5 p nanotubes chiara
TRANSCRIPT
NANOTUBI DI CARBONIO : struttura, proprietà, sintesi, applicazioni….. (SEMINARIO di CHIARA CASTIGLIONI)
Here we have what is almost certainly the strongest, stiffest, toughest molecule that can ever be produced, the best possible molecular conductor of both heat and electricity. In one sense the carbon nanotube is a new man-made polymer to follow on from nylon, polypropylene, Kevlar. In another, it is a new “graphitic” filler, but now with the ultimate possible strength. In yet another, it is a new species in organic chemistry, and potentially in molecular biology as well, a carbon molecule with the almost alien property of electrical conductivity, and super-steel strength.
R.E. Smalley, Chemistry Nobel 1996
Pres
sure
(GPa
)
A: commercial synthesis of diamond fromgraphite by catalysis;
B: P=T threshold of very fast (<1 ms) solid-solid transformation of graphite to diamond;
C: P=T threshold of very fast transformation of diamond to graphite;
D: single crystal hexagonal graphite transformsto retrievable hexagonal-type diamond;
E: upper ends of shock compression/quenchcycles that convert hex-type graphite particlesto hex-type diamond;
F: upper ends of shock compression/quenchcycles that convert hex-type graphite to cubic-type diamond;
B, F, G: threshold of fast P=T cycles, howevergenerated, that convert either graphite or hexagonal diamond into cubic-type diamond;
H, I, J: path along which a single crystal hex-type graphite compressed in the c-direction at room temperature loses some graphitecharacteristics and acquires propertiesconsistent with a diamond-like polytype, butreverts to graphite upon release of pressure.
Phase diagram of carbon emphasizing graphite, cubic diamond, and hexagonal diamondphases, as well as liquid carbon. Solid lines represent equilibrium phase boundaries.
OTHER CARBON MATERIALS
disordered carbons
“graphitic”
– micro and nanocrystalline graphites– carbon fibers– glassy carbon– porous graphites– carbon black
mixed sp2, sp3, spC atoms
– amorphous carbons– diamond like carbons (DLC)
fullerenes
nanotubes
D. Donadio, L. Colombo, P. Milani, G. Benedek, Phys. Rev. Lett., 83, 776-779 (1999)
Carbon nanotubes, M.S. Dresselhaus, G. Dresselhaus,Ph. Avouris (Eds.) Springer (2001)
– fullerenes– nanotubes– amorphous carbons
– carbon nanotubes– porous graphites
– carbon fibers, amorphous carbons and DLC hard coatings
APPLICATIONS
electronics
energy storage, batteries, sensors
mechanical and tribologicalapplications
Legame σ tra orbitali atomici di tipo np (pz)
Legame π tra orbitali atomici di tipo np (px,py)
L'ibridazione nel carbonioC (Z = 6)configurazione elettronica: 1s2 2s2 2p2
1s2 shell Kalto potenziale di ionizzazionenon e' interessata allaformazione del legame chimico
2s2 2p2 shell Lincompleta, a piu' alta energia(minore potenziale di ionizzazione)Responsabile del legame chimico
Ibrido sp3: lobi diretti nello spazio secondo i vertici di un tetraedro il cui centro corrisponde al nucleo del carbonio
( )zyx ppps 222221
1 +++=ψ
( )zyx ppps 222221
2 −−+=ψ
( )zyx ppps 222221
3 −+−=ψ
( )zyx ppps 222221
4 +−−=ψ
Si ottengono 4 orbitali ibridi dalla combinazione di 1 orbitale scon 3 orbitali p notazione sp3
x
y
z
(-1,-1,1)
(0,0,0)
(1,1,1)
(-1,1,-1)
(1,-1,-1)
Giustificazione dell’orientamento spaziale degli orbitali ibridi sp3
( )zyx ppps 222221
1 +++=ψ
( )zyx ppps 222221
2 −−+=ψ
( )zyx ppps 222221
3 −+−=ψ
( )zyx ppps 222221
4 +−−=ψ1
23
4
Ibrido sp2
3 elettroni di valenza
1 elettrone di valenza
( )xps 2223
11 ⋅+=ψ
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅+⋅−= yx pps 2
232
212
31
2ψ
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅−⋅−= yx pps 2
232
212
31
3ψ
zp2
Ibrido sp
yp2xp2
Restano non ibridizzati( )zps 22
21
1 +=ψ
( )zps 222
12 −=ψ
Ibrido sp
Esempio di molecole con carbonio in stato diibridazione sp3: metano
Esempio di molecole con carbonio in stato diibridazione sp3: etano
Esempi di ibridi sp2: copresenza di legame σ e π
σ
π
Etilene,
H2C=CH2
Esempi di ibridi sp2: copresenza di legame σ e π
σ
π
Butadiene,
H2C=(CH)-(CH)=CH2
Esempi di ibridi sp2: copresenza di legame σ e π
σ
π
Benzene,
C6H6
Esempi di ibridi sp: copresenza di legame σ e π
Acetilene,H-C≡C-H
Triplo legame:1 di tipo σ, 2 di tipo π
Struttura del diamante (ibridazione sp3)
metano (n=1)
etano (n=2)
propano (n=3)
esano (n=6)
butano (n=4)
pentano (n=5)
ALCANI (ibridazione sp3)
Struttura della grafite (ibridazione sp2)
Vista lungo l'asse c
Ass
ec
1D π conjugated systems:
polyenes
2D π conjugated systems:
PAH, Polycyclic Aromatic Hydrocarbons
POLYCONJUGATED MOLECULES
conjugated 2pz orbitals
Grafite nanostrutturataPAHPolycyclicAromaticHydrocarbons
Nanotubi di carbonio(ibridazione prevalente sp2)
Stable forms of carbon clusters: (a) a piece of a graphene sheet, (b) the fullerene C60, and (c) a model for a carbon nanotube.
