• Carbon contains six electrons with electronic structure: (1s2), (2s), (2px), (2py), (2pz). Outer s orbital together with three p orbitals form the chemical bonds of carbon with other atoms. • Conventionally, solid carbon has two main structures called allotropic forms: diamond and graphite: - Diamond is tetrahedrally bonded through sp3 hybrid bonds that form a 3D network. - Graphite has a layered structure with each layer called graphene formed by sp2 hybrid bonds that make 120° angles with each other. Hexagonal graphene sheets are held together by weak van der Waals forces. Z
Allotropies of C
Types of spn hybridization:
• Graphene is a flat monolayer of sp2-bonded carbon (C) atoms tightly packed into a 2D honeycomb lattice. It is a basic building block for graphitic materials of all other dimensionalities. • It can be wrapped up into 0D fullerene, rolled into 1D nanotube, or stacked into 3D graphite. • The C-C bond length in graphene is about 0.142 nm. • Andre Geim and Konstantin Novoselov shared the Nobel Prize in Physics 2010 for the groundbreaking experiments regarding the 2D graphene.
Type of spn hybridisation Digonal sp Trigonal sp2 Tetrahedral sp3
Example Acetylene C2H2 Ethylene C2H4 Methane CH4
Orbitals used for bond s, px s, px, py s, px, py, pz
Bond angle 180° 120° 109.5°
Digonal bond (sp) Trigonal bonds (sp2)
Tetrahedral bonds (sp3)
Fullerene (C60): • C60 was named after the architect R. Buckminster Fuller who designed the geodesic dome that resembles the structure of C60. • C60 has 12 pentagonal (5 sided) and 20 hexagonal (6 sided) faces symmetrically arrayed to form a molecular ball. • Existence of C60 had been envisioned by theoretical chemists for years before it was experimentally confirmed by Huffiman and Kratschmer. • In fact, C60 has the same geometric configuration as soccer ball. 4-5
Model for Formation of Single-Walled Carbon Nanotube (SWCNT): • A graphene sheet showing Tz Tc • basic vectors a1 and a2 of a 2D unit cell. Formation of a SWCNT is modeled as a sheet of graphene rolled into a tube with bonds at the end of the sheet forming the bonds that close the tube. T: axis vector about which the sheet is rolled to form SWCNT. C: circumferential vector (rolling direction) vertical to T. n: No. of units of a1 m: No. of units of a2 Different rolling directions on the sheet generate zigzag, armchair and chiral CNTs. 4-6
Cz, (n,0) zigzag Cc, (n,m) chiral
Ca, (n,n) armchair Graphene • • •
Sketch of three different SWCNT structures: a) zig-zag b) armchair c) chiral
• CNTs are generally closed at both ends. • Almost all C atoms are only involved in hexagonal aromatic rings, except some atoms at the ends are involved in pentagonal rings. • C=C bonds in aromatic rings are no longer planar as they should ideally be. This means that hybridization of C atoms is no longer pure sp2 but getting some percentage of sp3, in a proportion increasing as the tube radius of curvature decreases.
Constraints by Minimum Energy Principle: • A SWCNT can have a diameter as small as 1 nm and a length from µm to cm, making it effectively a 1D structure with a huge aspect ratio. Geometrically, there is no restriction to CNT diameter. But energetically, collapse of a SWCNT into a flattened twolayer ribbon is more favorable than maintaining its tubular morphology when the diameter of SWCNT 2.5 nm. On the other hand, the smaller the radius of curvature, the higher the stress and the energetic cost. Thus, a suitable energetic compromise is: the diameter of SWCNT 1.4 nm.
Schematic Views of CNTs: Multiwalled CNT (MWCNT): An easiest MWCNT to imagine is the concentric type, in which SWCNTs with regularly increasing diameters are coaxially displayed according to a Russian-doll...