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Molecular Nanostuctures
1. Introduction. Carbon hybridization and allotropes
Alexey A. Popov, IFW [email protected]
Carbon
6 CCarbon
Mass fraction in the Earth‘s crust: 0.087%Atomic mass: 12.011Isotops: 12C (98.9 %)
13C (1.1 %)14C (nicht stabil, < 10−9 %)
Electron configuration: 1s2 2s2p2
...
Material
Carbon Nano-Material
6 CCarbon
Material
Bonding
Molecular Structure
Compounds
Crystal Structure
Carbon Nano-Material
6 CCarbon
Material
Bonding
Molecular Structure
Compounds
Crystal Structure
Properties
Applications
Characterization methods
Theory
Methods of Synthesis
Carbon Nano-Material
Ene
rgie
Carbon: atomic structure
main quantum number
Ene
rgie
Ground state
C: 1s2 2s2p2
Carbon: atomic structure
main quantum number
Ene
rgie
main quantum number
Ground state Excited state
C: 1s2 2s2p2 C: 1s2 2s1p3
Carbon: atomic structure
Carbon: hybridization
C-sp3
C-sp2
C-sp
Excited state
C-sp
𝑠𝑝𝛼=√0.5 ∙(2𝑠+2𝑝𝑧)
𝑠𝑝𝛽=√0.5 ∙(2 𝑠−2𝑝𝑧)
180º
Carbon: sp-hybridization
C-sp2
Three sp2 hybrid orbitals
120º
Carbon: sp2-hybridization
C-sp3
Four sp3 hybrid orbitals
109.5º
Carbon: sp3-hybridization
Excited state C-sp3
C-sp2
C-sp
Carbon: hybridization
Bonding between atoms: H2 molecule, σ-bondingConstructive
overlap
𝜎 1𝑠=√0.5 ∙ {1𝑠 ( 𝐴 )+1𝑠 (𝐵 )}
𝜎 ∗1𝑠❑ =√0.5 ∙ {1𝑠 ( 𝐴 )−1𝑠 (𝐵 ) }
antibonding σ*-Orbital
bonding σ-Orbital
Bonding between atoms: H2 molecule, σ-bonding
antibondingσ*-orbital
bondingσ-orbital
Atomic orbitals Molecular orbital
bondingπ-orbital
antibondingπ-orbital
Bonding between atoms: σ- and π-bonding
Molecular orbitalAtomic orbitals
Bonding between atoms: σ- and π-bonding
+
C-sp3 compounds: ethane C2H6, single bond
Only σ-bondng, single bond
C-sp2 compounds: ethylene C2H4, double bond
σ-bonding π-bonding
σ- and π-bonding, double bond
C-sp2 compounds: ethylene C2H4, double bond
σ-bonding π-bonding
σ- and π-bonding, double bond
C-sp compounds: acetylene C2H2, triple bond
π-bonding
σ-bonding
σ- and 2 π-bondsTriple bond
Single- versus double- versus triple- CC bonds
Bond length Bond energy
1.53 Å 368 kJ/mol
1.34 Å 611 kJ/mol (+243)
1.20 Å 820 kJ/mol (+209)
Rotation around C-C bond has low barrier (free rotation at room temperature)
Rotation around C=C bond requires breaking of π-bonding, hence high barrier (no rotation at room temperature, rigid framework)
C-sp3 Bonding: Diamond
The lattice structure of cubic diamond and ist elemntal cell
The lattice structure of hexagonal diamond (Lonsdaleit).
C-sp bonding
R(−C≡C−)nR, n = 2–14
The existence of carbyne is myth based on bad science and perhaps even wishful thinking.
