Fullerenes 1

More documents

Recommendations

Info

Fullerene counting By substituting vv, , ee and ff (as below) in (3) one obtains: 3 v = ∑ s ⋅ f e s s = 2 f ∑ = s ∑ f s s s) f s ( 6 − = 12( 1− g) (1’-2’) (1’ 2’) •For For a given genus of the surface, (5) ( ) gives the number of s-polygons. polygons. This condition is independent of the number of hexagons, hexagons, which is therefore arbitrary. arbitrary •Special Special cases are the Platonic Platonic tilings, tilings, with a single kind of polygons, polygons, and the Archimedean Archimedean tilings, tilings, with two different kinds of polygons, polygons, one of which being here the hexagon. •In In Platonic fullerenes (gg = 0): from (5), 5 ff =12, or Archimedean fullerenes must always contain 12 5; ff thus from (1’-2’): (1 ): 5ff 5 + 6 6ff 6 = 60+ 6 6 = 3 3v v ; 6 = (v/2)-10 (v/2) 10. = 60+ 6ff 6 ; ff 6 (4) (5) or 4 ff = 6 or 3 ff = 4. ; thus 6 ff comes out 20
Spiral code • Spiral conjecture: 1 the surface of every fullerene polyheron may be unwound in at least one way as a continuous spiral strip of of edge-sharing edge sharing faces. • Spiral code implies the existence of a Hamiltonian path. path. • Spiral code is useful in: – systematic nomenclature – enumeration and construction of isomers Non-spiralability, Non spiralability, 2 in: - fused triples or quadruples of pentagons - between 20
Page 1 and 2: Fullerenes 1 Mircea V. Diudea Facul
Page 3 and 4: Fullerenes: Short History (by Kroto
Page 5 and 6: Aulonia Aulonia hexagona hexagona (
Page 7 and 8: First Considerations • Eiji Osawa
Page 9 and 10: Calculations and Nomenclature • D
Page 11 and 12: Nanotubes and Tori • S. Iijima, I
Page 13 and 14: Isolated Fullerenes • N N = 20, 3
Page 15 and 16: C Nomenclature 60 Nomenclature 60 1
Page 17 and 18: Planar Graph A graph is planar plan
Page 19: Fullerene counting Rewrite relation

Fullerenes 1

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?