A Paper-Pattern System for the Construction of Fullerene Molecular Models John M. Beaton
The Upjohn Company, Kalamazoo, MI 49001 The spheroidal structure of CGO (Duckmin~terfuUercncJ, isolated in ouantitv in I990 ( 1 1 .was oredicted in 1985 (21 and confirmed b i x - r a y crystallog&phy even more recently (3). The ellipsoidal structure of the less abundant CvOwas established spectroscopically ( 4 ) showing the expected five resonances in the 13C-NMR spectrum. Advances in this field are prompting frequent reviews (5, 6)
Figure 1. Photograph of a cutout ring of six paper hexagons, overlapped and glued to form a nonplanar ring with a pentagonal hole, and an assembled model of Cso. and new members of the fullerene family (homolorn of C d are being isolated and characterized 17): The visu&atio" of oossiblc structures for the reoorted C.~-,G CAI. . .. CqI. . ... Cqd. ... and otker homologs is logically approached through the construction of symmetrical molecular models. Conventional ball-and-stick models as well as computer simulations have been used in the scientific literature and the popular press to illustrate the interesting fullerene geometry.
Conventional models focus on individual atoms of different elements with various types of bonding. Fullerene structures consist of only rings of carbon atoms with uniform interatomic bonding, so modelling can be simplified if the units are reduced to hexagons and pentagons. Although Csois described as having 20 hexagonal rings and 12 pentagonal rings, there is redundancy here. Csacan he viewed as 12 pentagons evenly distributed on the surface of a sphere, each connected to its five nearest neighbors by a bridge bond. This bridging generates the 20 hexagons. A more useful way to look at Csois to focus on an array of 20 fused hexagons on the surface of a sphere with 12 pentagonal holes among them. All fullerenes have 12 pentagonal rings (8)and the symmetry can be analyzed more easily if these are distinctively marked relative to the arbitrary number of hexagons in the surrounding pattern. This is easily done if the hexagons are solid and the pentagons are holes. An inexpensive and convenient material of construction is hexaeonallv marked oaoer. If a cluster of seven hexagons is-cut radially and t6e middle hexagon excised, the resulting flat ring of six hexagons (Fig. 1)can be reduced by overlap of hexagons adjacent to the radial cut to give a cup-shaped ring of five hexagons. Glue or doubled-coated tape secures the structure. Twelve such cups arranged so that each overlaps with its five nearest neighbors gives a model of Can. .... A more oractical wav " to eenerate the strutturc 1s from an extended planar array on hexagonal paper with aoorooriatelv laced hexagonal holes(Firr. 21. Bv simply overlapping neighboring hexagons around the hexagonal holes, these are reduced to pentagonal holes and the truncated iwsahedral structure of Cm appears (Fig. 1).A
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Figure 2. Cutout paltern for construction of Gomodel. 610
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Figure 3. Cutout pattern for construction of C,, model.
Figure 4. Cutout pattern for the most symmetrical of several isomeric models of C,,. small modification of this att tern that involves insertine five more hexagons, a pattern for C7o (Fig. 3). Separation of the holes by a group of three hexagons instead of a single hexagon generates a symmetrical pattern (Fig. 4) that in turn produces a symmetrical model for one 5). of at least four reasonable structures for C.."" (Fie. . . Paper patterns and derived models for a large number of fullerenes including structural isomers and chiral pairs have been generated. The pattern shown in Figure 6 leads to an almost spherical model for C7e (Fig. 5). Analysis of this model reveals its point group to be Td. Such a s t m ture would be expected to show five resonances in the I3CNMR spectrum with intensities in the ratio 4:12:12:24:24. This is not in agreement with the data very recently pubFigure 5. Photograph of assembled models of Cqa, C ,,, and C,,. lished (9)showing that a purified sample of C76prepared
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Figure 6. Cutout pattern for construction of a G6model with Tdsymmetry.
Figure 7. Cutout pattern forconstruction of a G6model with 4 symmetry as previously (7) exhibits 19 resonances of near-equal intensity, wmpatible only with a chiral structure of D2 symmetry. Among several depictions of this novel structure (9) is a photograph of an enantiomeric pair of CT6models constructed from paper hexagons and pentagons. One enantiomer is conveniently represented by the planar paperpattern shown in Figure 7. Literature Cited l.Krstmhmer,W.; Lamb, L.D.;Fostimpodhs,K.;HuBman,D.R.NoNn 1880,347,254.
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2. Kmto, H. W.:Heath, J. R.: O'Brien, C.; Curl, R. F.: SmaUey, R. E.Noture 1985,318. 162. 3. nawkina, J. M.;M ~A,; kwis, ~ ~T A,;~LO-,, s.;~ ~ uS.R.~scirir~ ISSI. d ~252,~ 312. 4. Aiie, H.; Nv-, M. M.; h,S.J.;Beek. R. D.; ~ i e d e r i hF; , ~oatimpoulos.K, HUB. man,D.R:Kr&tmhma,W.; Rubin.Y.;Sehriveq K E.; S e n a h m a . D.;Whettea,R. L.J. PAYS. them. 1890,94,ffi30. 5. Stoddart, J. F ~ n s e wc k m . ~ n~d t EWI. 1981,30,70. 6. n e d e c h , F.;metten, R. L A ~ P Wc b m . I"
