Molecular Nanostuctures

1. Introduction. Carbon hybridization and allotropes

Alexey A. Popov, IFW Dresdena.popov@ifw-dresden.de

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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Kroto et al, Nature 1985

Wolfgang Krätschmer Donald R. Huffman

Fullerene formation mechanism:molecular dynamics