M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 3
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The most important biological discoverysince Darwin’s theory of evolution was the double helical structure ofthe matter of heredity, DNA, by Francis Crick and James D. Watson(Figure 1-2) [8]. In addition to the translational symmetry of helices(see, Chapter 8), the molecular structure of deoxyribonucleic acid asa whole has C2 rotational symmetry in accordance with the complementary nature of its two antiparallel strands [9].
The discovery of thedouble helix was as much a chemical discovery as it was importantfor biology, and lately, for the biomedical sciences.In the 1980s, two important discoveries in molecular science andsolid-state science were intimately connected with symmetry. OneFigure 1-1. Kenichi Fukui (left), 1994, and Roald Hoffmann, 1994 (photographsby the authors).41 IntroductionFigure 1-2. Left: James D. Watson, 2003; Center: a sculpture of the double helixby Bror Marklund at Uppsala University; and Right: Francis Crick (photographs bythe authors).was the C60 molecule, buckminsterfullerene [10] and fullerene chemistry.
It has greatly contributed to the emergence of nanoscienceand nanotechnology. The other discovery was the quasicrystals [11].Buckminsterfullerene will be mentioned again in Section 3.7. andthe quasicrystals in Section 9.8. Here, we present only some generalconsiderations.The C60 molecule was named after Buckminster Fuller (1895–1983), the American designer (Figure 1-3).
The U.S. Pavilion at theMontreal Expo 1967 (Figure 1-4) was built according to his designand it inspired the discoverers of buckminsterfullerene in finding theFigure 1-3. Left: Buckminster Fuller, 1973 (photograph by and courtesy of LloydKahn, Bolinas, California); Right: Avogadro and his law on an Italian stamp.1 Introduction5Figure 1-4. The U.S. Pavilion at the Montreal Expo 1967 with a pentagon indicatedin the close-up (photographs taken in 1995 by the authors).structure of C60 . Fuller was not a bona fide scientist, but geometry wascentral to his peculiar philosophy. To him Avogadro’s law (Figure 1-3)showed that chemists considered volumes as material domains and notmerely as abstractions. Fuller recognized the importance of synergyfor chemistry [12]:Chemists discovered that they had to recognizesynergy because they found that every time theytried to isolate one element out of a complexor to separate atoms out, or molecules out, ofcompounds, the isolated parts and their separatebehaviors never explained the associated behaviorsat all.
It always failed to do so. They had to dealwith the wholes in order to be able to discover thegroup proclivities as well as integral characteristicsof parts. The chemists found the Universe alreadyin complex association and working very well.Every time they tried to take it apart or separate itout, the separate parts were physically divested oftheir associative potentials, so the chemists had torecognize that there were associated behaviors ofwholes unpredicted by parts; they found there wasan old word for it—synergy.Curiously, Avogadro has also been proposed to be the godfather offullerenes for he was the inventor of the concept of monoelementalcompounds [13].
The suggestion came from D. E. H. Jones who had61 Introductionbrought up the idea of the hollow-shell graphite molecule almost twodecades prior to the discovery of buckminsterfullerene [14]. Jones alsoreferred to a biological analogy of what would be considered today amodel of a giant fullerene molecule. A few pentagons are seen interspersed in the generally hexagonal pattern of Aulonia hexagona shownin Figure 1-5 [15].
The similarity is striking to Fuller’s GeodesicDome at the 1967 Montreal Expo.In chemistry, the first suggestion of a C60 molecule came from EijiOsawa (Figure 1-6) who tried to construct closed three-dimentionalmolecules with aromaticity and hit on the truncated icosahedral shapepurely on the basis of symmetry considerations [17].
The next stepwas the computational work by Gal’pern (Figure 1-6) and Bochvarwho determined the truncated icosahedral shape for C60 to representan energy minimum [18]. These early reports originally appearedin Japanese and in Russian, respectively. They had no impact andreceived recognition only after the work of Harry Kroto, RichardSmalley, Robert Curl (Figure 1-7), and their students had broughtgreat publicity to the new molecule.The Geodesic Dome played an important role in leading thediscoverers of buckminsterfullerene to the right hypothesis about itsmolecular structure. Both Kroto and Smalley had visited the Domealmost two decades before, and what they could vaguely rememberassisted them and their colleagues to arrive at the highly symmetricaltruncated icosahedral geometry (Figure 1-8) (see, also, Section 2.8Figure 1-5.
