## Activities and Problems for Students

Fullerene-Science Module

Below is the list of activites and problems that accompany the Fullerene-Science module.

### ACTIVITIES

• Activity II.D:
Construct a 60 atom piece of graphite using your Cochrane's Molecular Models.

What is the minimum number of unsatisfied valences?

• Activity III.A:
Build the proposed structure for buckminsterfullerene (C) using your Cochrane's Molecular Models. Consider the following questions while inspecting your model.

1. How many five- and six-membered rings are there in the truncated icosahedron?
Answer: twelve 5's and twenty 6's.

2. Are the five-membered rings isolated or contiguous?

3. How many different kinds of vertices are there?

4. How many different kinds of edges are there?
Answer: two, those that lie between two six-membered rings and those that lie between one six- and one five- membered ring.

5. How many of each kind of edge are there?
Answer: 30 of the 6-6 variety and 60 of the 6-5 type.

6. Given that the average edge is approximately 1.4 Å long, estimate the size of the cavity (diameter and volume).
Answer: Diameter is ~ 7 Å and volume is ~ 180 Å.
• Activity III.C:
Build a model of the seventy-atom fullerene in which there are no contiguous pentagons. A model of C can be constructed from the C model by separating C in halves and then inserting a ring of ten additional atoms. The result is a football-shaped molecule. Consider the following questions while inspecting your model.

1. How many five- and six-membered rings are there in C?
Answer: twelve 5's and twenty-five 6's.

2. How many different kinds of vertices are there?

3. How many of each kind of vertex are there?
Answer: The five kinds of vertices are present in a ratio of 10:10:20:20:10.

4. How many edges are there?

5. How many different kinds of edges are there?
Answer: eight. There are four types of 6-6 ring fusions and four types of 6-5 ring fusions.

6. How many 6-6 ring fusions and 6-5 ring fusions are there?
Answer: 45 of the 6-6 variety and 60 of the 6-5 type.

7. Given that the average edge is approximately 1.4 Å long, estimate the size of the cavity (length and width).
Answer: Length is ~ 7.6 Å and width is ~ 6.4 Å.
• Activity IV (Optional):
Demonstration: Synthesis of C/C (Optional)

An in-class demonstration of the synthesis of C/C using the carbon-arc method can be carried out. Relatively simple reaction kettle/electrode assemblies have been described in the literature (Iacoe, 1992 and Craig, 1992). There are two concerns. One is the cost of constructing the apparatus, which will require the assistance of a capable glassblower. The second is the issue of safety. Fullerenes, like the condensed ring aromatic molecules, may have carcinogenic properties. In addition, they are known to be efficient sensitizers for the formation of highly reactive singlet oxygen. Hence, the entire reactor assembly, including the vacuum pump, should be placed in a good hood during the demonstration.

• Activity VI.C:
K has an ionic radius of 1.33 Å (diameter = 2.66 Å), while Cs has an ionic radius of 1.69 Å (diameter = 3.38 Å). On the scale of our models, these correspond to spheres of approximate diameter 6.1 cm (2.4 inches) and 7.6 cm (3.0 inches), respectively. Place a ball of appropriate size inside C and C fullerenes in order to get a physical picture of the "shrink-wrapped" endohedral fullerene complexes.

### PROBLEMS

• Problem VII.A:
In the case of C, where the lattice constant (a) was measured to be 14.17 Å,

1. Calculate the distance between nearest neighbors.

2. Given that the radius of C is approximately 3.53 Å, calculate the distance between spheres.

Note: This compares to a distance of 3.35 Å between the planar sheets of carbon atoms in graphite.

• Problem VII.B:
Using Figure VII.B.2,

1. Calculate the number of spheres in an fcc unit cell. Note that corners are shared by 8 unit cells, while faces are shared by 2 unit cells.