12 Raman Effect
Contents:
1. Introduction: A brief about Sir Chandrasekhar Venkata Raman
2. Raman Effect
3. How Raman Measures the Effect of Light Scattering?
4. Classical theory of Raman Effect
5. Limitations of the Classical Theory
6. Quantum theory of Raman Scattering
7. Why the Stokes lines are higher in intensity than the Anti- Stokes lines?
8. Setup used for Raman Effect
Summary
The students will be able to learn about the Raman Effect and its classical and quantum theory. Also to understand the instrumentation for Raman spectroscopy.
1. Introduction: A brief about Sir Chandrasekhar Venkata Raman
Chandrasekhar was born in 1888 in a village in southern India. As a child, Raman was precocious, curious and highly intelligent. His father was a college lecturer in mathematics, physics and physical geography, so the young Raman had immediate access to a wealth of scientific volumes. By the age of 13, he had read Helmholtz’s Popular Lectures on Scientific Subjects.
Raman was deeply interested in music and acoustics. While in college, he read the scientific papers of Lord Rayleigh and his treatise on sound as well as the English translation of Helmholtz’s The Sensations of Tone. This initiated Raman’s later interest in the physics of drums and stringed instruments such as the violin. He used fine-chalk powder and photography to investigate the vibrational nodes of drums; the white chalk remained only at the nodes of the vibrating membrane.
2. Raman Effect
The phenomenon is named after the great Indian Physicist Sir Chandrasekhar Venkata Raman, who first published observations of the effect in 1928.
When a parallel beam of monochromatic light goes through a gas or liquid or transparent solid, a part of light is scattered in all directions (It may be reflected, absorbed or scattered in same manner). The intensity of scattered light is inversely proportional to the fourth power of wavelength. It is found that the scattered light contains exactly the same wavelength as the incident light. This scattering is called as Rayleigh scattering (Elastic Scattering). Apart from this wavelength, the scattered light also contains some weak additional lines. As said earlier that this phenomenon was first discovered by Raman and his collaborators and is known as Raman Effect. A comparison of the wave numbers of these additional lines shows that these Raman lines are independent of the wavelength of the incident light but depends on the nature of scattering substance. For different scattering substance, the displacements of the Raman lines from the incident light are different. Thus, the displacements are characteristics of the scattering substance
Remarks:
- Raman spectroscopy studies the frequency change of light due to the interaction with matter.
- The energy of a vibrational mode depends on molecular structure and environment.
- Raman signal is 10−6 times weaker than incident light. Photon are not absorbed.
- To observe Raman scattering the molecule must be polarisable.
3. How Raman Measures the Effect of Light Scattering?
It is the scattering of the radiation that occurs and gives information about molecular structure Analysis of light scattered by a liquid is not an easy task, and much of the early work in Calcutta was done by the visual observation of color rather than precise measurements of the light’s wavelength as shown in Fig. 1. The fundamentals of Raman’s crucial experiment are outlined in Fig. 2.
The violet light of the solar spectrum is isolated with a violet filter and passed through the liquid sample. Most of the light emerging from the liquid sample is the same color as the incident violet beam: the so-called Rayleigh scattered light. However, Raman and his co-worker K. S. Krishnan were able to show that some of the scattered light was a different color that they could isolate by using a green filter placed between the observer and the sample. The advantage of using a visual observation is that several substances can be studied quickly. In his first report to Nature, titled “A New Type of Secondary Radiation,” Raman indicated that approximately 60 different liquids had been studied, and all showed the same result — some scattered light had a different color than the incident light. “It is thus,” Raman said, “a phenomenon whose universal nature has to be recognized.”
“When light passes through a transparent medium then scattering of light takes place as well as light undergoes a change in frequency and random alteration in phase due to a change in rotational or vibrational energy of the scattering molecules which is called Raman Scattering”.
Thus, Raman Spectroscopy is the intensity Analysis of Raman scattered monochromatic light as a function of frequency of the scattered light.
4. Classical Theory of Raman Effect:
The classical theory of Raman Spectroscopy for molecules is described as a group of atoms performing simple harmonics vibrations, without taking into account the quantization of the rotational and vibrational energy levels.
According to the classical theory, the incident electromagnet field induces an electric dipole moment of scattering system (molecule or solid). Such an induced dipole moment is oscillating with the frequency of the incident radiation and is acting as a secondary source for electromagnetic radiation.
