Lecture 6Raman spectra of carbon nanotubes

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

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

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

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).

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

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.

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

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

Time axis

Net dipole

IR radiation

resonance

Types of vibration

Symmetrical stretching

Asymmetrical stretching

Scissoring twisting

wagging rocking

Different vibrations give different frequencies (same molecules)

C

HH

C

HH

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

Laser beam

Raman spectrum of arbon nanotubes

20-30

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

at higher frequency

A1g mode at low frequency

g: Ramanu: IR

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?

Different bond lengths Different bond lengths

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.

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).

Such a C-C vibration is very sensitive to periphery regions, and is dependent of sheet size.

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

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

D-band G-band ID/IGID/IG

2 nm <

Various diameters of tubes

514 nm laser

613 nm

shift

RBM also depends on temperature

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

radial vibrationC-C stretching

C-C bending

Thermal expansion of a tube

C-C stretching undergoes the greatest influence by temperature variation

Why longer bond length gives lower vibration frequency?

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