Graphene ribbons terminated by (a) armchair edges and (b) zigzag edges, indicated by filled circles. The indices denote the atomic rows for each ribbon.
(a) as obtained from an electricarc deposit, the particles display a well-defined faceted structureand a large inner hollow space
(b) the same particles after beingsubjected to intense electron irradiation. The particles nowshow a spherical shape and a much smaller central empty space.
High-resolution electron micrographs of graphitic particles
Sketch of the cross section of a PAN carbon fiber along the fiber axis direction.
Here the in-plane (La) and c-axis (Lc) structural coherencelengths are indicated.
Schematic model for the microstructure of activated carbon fibers
Fiber after some heattreatment, showing partialalignment of the basic structural units.
High surface area fiberwhere the basic structuralunits are randomlyarranged
D. Donadio, L. Colombo, P. Milani, G. Benedek, Phys. Rev. Lett., 83, 776-779 (1999)
Nanostructured amorphous carbon films
Reference book:Carbon nanotubes, M.S. Dresselhaus, G. Dresselhaus, Ph. Avouris (Eds.) Springer (2001)
S.Ijima, Nature 358, 220 (1991)Nanotubi cresciuti sul catodo durante una scarica ad arco tra 2 elettrodi di grafite (T≈ 3000 K)
Multi-walled carbon nanotubes
Multi-walled carbon nanotubes
Fullerenes within SWNTs: peapods
La@C82
Heat treatment of peapods producesdouble-wall NT
Carbon nanotubes, M.S. Dresselhaus, G. Dresselhaus,Ph. Avouris (Eds.) Springer (2001)
(5,5)
(10,5)
(9,0)
Ch = 4 a1+ 2 a2 nanotubo (4,2)
Rosso: 3,3 armchair, θ=45°
Rosso: (5,0) zig-zag θ=0°
The unrolled honeycomb lattice of an Armchair nanotube
Ch = Chiral vectorT = Translation vector (k)
structural unit
Electronic 1D density of states per unit cellof a 2D graphene sheet for two (n,0) zigzag nanotubes:
(a) the (10,0) nanotube which hassemiconducting behaviour,
(b) the (9,0) nanotube which has metallicbehaviour.
Also shown in the is the density of states for the 2D graphene sheet (dotted line).
Derivative of the current-voltage dI/dVcurves obtained by scanning tunnellingspectroscopy on various isolated single-wallcarbon nanotubes with diameters near 1.4nm. Nanotubes #1 - 4 are semiconducting and #5 - 7 are metallic.
