lecture 6 raman spectra of carbon nanotubes. infrared (ir) spectroscopy ir 700 nm3500 nm400 nm...
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Lecture 6Raman spectra of carbon nanotubes
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Infrared (IR) spectroscopy
IR
700 nm 3500 nm400 nmVisible light
IR
IR spectra can be used to identify the types of molecules or functional groups
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Energy
Inter-nuclear distance (r)
req
Bond extensionBond compressionCoulomb attractionCoulomb repulsion
2. Hooke’s law: = -k(r – req)..(1) : restoring forcek: force constant
E1
E2
1. E1 E2, vibration frequency remains the same but vibration amplitude increases (r).
3. Energy E = k(r – req)2/2…(2)
Diatomic vibration
4. The minimum energy (stable state) is when r = req, E = 0
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A simple harmonic oscillator
Vibration frequency osc = (1/2)(k/)1/2Hz...(3)
: reduced mass of system
osc = (1/2c)(k/)1/2cm-1….(4)
c: velocity of light
This is Hz in unit, if one converts Hz into wavenumbers, Eq(3) can be expressed as
Vibration energy is quantized
E = ( + ½)ħosc (joules)…(5)
= 0,1,2,3….(vibrational quantum number)
Convert E into wave number unit, we have
= E/ c = (ħ + ½)osc (cm-1)…(6)
Eq(6) is energy allowed to a simple harmonic oscillator
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Energy
cm-l
reqInter-nuclear distance (r)
= 0osc1/2
osc3/2
osc5/2
osc7/2
osc9/2
= 1
= 2
= 3
= 4
= ( + ½)osc
Any molecules can never have zero vibration energyor atoms can never be completely at test relate toeach other---(zero point energy E0 = ħosc/2 (joules) or o = osc/2 (cm-1).
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Vibrational changes due to interaction with radiation (electromagnetic wave)
Vibrational changes can only be = 1 (selection rules)
+ 1
- 1
+ 2
- 2
wrong!
Emission = ( + 1 + 1/2)osc - ( + 1/2)osc
= osc
Adsorption = osc
Vibrational change always involves the same energy
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1.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.
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How a molecule produces a dipole ?
Example: water molecule (H2O)
OH H
-+ +
dipole momentdipole moment
Net dipole = 0
O
H H
Linear form
V-form
Net dipole 0
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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 stretchingNet dipole 0
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Time axis
Net dipole
IR radiation
resonance
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Types of vibration
Symmetrical stretching
Asymmetrical stretching
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Scissoring twisting
wagging rocking
Different vibrations give different frequencies (same molecules)
C
HH
C
HH
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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
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Laser beam
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Raman spectrum of arbon nanotubes
20-30
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High frequency region:
D band: 1370 cm-1(disorder structure)
G band: 1580 cm-1(graphitic structure)
Low frequency region
Radial breathing mode (RBM): < 300 cm-1
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at higher frequency
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A1g mode at low frequency
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g: Ramanu: IR
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ID/IG: determination of graphitization
Smaller ID/IG highly graphitizationLarger ID/IG less graphitization
Why D-band means disorder structure and G-band for graphitized structure?
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Different bond lengths Different bond lengths
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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 andtwo types of bond lengths at periphery.
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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).
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Such a C-C vibration is very sensitive to periphery regions, and is dependent of sheet size.
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When sheet size increases, what happens?
The central region increases, so amount of C-C stretching motion increasesE2g 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
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When sheet size decreases, intensity of E2g mode decreases and A1g
mode increases, why? and we said before that A1g is sensitive toSize, why?
Periphery region (two types of bond lengths)
Central region (one type of bond length)
because
increases
1580 cm-11370 cm-1
1.42Å1.36Å1.46Å
Small size of sheetLarge size of sheet
decrease
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D-band G-band ID/IGID/IG
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2 nm <
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Various diameters of tubes
514 nm laser
613 nm
shift
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RBM also depends on temperature
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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
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radial vibrationC-C stretching
C-C bending
Thermal expansion of a tube
C-C stretching undergoes the greatest influence by temperature variation
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Why longer bond length gives lower vibration frequency?
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1. Inter-tube spring is a function of van der waals interaction
1
2
2. intra-tube spring is a function of C-C bond strength and tube diameter.
CC
R
R
2 > 1