The light is scattered in all the directions
Now, if E is the electric field strength then time varying electric field is given by
According to the laws of classical electrodynamics, an oscillating electric dipole emits radiation of the same frequency at which the dipole oscillates. If the polarizability ‘α’ does not change with time [α = constant], then the induced dipole will re-emit the incident radiation of the same angular frequency. If the molecule is vibrating with a frequency ?v then nuclear displacement q can be written as
Here q0 is vibrational amplitude and if the vibrational amplitude is small, then polarizability can
be expanded in a Taylors series around its equilibrium position
(A small portion is in elastically scattered Raman Scatter composed of Stokes and anti-stokes portions)
5. LIMITATIONS OF THE CLASSICAL THEORY
The classical theory gives very good agreement for Rayleigh scattering and vibrational Raman scattering on frequency dependence. Classical theory is good enough to obtain characteristic molecular vibrational frequencies and use them as molecular signatures in the qualitative analysis.
However, the classical theory has many limitations. It cannot be applied to molecular rotations as classical theory does not ascribe specific discrete rotational frequencies to molecules.
Also classical theory cannot provide information as to how polarizability is related to the properties of the scattering molecule, in particular its characteristic transition frequencies, and to the frequency of the incident radiation. The quantum mechanical theory provides this information and forms the basis for a complete treatment of all aspects of Raman scattering. Quantum mechanical treatment discloses that Raman scattering is a powerful and versatile tool that can be used to determine molecular parameters and to explore in some detail the spectroscopic properties not only of the ground electronic state but also of upper electronic states of molecules. It is noteworthy that every compound/molecule has its Raman Spectra characteristics that help to further identify the molecules in even some devices for many applications.
6. Quantum theory of Raman scattering:
When the incident light of frequency υ collides with a molecule, it is either scattered elastically or inelastically. The light quanta can add or subtract from the system the amounts of the energy equal to the energy difference between the stationary states of the system and let E be the energy difference between two levels. If the system is initially in the lower state and is brought to the upper state by scattering of light quanta, the energy ΔE being subtracted from the light quantum.
This scattering of radiation is two-step process:
Step 1- photon of energy hυ is absorbed exciting the molecule from the lower state (Ea) to some upper state (Em)
Step 2- the molecule emits a photon of energy hυ – E and is deexcited from the upper state (Em) to some final state (Eb).
The two steps can occur in reverse order, i.e. the photon of energy hυ is absorbed by the molecule raising it from excited state (Eb) to the state (En) and molecule emits a photon of energy hυ + E and is deexcited from state En to lower state Ea. If the final state Eb of the molecule is the same as the initial state E1, the emitted radiation has the same frequency as the incident radiation. This process is called Rayleigh scattering.
If the final state is different from the initial state, the scattering is inelastic and law of conservation of energy gives
H υ’ = hυ ± (Eb – Ea)
This inelastic scattering process is called Raman scattering or simply the Raman Effect.
Now, If υ’ < υ, the observed line is called Stokes line and for υ’ > υ, the observe line is called the anti-Stokes line.
The intermediate state Em or En need to have opposite parity to the state Ea and Eb for the electric dipole transition to take place. Thus Raman scattering does not change the parity of the molecule.
Raman Effect can take place for any frequency of the incident light. Raman Effect does not require the presence of a permanent electric dipole moment, but rather an induced dipole moment developed under the electric field of incident radiation and therefore, Raman lines are observed for Homonuclear molecules like H2, O2 etc. that do not exhibit pure rotational or vibrational spectra.
The Raman and Infrared spectra are complementary to each other because of the different nature of the processes involved in the two effects.
Raman process is a scattering effect involving an induced dipole, that depends on the change of molecular polarizability during vibration while infrared spectroscopy is an absorption process caused by the change in the permanent molecular dipole.
According to Quantum theory, the Raman Effect is the outcome of the collision between the light photon and molecules of the substance.
Suppose a molecule of mass m in the energy state moving with a velocity v and is colliding with a light photon m. Let this molecule undergoes a change in its energy state as well as in its velocity. Let this new energy state be and the velocity be v’ after suffering a collision. If we apply the principal of conservation of energy, one can write:
Now three cases are arise:-
If ?? − ?b the frequency difference (Raman Shift) ∆E is zero. If means that v1 =v and this refer to the unmodified line where the molecule simply deflects the photon without receiving any energy from it. This collision is elastic and is analogous to Rayleigh scattering.