Ch = 4 a1+ 2 a2 nanotube (n,m) → (4,2)
1 2
1 21
1 1
2
2 2
(0,-1) (1,0)
(-1,0) (0,1)
Hamiltoniano elettronico H = H(θ1,θ2) alla Hückel(i.e. tight-binding ristretto a orbitali 2pz)
θi = k•ai
a1
a2
T
Ch
ϕ1τ1
τ2
ϕ2
Curve di dispersione elettronica (4,2)
Funzione del numero quantico μ = 0 .. 25
Ener
gia
in u
nit à
di β
μ = 0
μ = 1
EF
π∗
πμ = N - 1
ξ = π
ξ = -π
Γ0
K
M
μ = 1
μ = 2
μ = 3
ξ = 0
μ = 0
K1
K2
K K
KK
K
Curve di dispersione elettronica (6,3)
Funzione del numero quantico μ = 0 .. 41
Ener
gia
in u
nit à
di β
NT conduttore
Curve di dispersione elettronica (17,8)
Ener
gia
in u
nit à
di β
Funzione del numero quantico μ = 0..325
Densità di stati elettronicidi due nanotubi chirali
metallici
(14,5)(11,8)
EF
EF
Van Hovesingularities
Zigzag: (10,0) Ch ≅ 2.42 nm
Armchair: (10,10) Ch ≅ 4.2 nm
( ) ( )( )[ ]{ } 2121cos1cos12cos23, ϕϑϕϕθε ++±+= mp
( ) ( )( )[ ]{ } 2121cos1cos12cos23, ϕϑϑϕθε ++±+= mp
Analytic expressions for the electronic energies have beenobtained with a symmetry treatment of Pz orbitals in the frame of Hückel Theory
ε ε
θ/π θ/π
(10,10) Ch ≅ 4.2 nm
(10,0) Ch ≅ 2.42 nm
Wave function, Van Hove peak at energy -0.95 Beta units
Tube axis
Energy dispersion and density of states for(9,0) zigzag nanotube
Density of states for (150,150) armchair nanotube
(150,150) Ch=63 nm
Figure 5: TEM micrographs of seaweed-like carbon objects produced at 6.5 GPa and 950°C.Figure 4: TEM micrograph (a) at low magnification
and (b), (c) at high magnification of MWNT treated at 5.5 GPa and 950°C.
100
200
300
400
500
600
700
800
900
1000
1100
1200
Abs
orba
nce
1400 1600 1800 2000 Wavenumbers (cm-1)
1580G
100
150
200
250
300
350
400
450
500
550
600
650
700
750
800
850
900
Abs
orba
nce
1400 1600 1800 2000 Wavenumbers (cm-1)
1573
1330D
G
Raman spectra of graphite and amorphous carbon
Crystalline graphite
Disordered graphite
Annealed amorphous carbon courtesy of A.C. Ferrari
Dept. of EngineeringCambridge (UK)
Ram
an Intensity
Ram
an Intensity
Wavenumbers (cm-1)
Wavenumbers (cm-1)
Ram
an Intensity
GD
Wavenumbers (cm-1)
Spettri Raman Risonanti di un campione di nanonotubi singola parete contenente nanotubi di diversi diametri
A.M. Rao, E. Richter, S. Bandow, B. Chase, P.C. Eklund, K. W. Williams, M. Menon, K. R. Subbaswamy, A. Thess, R. E. Smalley, G. Desselhaus, M.S. Dresselhaus, Science 275 (1997) 187
Room temperature RBM spectra for bundlesof SWNTs produced by pulsed
laser vaporization using an Fe/Ni catalyst in a carbon target. Spectra (a)-(d) are
collected at fixed laser excitation energy (1.17 eV; Nd:YAG) from samples grown at
T = 780, 860, 920 and 1000 °C, respectively. Note that the spectral weight shifts to
smaller RBM frequencies with increasinggrowth temperature (Tg) indicating thatdiameter
increases with increasing Tg. The intensitiesand frequencies of the RBM bands in
spectra (e)-(g) collected from the same sample(Tg=1000°C) but with different laser
excitation energies (488nm; 514.5nm; 647 nm; 1064nm) are quite different, demonstrating how different diameter tubesare excited as the excitation energy changes.
Taken from:S.K. Doorn et al., PRL 94, 016802 (2005)
G+
G+G-
Raman spectroscopy is used to characterize carbon nanotubes; the G band brings important structural information
Studying a metal/semiconductor junction in a nanotube using space-resolved Raman
G- is associated tometallic tubes: why ?
Carbon nanotubes:
extended π-conjugated systems
long range electronic and vibrational interactions
crucial dependence of the electronic structure on the geometric structure (n,m)
phonons do experimentally depend on the diameter and electronic structure of the tube
⇒ Fairly challenging system to model !
Polyconjugated carbon systems
Kohn Anomalies and Electron-Phonon Interaction in Graphite (S. Piscanec, M. Lazzeri, F. Mauri, A. C. Ferrari, and J. Robertson, PRL, 93 (2004))
Graphite & Carbon Nanotubes
See poster 39-M, M. Tommasini, A. Milani, A. Lucotti, M. Del Zoppo, C. Castiglioni, G. Zerbi
… Polyynes also !
