Paper Models for Fullerenes C60-C84 John M. Beaton 6439 Killington, Kalamazoo, MI 49009
When Buckminsterfullerene ( C a J was discovered i n 1985 ( I ) paper models played a n important role in the realization that i t had the shape of a truncated icosahedron (2). The first paper model had paper hexagons and pentagons for its 32 faces. Later, a model having 10 open and two closed pentagons was described (3).As the fullerene family of spheroidal carbon molecules was being observed experimentally (4-6) computational techniques were being developed to define all the possible structures for the fnllerenes (7-13), narrowed down by the Isolated Pentagon Rule that says that none of the mandatory 12 pentagons can be abutting. The structures emerging from the theoretical studies were represented as planar diagrams (7,131 and by a linear sequence of the numerals five and six conveying the information needed to build models (81, or by orthogonal views of the three-dimensional models (8.14). Construction of models from the diagrams requires the appropriate modelling kit and a great deal of patience. I n 1992 this author described a system for the construction of a few fullerene models from planar paper patterns (15)and subsequently has used the method to follow developments in the structural elucidation of the higher fullerenes (16). The system is expanded here with slight modifications to provide paper models of all 51 of the possible fullerene isomers fGom CS0through Cs4. The is to provide students, teachers, and even specialists with an inexpensive mechanism to follow the literature interplay on fullerene structures. The Stone-Wales transformation (17) and its ramifications for C a 2 , and Ca4 (6, 12, 18) make a particularly interesting study, impossible without tangible models. There is also much discussion in the literature about which two isomers of Csa are those actually isolated rather than the 22 others not so far observed (8. 18-24). One is shown by 1 3 C - N M R to be C a d - D a - 2 3 and the ~robablv or other is one of four DIstructures 123). . " CsL-D9-5 "- " C 8 4 - D z - 2 2 , the latter-being favored by most authors. The three most abundant fullerenes are.. res~ectivelv. . .. Can. .... Cvn. and C,,. l'hr first resembles a modern soccer ball, the serond a ruabv bnll. and tht: proven component of the ia~latwi C Rhas ~ the same D a symmetry and a superficial resemblance to the pattern on a baseball. softball. or tennis ball. A modified for C 8 4 - D a - 2 3 i s labellkd "baseballerene" in the list of patterns below. To construct a model from a particular pattern, the planar fimre should be ~hotoenlareedto make the hexaeons aboutlone-inch wide..~hisallows easy finger access t o t h e interior before closure. The enlarged pattern is then cut around the perimeter, and hexagons bearing a bold numeral five are cut into a t the dotted vertex and excised to become pentagonal holes later. The hexagons marked with a T will be the tabs (usually 11)to which double-coated adhesive tape is applied. starting with the excised hexagons, a taped tab is covered neatly by a n adjacent hexagon to form a pentagonal hole and the process is continued until closure is complete. The hexagonal vertices and edges not involved with pentagons are emphasized as bold dots or bold lines. This, coupled with the contrasting pentagonal holes makes svmmetrv analvsis easier. I n some cases the symmetry can be identified in the planar pattern (e.g., C 8 2 isomers 1-6 show alternatmg C 2 , C,symmetry even in