If ?? − ?b then ?′ > v that refers to the anti-stoke’s lines. It means that the molecule was previously in the excited state and it transfered some of its intrinsic energy to the incident photon and thus, the scattered photon has greater energy.
If ?? − ?b , then ?′ < v this corresponding to Stoke’s line. The molecule has absorbed some energy from the photon and consequently the scattered photon will have lower energy.
A change in the intrinsic energy of the molecule is governed by the quantum rule, as
?? − ??=±?ℎ?c (n=1,2,3………..)
vc-characteristic frequency of the molecule so, when n=1
?1 = ? ± ?c
Frequency difference between the incident and scattered photon in the Raman Effect corresponding to characteristic frequency of the molecule.
Now considering a system where E0 is the ground electronic state and υ′′ =0, 1… are the vibrational states of the ground electronic state. If the light frequency ν0is allowed to incident on this system, three cases arise:
Case I: Molecules absorb the light of frequency h υ 0 and go to the vibrational state as shown in the figure. The vibrational state is created by the light and molecular interaction and exists as long as the light exists. It is not the Eigen state of the system but is a linear combination of all the Eigen states of the molecule. The lifetime of this virtual state is quite small and the molecule will back to the ground vibrational state (υ = 0) and will emit the same frequency ν0. This is the same as Rayleigh scattering.
Case II: Molecules are transferred to the vibrational state by υ0 light and these excited molecules may come back to the higher vibrational state υ′′ = 1. In this case the emitted frequency is υ0 − υ. According to the energy conservation, the energy will be lost from the incident photon energy hυ 0 to excite the vibrational frequency of the molecule and thus, the emitted photon energy,
hνstokes= h υ 0-h υ ν
Case III: In thermal equilibrium, the excited vibrational levels are also populated and molecules there can also absorb light and go to the virtual state. While coming back to the same vibrational state, this will emit frequency υ0. But if molecules come back to ground vibrational state (υ = 0)then the emitted frequency will be (υ 0+ υ ν). Again, according to the energy Conservation, the photon energy adds up the vibrational energy and emitted frequencies will be
hνantistoke= h (υ 0+ υ ν)
7. Why the Stokes lines are higher in intensity than the Anti- Stokes lines?
The population to these vibrational states depends on the Maxwell Boltzmann distribution. The origin of Anti-Stokes lines is from the higher vibrational levels and the population is lower in those states than the ground vibrational level. As the intensity of transitions lines not only depend on the transition probability, but also depend on the population of the initial state. This is the reason for the lower intensity of anti-Stokes lines than the Stokes lines
8. Set up for Observing Raman effect:
A Raman system broadly consists of four major components:
1. Excitation source
2. Sample illumination system and light collection optics
3. Wavelength selector (Filter or Spectrophotometer).
4. Detector (Photodiode array, CCD or PMT).
A sample is illuminated with a laser beam in the ultraviolet (UV), visible (Vis) or near infrared (NIR) range. Scattered light is then collected with a lens and is sent through interference filter or spectrophotometer to obtain Raman spectrum of a sample. The main difficulty of Raman spectroscopy is separating it from the intense Rayleigh scattering as spontaneous Raman scattering is very weak. It is also noteworthy that the intensity of stray light from the Rayleigh scattering largely exceed the intensity of the actual Raman signal in the proximity to the laser wavelength. The remedy is to simply cut off the spectral range close to the laser line where the stray light has the most prominent effect. The commercially available interference (notch) filters that cut-off spectral range of ± 80-120 cm-1 from the laser line. This method is efficient in stray light elimination but it does not allow detection of low-frequency Raman modes in the range below 100 cm-1.The source of generation of Stray light is light dispersion on gratings and hence depends on grating quality. The modern Raman spectrometers use holographic gratings as the stray light produced by holographic gratings is about an order of magnitude less intense than from ruled gratings of the same groove density. Single-point detectors such as photon-counting Photomultiplier Tubes (PMT) have been used since long but the advancement in technology has replaced the detector to multi-channel detectors like Photodiode Arrays (PDA) or, a Charge- Coupled Devices (CCD).
Summary
- Sir Chandrasekhar Venkata Raman leads to the invention of Raman Effect
- The frequency change of light due to the interaction with matter is called Raman Effect
- In Classical Theory, the incident electromagnet field induces an electric dipole moment of scattering system (molecule or solid). Such an induced dipole moment is oscillating with the frequency of the incident radiation and is acting as a secondary source for electromagnetic radiation.
| you can view video on Raman Effect | |