C. Castiglioni, et al. Phyl. Trans. R. Soc. Lond. A., 362(2004)
PolyenesRaman dispersion with chain length
- Structural unit: 2 atoms- Screw axis symmetry- Real (curved) geometry
Modeling electrons and phonons in carbon nanotubes
A general treatment forany carbon nanotube
(n,m)
Bloch theorem and nanotube boundary
conditions
- band structure- DOS
Calculation of phonons on the basis of valence
coordinatesGFL = Lω2
(with curved geometry)
- phonon dispersion- vibrational displacements- phonon DOS
Ch = 4 a1+ 2 a2 (4, 2) nanotube
Describing the geometry of a generic (n,m) nanotube
μ = N - 1
ξ = π
ξ = -π
Γ0
K
M
μ = 1
μ = 2
μ = 3
ξ = 0
μ = 0
K1
K2
K K
KK
K
Electronic band structure of semiconducting (4,2) nanotube
Function of the quantum numbers μ,ξ
Ener
gy
(units
of β )
μ = 0
μ = 1
EF
π∗
π
(14,5)
EF
Ohno’s three parameters force field (1) generalised to graphite (2)(1) K. Ohno, J. Chem. Phys. 95, 5524 (1995)
(2) C. Mapelli, C. Castiglioni, G. Zerbi, K. Müllen, Phys. Rev. B (1999)
semiempirical parameters
( ){ }
'')','(),(
..)]','(*),()','(*),()][','(),(*)','(),(*[2
12121
21210
212102121021210212104, ϑϑϑϑ
ϑϑεϑθεϑϑϑθϑϑϑθϑϑϑθϑϑϑθ
π
π
π
λμμλνσσνπ
π
π
π
π
πνσλμ dddd
cccccccccc
e
eeee∫∫∫∫−−−− −
+++=Π
electronic structure (Hückel)
The vibrational force fieldis coupled to the
electronic structure
bond stretching force constants
bondorder
bond-bondpolarizability
jiij
Eββπ
∂∂∂
≡Π2
S. Piscanec, M. Lazzeri, F. Mauri, A. C. Ferrari, and J. Robertson, PRL, 93 (2004)Kohn Anomalies and Electron-PhononInteraction in Graphite
jiij
Eββπ
∂∂∂
≡Π2 Long range
stretching force constants
Phonon dispersion curves of graphiteKohn anomaly and long range
interactions
Ohnoforce field;
variablethreshold on
fij
Geometrical parameters of the (n,m) tube
Boundary conditions:
Brillouin zone integration
The correct long range behavior of the force field is dictated by the electronic-structure dependent bond-bond polarizabilities Π:
Generalization of the Ohno Force Field to nanotubesof any diameter and chirality
Method based on graphene cell (2 atoms) + screw axis symmetry
Metallic: slow decaySemiconducting: fast decay
Bond-bond polarizabilities Πij
jiij
Eββπ
∂∂∂
≡Π2
It is directly related to stretchingforce constants
The G matrix is specific for any given nanotube:
G = G(n,m)
tube curvature
The F matrix is specific for any given nanotube
electronic structure (Πij):
F = F(n,m)
All data shown are taken from:A. Jorio, A. G. Souza Filho, et al., Phys. Rev. B, 65, 155412 (2002)
G band:different frequency dispersion law(while changing the tube diameter) observed for metallic and semiconducting nanotubes
Raman spectra of individualsingle wall nanotubes
(18,9)
(19,1)
(11,2) (17,7)
metallic
semiconducting
(17,3)
(15,2)
G- transversal ?(dramatically
diameterdependent…)
G+ longitudinal ?(diameterindependent…)
Empirical force field(armchair tubes)
Experimental findingsby Jorio et al.
longitudinal G- transversal G+
longitudinal
transversal
A. Jorio, et al., Phys. Rev. B, 65, 155412 (2002)
Large longitudinal/transversalsplitting: favourably compareswith experiments and…
independent theoretical worksby M. Lazzeri et al. PRB 73, 155426 (2006)
μ=1
μ=0
Dispersion of the G line Full symbols: longitudinal phononsOpen symbols: transversal phononsCold colours: metallic CNTsWarm colours: semiconducting CNTs
Phonons of the chiral (6,3) metallic tube
Conclusions
1. Carbon nanotubes share long range interactionphysics similarly to other π-conjugated systems(polyacetylene, graphite)
2. A successful and general model of phonons in nanotubes has been introduced which couplesto the electronic structure of the given (n,m) tube
3. The correct longitudinal/transversal splitting of the Gphonon as a function of tube diameter is found. The assignment of the long./transv. character of G phonons for general tubes is proposed