1. Graphite, Graphene (= single sheet) 2D
Diamond 3D
Graphite, Graphene (= single sheet) 2D
Fullerene 0D
The curvature of nanotubes and fullerenes gives them some 3D character, which leads to an admixture of sp3 to the dominant sp2 configuration.
Nanotube 1D

2. 2D: Graphene, a single sheet of graphite
A graphene sheet can be obtained simply by multiple peeling of graphite with a sticky tape . A single sheet is visible to the naked eye under the right conditions.
With the right substrate, one can detect a single layer of graphite with the naked eye. This makes it possible to peel off flakes from a piece of graphite and search for single layer specimens. It is also possible to grow graphene on silicon carbide by segregating a carbon layer to the surface,
Graphene is very strong , has high electron mobility, and makes a trans-parent conductor for applications in displays and solar cells. It can now be fabricated “roll-to-roll” on plastic.

3. 1D: Carbon nanotubes
Carbon nanotubes are grown using catalytic metal clusters (Ni, Co, Fe,…).

4. 0D: Fullerenes 1996 Nobel Prize in Chemistry to Curl, Kroto, Smalley
Buckminster Fuller, father of the geodesic dome
Buckminsterfullerene C60 has the same hexagon + pentagon pattern as a soccer ball. The pentagons (highlighted) provide the curvature.
C60 solution in toluene

5. The many forms of carbon
Carbon is not only the basis of life, it also forms an enormous variety of structures for nanotechnology This versatility is partly due to the ability of carbon to form two stable bonding configurations (sp2, sp3) with different bond geometry (planar, tetrahedral).
sp sp3
-bonds
Note 1: Carbon is unique for life, because it forms long chains (biopolymers, such as proteins and DNA).
Note 2: The sp2 configuration has an additional pz orbital which leads to double bonds. + pz
-bond

6. - and -bonds in carbon
,  refer to the angular momentum l around the bond axis ( l=0 for  , l=1 for  , analogous to s , p in atoms )
-bond:
-bond:
 orbital
-orbital
* orbital
*-orbital + - E   * *
 bond energy
antibonding
bonding
-bond + -bond = double bond
Note 1: Carbon is unique for life, because it forms long chains (biopolymers, such as proteins and DNA).
Note 2: The sp2 configuration has an additional pz orbital which leads to double bonds.

7. Empty bond orbitals from X-ray absorption spectroscopy (XAS)
LUMO, located at the strained five-fold rings
Graphite
C 1s (core level)
photon * *
C 2s,2p
Fullerenes