In the Classroom
Tested Demonstrations
Kixium Monolayers: A Simple Alternative to the Bubble Raft Model for Close-Packed Spheres submitted by:
Keenan E. Dungey Department of Chemistry, Furman University, Greenville, SC 29613-1120;
[email protected] checked by:
George Lisensky Department of Chemistry, Beloit College, Beloit, WI 53511 S. Michael Condren Department of Chemistry, Christian Brothers University, Memphis, TN 38104
In general chemistry courses, the majority of the chemical examples are gas mixtures or aqueous solutions. However, the most prevalent state of the chemical materials encountered everyday is solid. Thus the recent emphasis on the teaching of solid-state materials in the general chemistry classroom (1). Any discussion of solid-state chemistry involves a description of structure (2). One of the basic structural themes in the solid state is that of close-packed spheres. Atoms are approximated as hard spheres that arrange themselves in such a manner as to reduce voids. The two close-packed structures, hexagonal closest packed (hcp) and cubic closest packed (ccp), and their derivatives are observed in the noble gases and many metals, and also in alloys and ionic and covalent compounds (3). Interestingly, other close packings are possible if the structures aren’t periodic (4, 5). The close packing model is therefore a powerful tool for explaining many solid-state structures. To facilitate learning of the close packing model, many demonstrations of closepacking spheres have been developed (6–11). Most of the models in the literature are static: spheres or circles are packed and stacked by hand and frozen into the familiar hexagonal lattice. Static models, though visually demonstrating the arrangement of spheres in a hexagonal array, don’t explore any of the other possible ways of packing spheres. Students may wonder why the instructor has to intervene to force the coins or balls to assume the right shape. A dynamic model, one that both demonstrates the close packed structure visually and spontaneously assumes this structure, is aesthetically more satisfying. Such a dynamic demonstration was exactly what Bragg and Nye reported in 1947 with the bubble raft model. This model has recently been adapted for overhead projection (1, 12). However, the apparatus involved in making the bubble raft demonstration is complex. Description of “Kixium” Model A simpler way of producing a dynamic model for closepacked structures is by floating cereal in a bowl of water. The same forces that hold a bubble raft together (capillary attraction) hold the cereal pieces together in a raft. Spherical cereal, such as Kix,1 works well (circular cereal, like Cheerios,1 didn’t yield satisfactory images). To project the image of the resulting raft, a 10-in. Pyrex pie plate or a glass crystallization dish (e.g., 170 × 90 mm) is placed on an overhead projector. The dish is filled with a just enough water (about 1 cm) to float the 618
cereal but not enough to move the cereal raft out of the focal plane of the projector. Pieces of cereal are added slowly until a monolayer is obtained.2 The image of the cereal rafts clearly shows the hexagonal lattice of two-dimensional closest packed spheres. When different sizes and shapes of dishes are used the same hexagonal array is produced, thus demonstrating to the students’ satisfaction that this way of packing spheres is preferred to other ways. Although one could stack multilayers of cereal spheres onto the rafts, the resulting projected images aren’t clear, owing to the opacity of the cereal. To extend the discussion of close packing into three dimensions, I switched to a static model similar to one previously reported (8). Alternatively, a hands-on activity for the students could be used (13). The cereal raft model can be used in further teaching applications. Since the cereal doesn’t consist of uniform spheres, defects are produced in the lattice, which could lead to a discussion of crystal defects. By adding a few pieces of Cheerios, an alloy can be modeled. The cereal raft model can be extended to describe Langmuir–Blodgett film formation or self-assembled monolayers. Additionally, a discussion of the intermolecular forces involved in building the cereal rafts could be a transition device in the curriculum between intermolecular forces and solid state structure. The “Kixium” monolayer model simply and quickly demonstrates the closest packing of spheres in two dimensions. And it’s edible! Acknowledgments I thank Laura L. Wright for helpful discussions and the Camille and Henry Dreyfus Foundation for financial support. Notes 1. Trademark of General Mills. 2. To improve the size uniformity of the cereal pieces, a reviewer suggested pouring the Kix through a hardware cloth (1⁄2-in. mesh) to discard the largest pieces.
Literature Cited 1. Ellis, A. B.; Geselbracht, M. J.; Johnson, B. J.; Lisensky, G. C.; Robinson, W. R. Teaching General Chemistry: A Materials Science Companion, 3rd ed.; American Chemical Society: Washington, DC, 1993.
Journal of Chemical Education • Vol. 77 No. 5 May 2000 • JChemEd.chem.wisc.edu
In the Classroom 2. Galasso, F. J. Chem. Educ. 1993, 70, 287. 3. West, A. R. Basic Solid State Chemistry; Wiley: New York, 1988. 4. Van de Waal, B. W. J. Chem. Educ. 1985, 62, 293. 5. Müller, U. Angew. Chem., Int. Ed. Engl. 1992, 31, 727. 6. Bragg, L.; Nye, J. F. Proc. R. Soc. London 1947, 190, 474; reprinted in Feynman, R. P.; Leighton, R. B.; Sands, M. The Feynman Lectures on Physics; Addison Wesley: Reading, MA, 1964; Vol. II.
7. Crowe, M. L. School Sci. Rev. 1970, 52, 380. 8. Cleeve, H. N. School Sci. Rev. 1971, 52, 619. 9. Miller, W. A.; Weatherly, G. C. Metals Mater. 1972, 6, 158. 10. Mann, A. W. J. Chem. Educ. 1973, 50, 652. 11. Lloyd, D. R.; Silver, J. J. Chem. Educ. 1977, 54, 685. 12. Geselbracht, M. J.; Ellis, A. B.; Penn, R. L.; Lisensky, G. C.; Stone, D. S. J. Chem. Educ. 1994, 71, 254. 13. Martin, D. F. J. Chem. Educ. 1992, 69, 495.
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