Architect: Buckminster Fullerw3.phys.nthu.edu.tw/~mou/teach/Fullerenes.pdf · Architect:...

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Fullerenes Fullerenes Fullerenes Fullerenes Architect: Buckminster Fuller

Transcript of Architect: Buckminster Fullerw3.phys.nthu.edu.tw/~mou/teach/Fullerenes.pdf · Architect:...

  • FullerenesFullerenesFullerenesFullerenesArchitect: Buckminster Fuller

  • OrbitsOrbitsbondπ

    OrbitsOrbitsbondπ

    ...... C C

    bondσ bondσ

    2 2 21S 2SC rbon 2Pa 1S 2SC rbon 2Pa2 34 electrons in bonds (SP ) + bond or SPσ π4 electrons in bonds (SP ) bond or SPσ π

  • Euler’s TheoremEuler’s Theorem

    F=E-V+2F E V 2

    F number of facesF = number of facesE = number of edgesE number of edgesV = number of verticesV = number of vertices

    2

  • nC n = number of carbon atomsEach carbon has three edges.

    3V V3V 22 2

    VE F∴ = = +2 2

    SS

    F F=∑

    SF S= 面形之數目12

    S

    SS

    E SF= ∑ (6 ) 12SS

    S F− =∑213

    S

    SS

    V SF= ∑S

    3

    3 S

  • ∑Molecules with 5Molecules with 5--fold symmetryfold symmetry

    6(6 ) 12 is arbitrary.SS

    S F F− = ⇒∑

    12 t 3 5 6C V F F個606 6

    5 6

    20 12 pentagon 3 5 6

    3 60 5 12 6C V

    FF F

    F= +

    ∴ × = × + =

    ∵個

    6 6 203 60 5 12 6 FF∴ × × +

    70 5 6 12 pentagon 3 5 6C V F F= +∵個

    6 6 253 70 5 12 6 FF∴ × = × + =

  • 5Nature 409, 304(2001)

  • 奈米碳管奈米碳管

    6

  • Graphene: Graphite sheetNanotube

    NanoribbonNanoribbon

    Nanoparticle

    7

  • 石墨的結構石墨的結構

    U it llU it llUnit cellUnit cell

    8

  • Crystal and Orientations of CCrystal and Orientations of C6060yy 6060

    250T C°>Free rotational motion

    isotropic→ isotropic→

    250 corner, 3 face atoms form T C°<4 penetrating Simple Cubic latticeswith 4 different orientation of 3-fold axes along 4 g(rotation about these axes smeared out 5-fold symmetry)

  • 2D Crystal with 52D Crystal with 5--fold symmetric moleculesfold symmetric molecules

    100 100A A100 100Orientation Sudden

    A A×Orientation Sudden Changed across domain

    Nature 409, 304(2001)