# Classical Description Of Raman Effect - Assignment Example

The traditional description of the Raman Effect is given by Placek that is

p=µ0 +α E

Here E represents incident wave’s electric field amplitude and p is the dipole moment of the molecule.

µ0 is permanent dipole moment, E represents the magnitude of the applied electric field and α represents polarizability.[1]

## Modes Of Vibration

Atoms of a molecule are always in motion otherwise they will contradict the Heisenberg’s uncertainty principle (because one would predict the actual position and momentum of the particle). Molecules generally exhibit three modes of vibration, and they are rotational, vibrational and translational. Polyatomic ions show more aggregate fluctuations that are known as Normal Modes. The normal modes of vibration are as follows:

1. Asymmetric wave
2. Symmetric wave
3. Wagging
4. Twisting
5. Scissoring
6. Rocking

Figure 1.2- Different modes of vibration (source: this figure has been taken from reference 8)

### Calculation Of Number Of Modes

First of all, we will define the term degree of freedom ., it is defined as the number of variables required to represent a motion completely. For example, for a particle moving in 3-dimensional motion three coordinates are sufficient to describe this motion. Hence the degree of freedom, in this case, is three. Now if the molecule has N number of particles, then the degree of freedom becomes 3N.

For linear molecule
The number of degree of vibration modes is given by the formula: 3N-5

For nonlinear molecule
The number of degree of vibration modes is provided by the method: 3N-6[11]

Symmetric Stretch Bending vibration

Asymmetric Stretch
0—-0—-0 0—-0—-0
0—-0-0

Change in dipole moment wrt coordinate q =0 or dµ/dq=0 Change in dipole moment wrt coordinate q or dµ/dq≠0 Change in dipole moment wrt coordinate q or dµ/dq≠0
Change in polarizability wrt coordinate q or dα/dq≠0 Change in polarizability wrt coordinate q or dα/dq=0 Change in polarizability wrt coordinate q or dα/dq=0
Raman is an active Infrared active Infrared active in life.

Table 1: the table shows the comparison between symmetric stretch, bending vibration and asymmetric time. (source: this table is taken from reference 1)
The wave would be Raman active only when that vibration brings change in the polarizability of the molecule.

#### Introduction Of Lasers In Raman Spectroscopy

Even after the discovery of Raman effect in 1928, it remained as a theoretical concept only. So many drawbacks were responsible for this ineffectiveness of the Raman effect. One of the main drawbacks was its low sensitivity. In the time when there were no lasers available, the main drawback of Raman spectroscopy was the lack of appropriate intense radiation sources. The use of lasers in Raman spectroscopy made a considerable change. The very first Raman spectra using laser was obtained by using a pulsed Ruby laser as a radiation source and was photographed by Porto, Wood, and Stoicheff.

Just because of the introduction of lasers, following changes took place in the field of classical Raman spectroscopy which was then in practice:

1. It helped in enhancing the sensitivity of spontaneous Raman spectroscopy.
2. It initiated new spectroscopic techniques that were based on stimulated Raman effect like:
a) Coherent anti-Stokes Raman scattering(CARS)
b) Hyper Raman spectroscopy[3]

#### Laser Raman Spectroscopy

INSTRUMENTATION

The main components of Raman Spectrometers are as follows:

1. Light source
Earlier due to the lack of great cause, it became difficult to increase the sensitivity of Raman spectroscopy. In recent times lasers are used to get an intense light beam.
2. Optical components
Optical components such as lenses and mirrors are used to focus the incident light on the sample and to obtain the scattered light by the molecule under investigation.
3. Spectrometer
Another component is the spectrometer itself.
4. Detector
The detector is used to collect Raman spectra. Usually, a CCD camera is used for the purpose.
5. Notch filters
Notch filters are used to filter the Rayleigh light from Raman light before it reaches the detector.

Figure 2- Raman spectrometer (source: this figure has been taken from reference 9)

#### Linear Laser Raman Spectroscopy

When there is a linear relationship between the dipole moment of the molecule and incident light’s amplitude, then that is known as linear laser Raman spectroscopy.

In early times there were many problems like the scattering cross sections were very small, and there were problems in detecting weak signals. So there were many advances in +early techniques.

1. The intensity of incident light can be significantly increased by the use of multiple reflection cells, intracavity methods or a combination of both.
2. Detection sensitivity has been enhanced by the development of image intensifiers and optical multichannel analyzers.
3. The time for the preparation of data for the result’s interpretation has been dramatically reduced by the use of computers for controlling experimental procedure, the calibration of Raman spectra and analysis of data.[1]

Some of the techniques used in Raman spectroscopy to make it more efficient and overcome its some of the significant drawbacks are mentioned below:

1. EXPERIMENTAL TECHNIQUES IN SOLIDS :

DIFFERENCE LASER RAMAN SPECTROSCOPY

In this technique, there are two cells. In one cell there is a simple molecule that is dissolved in liquid, and the other battery has only liquid.The laser light passes through these cells alternatively. The main advantage of this particular difference technique is that it helps in the cancellation of Raman bands of the solvent’s spectra that are unwanted. Small frequency shifts can be accurately determined that occurs due to interaction with the solvent molecules.