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the central pattern of abutting hexagons). The similarity between C s 4 - D z - 2 2 and C a 4 - D z d - 2 3 is evident in the pattern of bold lines. I t also appears that structures with many bold dots (isolated vertices surrounded by hexagons) are but energetically disfageometrically possible (e.g., C~O-I,J vored. The numbers assigned to the C 8 2 and Csa isomers correspond to those in ref 12 and ref 8.. res~ectivelv. Small . nume;als near lines connecting two pentagonal hoies indicate sites suitable for the Stone-Wales transformation (12, 17, 18). By a 90-degree rotation of the numbered bond the isomer in hand can be transformed in a formal sense to the isomer with the indicated number (or its enantiomer in can be transformed to some cases). For example, CRA-CI-12 -~ . any one of seven othir isomers by rotation of a selected Stone-Wales bond. Paper models have prartical a d v ; ~ n t ; i ~inr ivisual analysis of'symmeul\: T h w can be skewered d o n e axes of rotation, markedcircumferentially to indicate symmetry planes, numbered a t vertices for accounting purposes and analyzed segmentally to predict or confirm 1 3 C - N M R spectra of the fullerene isomers. Literature Cited 1. Kroto, H. W. : Heath, J . R.; O'Brien, S. C.; Curl, R. F:Srnalley R. E.Nolure 19%. 71s 1s"
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2. Kmto. H.WAneew. Chem. Inr. Ed. Enel. 1992.31.111. 3. ~ l t t a ~J.. J.~ .c L m . E ~ U C1 ~ 8 s66, . 282. 4. Diederich, F.; Ettl, R.;Rubin,Y.;Whetten,R. L.:Beek,R.;Alvarez, M.:Anr, S.: Sens h a m a , D.; Wudl. F ; Khernani, K C.: Koeh, A. Science 1991,252,648, 5. Ettl, R.: Chao, I.; Diederich, F.: Whetten, R. L.Nolure 1991.313, 149. 6 . Diederich, F.; Whetten, R. L.; Thi1-n. C.: Ettl. R.: Chao. I.; Alvarez, M. M. S r k m 9s" ,"em ."".,.">,.."". 300,
7 . Manolopoulos, D. E.; May, J. C.; Down, S. E.Chem. Phys Lett 1991,181, 105. 8. Manolopoulos. D. E.; Fowler, P W. JCkem. Phys. 1992,96, 7603. 9. Manolopouloa. D. E. J Ckem Soc. F o m d q %ns 1991.87.286 1. . w.: att ten, R. c.: M ~ ~ O I ~ ~ D ~ U E.IJ.Oc i~h.m . sor~~~~d~~nanr 1991, l o . ~ o w l e rP. 87. 3103. 1991.87.1945. 11. Fowier, P w J ckem. SX. pondqv Pans. 12. Manolopoulos, D. E.; Fowler, P W.: Ryan. R. P. JChem. Soc. Fnmdey P a n s 1992. P9 ,. ,996 . . .",
13. Liu, X.;Schmalr,T. G.:&in, D . J . Chpm Phyr k t , . 1992, 188,550. Chem.Php. 1998.98. 14. Zhang,B.L.;Wang,C.Z.:Ho.KM.;Xu,C.H.;Chan,C.T.J 3095. 15. Beaton. J . M. J . Chem Edur 1992,69,610. Billups. e~ W E.; 16. Thilgen, C.: Diedrieh. F;Whetten, R. L. In B u c k m i n s f w f u l l ~ ~ n , ~ e ~wo r k ,1993. Ciufalmi, M. A . ~ d sVCH, 17. Stone, A. J.; Wales, D. J. Chem Phvs. Lett. 1986.128, 50 1. 18. Fowler P. W.; Manolopoulos, D. E.:Ryan,R. P. J . Cham. Soc Chem. Commun. 1992. 20. ~ h . n g , B . L . : h n g , C. 2.; K M . J. Chem. Phys 1992.96, 7183. 21. Wang,X. Q.:Wsng, C. Z.;Zhang,B. L.: Ho, K. M. Chem. Phys. Lett. 1993,207, 349. 22. Kik"chi..K.: Nakahara, N.; Wakabayashi, T ; Honda, M.; Matarniya, H ; Moriwaki, T.; Sueuki, S.; Shirornaru. H.;Saifo. K;Yarnauchi, K,Ikernoto,I.:Aehibs,Y Chpm.
Editor's Note: In the November issue, The Journal of ChernicalEducation will announce an address for a new World Wide Web site that will include the tables of contents of past and current issues and abstracts for every atlicle in each issue. In addition, full text and/or supplementary material will be supplied for articles when appropriate. One such supplement will be the terndates in this article: each will be available as a Separate file in'gif format fordownloading and use in the classroom. Consult the November issue forthe new URL.
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