H. Kroto
C-sp2 bonding: butadiene, conjugation
Band gap
Free electron, time independent Schrödinger equation
22 ( ) ( )
2r E r
m
2 2 22
2 2 2x y z
( )( ) x y zi k x k y k zx y zr N N N e
2 2 22 2 2( ) ( )
2 2x y z
kE k k k k
m m
2 2 2x y zk k k k
1( ) i
r
e
k rk r
kinetic energy
k wave vector
standing plane wave
Particle in a box (electron in the infinite potential well)
0, 0( )
, 0,
x LV x
x x L
0 L x
V = 0V = ∞ V = ∞
Particle in a box (electron in the infinite potential well)
2 2
2( ) ( ) ( )
2 x xV x x E xm x
0, 0( )
, 0,
x LV x
x x L
( ) sin( ) ( )x x A kx Bcos kx
0 L x
V = 0V = ∞ V = ∞
Particle in a box (electron in the infinite potential well)
2 2
2( ) ( ) ( )
2 x xV x x E xm x
0, 0( )
, 0,
x LV x
x x L
( ) sin( ) ( )x x A kx Bcos kx
2 2
2n
n
kE
m
, 1,2,3,4,...n
nk n
L
sin( ), 0( )
0, 0,n
x
A k x x Lx
x x L
0 L x
V = 0V = ∞ V = ∞
Free electron versus electron in infinite well
2 2
2n
n
kE
m
2 2
2
kE
m
n
nk
L
continuousk
( ) sin( )x x A kx ( ) xik xx xx N e
infinite wellfree electron
dispersion relation
C-sp2 bonding: butadiene, conjugation
Band gap
2 22~ 1/
2
nn
kE L
m , 1,2,3,4,...n
nk n
L
Conjugated C-sp2 systems: π-electron as an electron in a box
C-sp2 bonding: increasing the conjugation length
Increase of the π-system → decrease of the distance between the levels, decrease of the gap
Kekulé
C-sp2 bonding: benzene, PAH(Polycyclic aromatic hydrocarbons)
Naphthalin Anthracen
Phenanthren
Tetracen
ChrysenCoronen (Hexabenzobenzol)
1.39 Å 564 kJ/mol
Bond length Bond energy
1.53 Å 368 kJ/mol
1.34 Å 611 kJ/mol
„Small molecule“ Organic Semiconductors: Acenes
pentacene
tetracene
naphthalene
anthracene
hexacene
3.97 eV
3.84 eV
2.72 eV
2.31 eV
1.90 eV
gap
popular material for OFET
C-sp2 bonding: graphite
3.35 Å
1.42 Å
C-sp2 bonding: graphite
CC Bindungen
1.53 Å 368 kJ/mol
1.34 Å 611 kJ/mol (+243)
1.20 Å 820 kJ/mol (+209)
1.53 Å 357 kJ/molDiamond
Graphite1.42 Å ~474 kJ/mol intra3.35 Å ~4.5 kJ/mol inter
Bond length Bond energy
1.39 Å 564 kJ/mol Benzene
Graphite versus Diamond
The Nobel Prize in Chemistry 1996 was awarded jointly to Robert F. Curl Jr., Sir Harold W. Kroto and Richard E. Smalley
"for their discovery of fullerenes".
The Nobel Prize in Physics 2010 was awarded jointly to Andre Geim and Konstantin Novoselov
"for groundbreaking experiments regarding the two-dimensional material graphene"
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Nanotube~66,000
Graphene~32,000
Statistics for carbon structures in the title of publications
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laser evaporation of graphite
Discovery of fullerenes
Mass-spectrometry analysis of the
clusters
Mass Spectrometry
Time of flightMagnet (Lorenz Force)
laser evaporation of graphite
Mass spectraC60
C70
Discovery of fullerenes
Mass-spectrometry analysis of the
clusters
laser evaporation of graphite
Mass spectra
C60
C70
Richard Buckminster Fuller1895–1983
“Buckminsterfullerene”
Monometallofullerenes
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Publication with “Fullerene” in the title
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160
Kroto et al, Nature 1985
Wolfgang Krätschmer Donald R. Huffman
Fullerene formation mechanism:molecular dynamics