Ernst Häckel’s Aulonia hexagona in D’Arcy W. Thompson, On Growthand Form [16].1 Introduction7Figure 1-6. Eiji Osawa (left), 1994 (photograph by the authors) and Elena Gal’pern(courtesy of Elena Gal’pern, Moscow).on Polyhedra) during the exciting days following the crucialexperiment [19].Mathematicians have, of course, known for a long time [21] thatone can close a cage of even-number of vertices with any numberof hexagons (except one), provided that 12 pentagons are includedin the network. The truncated icosahedron has 12 pentagons and20 hexagons, and it is one of the semi-regular solids of Archimedes(see, Section 2.8). Leonardo da Vinci (1452–1519) drew a hollowframework of this structure to illustrate the book De Divina Proportione by Luca Pacioli (Figure 1-8).
All such carbon substancesFigure 1-7. The principal discoverers of buckminsterfullerene: From left to right,Robert F. Curl, 1998; Harold W. Kroto, 1994; and Richard E. Smalley, 2004(photographs by the authors).81 IntroductionFigure 1-8. Models of the truncated icosahedron: Leonardo da Vinci’s drawing forLuca Pacioli’s De Divina Proportione (left) and decoration at the Topkapi Sarayi inIstanbul (photograph by the authors) [20].whose cage molecules contain 12 pentagons and various numbers ofhexagons, are called fullerenes, of which C60 has the special namebuckminsterfullerene.
Another artful representative of this shape isabove an entrance to an exhibition hall at the Topkapi Palace (TopkapiSarayi, in Turkish) in Istanbul (Figure 1-8).An early and beautiful example of the fullerene-type structureswas found in China [22].
Dragon sculptures are common in Chinaas guards standing in front of important buildings. They appear inpairs. The female has a baby lion under the left paw and the male hasa sphere under the right paw. This sphere is said to represent a ballmade of strips of silk which was a favorite toy in ancient China. Thesurface of the ball is usually decorated by a regular hexagonal pattern.We know, however, that it is not possible to cover the surface of thesphere by a regular hexagonal pattern.
Usually, there are considerablechunks of the sphere hidden by the dragon’s paw and the stand itselfon which the dragon and the sphere stand. There is at least one dragonsculpture (Figure 1-9) under whose paw the sphere is decorated by ahexagonal pattern interspersed by pentagonal shapes.
This sculpturestands in front of the Gate of Heavenly Purity in the Forbidden City,and dates back to the reign of Qian Long (1736–1796) of the QingDynasty. Balls made of strips of silk are popular decorations in Japan.They are called temari and patterns corresponding to the buckminsterfullerene structure occur among them [23].1 Introduction9Figure 1-9. Gold-plated dragon sculpture in front of the Gate of Heavenly Purity(Qianqingmen) in the Forbidden City, Beijing, with close-up (photographs by theauthors) [24].Incidentally, the stormy interest in buckminsterfullerene startedsubsiding a few years after the initial discovery because the originaldiscoverers only observed but failed to produce the substance, so nochemistry could have been performed on it. Wolfgang Krätschmerand Donald Huffman (Figure 1-10) and their students changed thissituation in 1990 when they obtained quantities of C60 from graphitein a discharge experiment [25].
Their work made the new substancecommonly available. The buckminsterfullerene story had an appealfor a broad readership even beyond chemists [26].The other important symmetry-related discovery was the quasicrystals. Both the truncated icosahedral structure of buckminsterfullereneand the regular but nonperiodic network of the quasicrystals arerelated to fivefold symmetry. In spite of this intimate connectionbetween them at an intellectual level, their stories did not cross. Theconceptual linkage between them is provided by Fuller’s physicalgeometry and this is also what relates them to the icosahedral structureof viruses (see, Section 9.5.2 on Icosahedral Packing).The actual experimental discovery of quasicrystals was aserendipity, notwithstanding some pertaining predictions [28].
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