atoms themselves.

Figure 5. Counting carbon atoms. The counting vectors (a1 and a2) point from an arbitrary “origin” atom towards the closest equivalent carbon atoms in the graphene lattice.

Activity II: Using vectors to create and count your own nanotube

This activity helps students understand how to better identify the three different CNT structures (armchair, zigzag, and chiral). For CNTs, the direction in which the graphene sheet looks like it was “rolled up” (such as in Figure 4) and a prediction of the nanotube’s properties can be determined by counting the number of carbon atoms it takes to get back to an equivalent position (Figure 5, p. 40). However, because a graphene sheet must be a lattice (i.e., it must form a continuous repeating pattern), there are only two allowed counting directions, a₁ and a₂. Starting from an arbitrary carbon atom, the a₁ and a₂ vectors point toward the closest equivalent carbon atoms in the lattice (Figure 5).

The nanotube type is determined by counting how many atoms in the a₁ direction (n) and how many atoms in the a₂ direction (m) it takes to go around the tube and get back to the starting point. Nanotubes are named as (n,m), where n and m are called the chiral numbers. Zigzag tubes are (n,0), armchair tubes are (n,n), and chiral tubes are (n,m), where n≠m.

For example, to count a (4,0) zigzag nanotube shown in Figure 6 (p. 40), students choose an arbitrary carbon atom as a starting point. Students should move to the closest carbon atom in the a₁ direction. This is count one. Students move again in the a₁ direction: two. Students continue counting along the a₁ direction until they reach their starting point. For the example shown in Figure 6, it will take four counts in the a₁ direction to return to the starting point.

Figure 6. Counting a (4,0) zigzag nanotube.
The red stars represent the same carbon atom; the stars would overlap if you were to "roll” up the graphene sheet into a tube.

Students can explore this by making their own nanotube and identifying its structure by using erasable markers, blue-tak, and hexagonal patterns printed on overhead transparencies. A graphene sheet pattern can be downloaded and printed from www.mrsec.wisc.edu/Edetc/cineplex/nanotube/graphene.pdf. Students pick an origin atom on the printed hexagonal pattern, draw a vector n carbons long in the a₁ direction and 0 carbons in the a₂ direction, then draw a dot at the (n,0) position. Place a small amount of blue-tak on the carbon at the origin, and roll the sheet so the two dots are superimposed and stuck to each other, making the atom at the (n,0) position and the origin atom the same. Now students can attempt to identify whether the (n,0) nanotube is armchair, zigzag, or chiral (it is zigzag). Additionally, students can find the circumference of the tube; in this case it is simply n units.

For armchair or chiral nanotubes, counting only in the a₁ direction never gets back to the origin. It is necessary to count along the a₁ direction, then turn and count along the a₂ direction in order to return to the origin atom. This difference from the zigzag nanotube is important for students to realize when they create their transparency nanotube.

To count the (3,3) armchair tube shown in Figure 7, students should choose an arbitrary carbon atom as their starting point or origin. Students should move to the closest carbon atom in the a₁ direction and move a total of three times in the a₁ direction. Students will notice that if they continue in the a₁ direction, they will not return to their starting point. From the same carbon atom just reached, students turn and move three times in the a₂ direction. Students should have returned to their starting point. Chiral and armchair nanotubes can both be counted in this manner.

Figure 7. Counting a (3,3) armchair nanotube. The red stars represent the same carbon atom; the stars would overlap if you were to “roll” up the graphene sheet into a tube. [Note: Once the transparency is rolled into a tube with the stars overlapping, the extra hexagons will overlap and “disappear’’ (see Figure 4B, C, and D).]

Again, students can explore armchair and chiral nanotubes with their transparency pattern. Teachers can assign several (n,m) vector pairs and have students draw the vectors, construct the nanotubes, find their circumferences, and identify their types. This activity also allows teachers to stress how vectors work by connecting them head-to-tail in series. To determine the circumference of these nanotubes students can count the number of hexagons on the nanotube, or resolve the vectors mathematically. The exact structure of a CNT determines its properties.

The information in this article provides some background on allotropes of carbon and explores the atomic structure of the carbon nanotube in more detail. Additional information on classroom activities concerning nanoscale carbon and other nanotechnology topics can be found on the education website of the University of Wisconsin–Madison Materials Research Science and Engineering Center on Nanostructured Interfaces (UW MRSEC 2005). This information ranges from handouts and videos that support the activities described above to a societal implications activity that explores potential uses of a carbon nanotube–based material. All information can be easily adapted for the high school classroom.

Olivia M. Castellini (olivia.castellini@msichicago.org) is an exhibit developer at the Museum of Science and Industry in Chicago, Illinois; George C. Lisensky (lisensky@beloit.edu) is a chemistry professor at Beloit College in Beloit, Wisconsin; Jennifer Ehrlich (jme2@oregon.k12.wi.us) is a chemistry teacher at Oregon High School in Oregon, Wisconsin; Greta M. Zenner (gmzenner@wisc.edu) is the assistant director of education for the Materials Research Science and Engineering Center (MRSEC) on Nanostructured Interfaces at the University of Wisconsin–Madison (UW) in Madison, Wisconsin; Wendy C. Crone (crone@engr.wisc.edu) is the director of education for the UW MRSEC and an associate professor in the UW department of engineering physics in Madison, Wisconsin.

Acknowledgments

The authors would like to thank Wendy deProphetis, Lola Nesius, and Amy Payne for initial work to create carbon nanotube activities, Mike Condren for assistance with photography, and the National Science Foundation through the MRSEC on Nanostructured Interfaces (DMR-0079983 and DMR-0520527) and through the Internships in Public Science Education program (DMR-0120897), both at the University of Wisconsin–Madison.

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