Figure 3.1-Rotating sample cell in difference Raman spectroscopy (1-motor, 2- motor block, 3- side parts, 4- motor axis, 5- set screw, 6- kinematic mount, 7- x-y precision ball glider, 8- adjustment screw, 9- divided liquid cell for difference Raman spectroscopy, 10- axis for trigger wheel, 12- trigger hole, 13- bar, 14- optoelectronic array consisting of a photodiode and transistor) source: this figure has been taken from reference 1

ROTATING SAMPLE TECHNIQUE

In some cases, the target molecule gets thermally decomposed due to the massive amount of heat generated at the place where the locus of the laser incident is so prominent. It usually occurs in those kinds of Raman molecules that are strongly absorbing in nature. In this particular technique, the molecule under investigation is made to rotate with some
angular speed.

The rotating sample technique allows input powers which are much higher and therefore one gets better signal-to-noise ratio. This technique can also be combined with different methods by mounting the cell on the rotation axis.

2. EXPERIMENTAL TECHNIQUES IN LIQUIDS

OPTICAL FIBER RAMAN SPECTROSCOPY

In this technique, a thin optical fiber filled with liquid is used. The refractive index of the liquid is more than the refractive index of the thin optical fiber. When the laser beam is incident on the fiber both lights (the laser light as well as the Raman light) are trapped in the core of tissue because of total internal reflection. This way it travels in the fine optical fiber. Using this technique extreme Raman intensity is achievable which is more than conventional techniques with the factor of 103.

3. EXPERIMENTAL TECHNIQUES IN GAS

In the gas phase also the sensitivity of Raman spectra can be increased appreciably by a combination of various detection techniques.

NONLINEAR RAMAN SPECTROSCOPY

When the incident light wave’s intensity has sufficiently increased the oscillation induced by the electron, exceed the linear range that it assumed earlier. This means now the dipole moment of the molecule is not linearly proportional to the amplitude of incident light. Now we have to generalize the equation that we used earlier. The modified equation will now include some powers of E.

p=µ+α E + βE2 +ѴE3

( where α is the polarizability,β is hyper-polarizability, and Ѵ is the second hyperpolarizability .)

For the case of the sufficiently small amplitude of electric field, the higher powers of the electric field that are nonlinear terms in the equation can be ignored and ultimately we will again get the linear relation between the dipole moment and the electric field amplitude.[1]

STIMULATED RAMAN SCATTERING

When the intensity of incident light is larger than a particular value, then the molecules that were there for a specific energy state will gain sufficient energy to go to an upper energy level. In this particular case, the intensity of Raman scattered light is enormous. Under this, we consider the interaction of the target molecule with two electromagnetic waves simultaneously. One of them would be the laser wave with frequency wL, and the other one would be the Stokes wave with frequency wS=wL-WV or the anti-stokes wave with frequency wA=wL+wV. Both the waves will now be coupled by the target molecule which is vibrating at the frequency Wv. This parametric interaction results in the exchange of energy between the pump wave and anti-stokes or stokes wave. This whole phenomenon is known as stimulated Raman scattering. This was first observed by Woodbury et al. and later on was explained by Woodbury and Eckhardt

Figure 5- Stimulated Raman spectroscopy (source: this figure has been taken from reference 1)

DIFFERENCE BETWEEN LINEAR (SPONTANEOUS) AND THE NONLINEAR (INDUCED) RAMAN EFFECT

Some of the main differences between linear and nonlinear Raman effect are as follows:

1) One can observe the phenomenon of stimulated Raman effect only above a threshold pump intensity. The value of this threshold value depends on the amount of the gain of Raman medium and pump region’s length.

2) The power of spontaneous Raman lines is proportional to the incident pump intensity, but the magnitude is much lower than that of the pump intensity. In contrast, the stimulated anti-Stokes or Stokes lines are not linearly dependent on the pump wave, but their powers are appreciably comparable to the power of pump wave.

3) For molecular spectroscopy, the prominent advantage of stimulated Raman effect can be benefited at higher concentrations of accelerated Raman lines. One will get better signal-to-noise ratio in the case of accelerated Raman effect than linear Raman effect if the same measuring is made available to both the cases.[1]

COHERENT ANTI-STOKES RAMAN SPECTROSCOPY (CARS)

Incoherent anti-Stokes Raman spectroscopy, two radiation sources of wavenumbers v1 and v2 are made to fall on the target molecule. Due to this four-wave mixing new radiation of wavenumber v3 is produced where the following formula gives v3:

v3=2v1-v2=v1+(v1-v2)

This is more efficient the value is v1-v2 =vi that refers to the Raman active vibrational or rotational transition’s wavenumber of the sample. The scattered radiation is on the anti-Stokes side and is coherent.