Raman%20spectra%20of%20carbon%20nanotubes

1
Lecture 6 Raman
spectra of carbon nanotubes
2
Infrared (IR) spectroscopy
IR spectra can be used to identify the types of
molecules or functional groups
IR
3
Diatomic vibration

• E1? E2, vibration frequency remains the
• same but vibration amplitude increases (r?).

req
Energy
Bond extension
Bond compression
Coulomb repulsion
Coulomb attraction
E2
E1
Inter-nuclear distance (r)
? restoring force k force constant
2. Hookes law ? -k(r req)..(1)
3. Energy E k(r req)2/2(2)
4. The minimum energy (stable state) is when r
req, E 0
4
A simple harmonic oscillator
Vibration frequency ?osc (1/2?)?(k/?)1/2Hz...(3)
? reduced mass of system
This is Hz in unit, if one converts Hz into
wavenumbers, Eq(3) can be expressed as
Vibration energy is quantized
? 0,1,2,3.(vibrational quantum number)
Convert E? into wave number unit, we have
Eq(6) is energy allowed to a simple harmonic
oscillator
5
? 4
? 3
Energy cm-l
? 2
? 1
? 0
req
Inter-nuclear distance (r)
6
Vibrational changes due to interaction with
radiation (electromagnetic wave)
Vibrational changes can only be ?? ? 1
(selection rules)
? 2
? 1
?
?
? - 1
? - 2
wrong!
Vibrational change always involves the same energy
7

• Electromagnetic wave only interacts (resonates)
• with molecules that can produce dipole moment.
• 2.Homogeneous molecules cannot produce dipole
• moment, so they do not have IR adsorption
• (e.g. N2, H2). Heterogeneous molecules can
• produce dipole moment so they have IR
• adsorption (e.g. CO2, OH, cooH..)

3. For adsorption, the vibrating molecule only
interacts (resonates) with electromagnetic
wave at the same frequency.
8
How a molecule produces a dipole ?
Example water molecule (H2O)
dipole moment
dipole moment
-


Linear form
Net dipole 0
H
H
O
H
H
O
V-form
Net dipole ? 0
9
Molecular dipole produced by vibrations
A static linear H2O do not have a dipole
But when molecule vibrates dipole may not be zero
Symmetrical stretching Net dipole 0
Asymmetrical stretching Net dipole ? 0
10
resonance
11
Types of vibration
Symmetrical stretching
Asymmetrical stretching
12
Scissoring
twisting
H
H
H
H
C
C
wagging
rocking
Different vibrations give different frequencies
(same molecules)
13
What if molecules have no intrinsic dipole, e.g.
graphite
No dipolar
In this case, we induce dipole by laser beam
(excitation) ? Raman
Raman is a name and he was a Indian
14
Laser beam
15
Raman spectrum of arbon nanotubes
? 20-30
16
High frequency region D band 1370
cm-1(disorder structure) G band 1580
cm-1(graphitic structure)
Low frequency region Radial breathing mode
(RBM) lt 300 cm-1
17
at higher frequency
18
A1g mode at low frequency
19
g Raman u IR
20
(No Transcript)
21
(No Transcript)
22
ID/IG determination of graphitization
Smaller ID/IG ? highly graphitization Larger
ID/IG ? less graphitization
Why D-band means disorder structure and G-band
for graphitized structure?
23
Different bond lengths
Different bond lengths
24
Bond length becomes roughly the same when
approach center, but bond length remains great
differences at periphery, so we can say That
only one type of bond length at the center of the
sheet and two types of bond lengths at periphery.

25
Such a C-C stretching motion mainly occurs at the
central region of graphene sheets. E2g mode is
independent of sheet size and C-C vibration is
locally. When size of graphene sheet increases
the amount of vibration also increases, which
leads to greater intensity of E2g mode (G-band).
26
Such a C-C vibration is very sensitive to
periphery regions, and is dependent of sheet
size.
27
When sheet size increases, what happens?
The central region increases, so amount of C-C
stretching motion increases E2g intensity
increases.
When sheet size decreases, what happens? The
ratio between periphery and central regions
increases. So amount of C-C stretching motion at
central region decreases, and E2g intensity
decreases
28
When sheet size decreases, intensity of E2g mode
decreases and A1g mode increases, why? and we
said before that A1g is sensitive to Size, why?
because
Periphery region (two types of bond lengths)
increases
Central region (one type of bond length)
decrease
1.36Å 1.46Å
1.42Å
1370 cm-1
1580 cm-1
Large size of sheet
Small size of sheet
29
ID/IG
D-band
G-band
ID/IG
30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
2 nm lt
34
shift
613 nm
Various diameters of tubes
35
(No Transcript)
36
(No Transcript)
37
(No Transcript)
38
(No Transcript)
39
(No Transcript)
40
(No Transcript)
41
RBM also depends on temperature
42
Band shift to lower wave number is called
softening, and shift to higher wave number is
called hardening
Why temperature increase causes softening to SWNTs
43
(No Transcript)
44
(No Transcript)
45
Thermal expansion of a tube
radial vibration
C-C stretching
C-C bending
C-C stretching undergoes the greatest influence
by temperature variation
46
Why longer bond length gives lower vibration
frequency?
47
1. Inter-tube spring is a function of van der
waals interaction
R
1
C
C
R
2
2 gt 1
2. intra-tube spring is a function of C-C bond
strength and tube diameter.