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Infrared Spectroscopy
The Electromagnetic Spectrum
History: Discovery of Infrared Light
Molecular Spectra
Quantitative Analysis
Fourier-Transform Spectrometry
Laser Diode Spectrometry
Remote Sensing
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The Electromagnetic Spectrum
http://www.lbl.gov
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Spectroscopy
•
Spectral nature of light present in the rainbow, but beyond ability
of early humans to explain it
• Newton (1666): white light from the sun could be dispersed
into series of colors
• Newton introduced the word spectrum
• Instrument: aperture, lens, glass prism and a screen to display
the resulting spectrum
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History
•
1666 Newton observes spectrum obtained from a prism
•
1678 Huygens proposes wave theory of light
•
1729 Pierre Bouger notices attenuation of light as it passes through successive
thicknesses of glass
•
1752 Thomas Melville writes of yellow light in flame when sea salt mixed with alcohol
•
1760 Johann Lambert gives mathematical formula to Bouger
•
1776 Alessandro Volta notes different colors when using different sparking materials
•
1800 F.W. Herschel discovers infrared light
http://www.cofc.edu/~deavorj/521/spechist.html
http://web.mit.edu/spectroscopy/history/history-classical.html
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History: Discovery of Infrared Light
• Sir Friedrich Wilhelm (William) Herschel (1738-1822)
• Discovery of the planet Uranus in 1781
• Discovery of infrared light (1800)
Prism
Thermometers
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History (Continued)
•
1801 J.W. Ritter discovers ultraviolet light
•
1802 Thomas Young demonstrates wave nature of light by using a transmission
grating
•
1817 Josef Fraunhofer maps details of absorption lines in solar spectrum
•
1826 W.H.F. Talbot notices different salts yield different colored flames
•
1852 August Beer shows logarithmic relation of Lambert
•
1859 G. Kirchoff and R.W. Bunsen are the first to state that elements have both
characteristic absorption and emission spectra
•
1891 A. A. Michelson invents interferometer (Nobel Prize in Physics 1907)
http://www.cofc.edu/~deavorj/521/spechist.html
http://web.mit.edu/spectroscopy/history/history-classical.html
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Definitions
• Wavenumber σ = ν/c , ν: frequency, c: velocity of light (vacuum)
Unit of wavenumber ([σ] = 1 Kayser = 1 cm-1) is used as frequency unit
• Radiance L: Power (radiant flux) Φ per solid angle and area, perpendicular to
direction of propagation: L=d2Φ/(dAdΩ cosϑ)
• dΩ solid angle, dA area, ϑ angle between direction of propagation and
normal vector of dA
• Spectral radiance: Lσ = dL/dσ
• Irradiance (Intensity): I = Φ/A
A: Area
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Energy Levels of Molecules
• Energy
is the sum of energy of the electrons, vibrational energy, and
rotational energy
E = Eel + Evib + Erot
• Energy difference between different levels (orders of magnitude)
∆Eel ≈ 10 eV
λ ≈ 100 nm σ ≈ 105 cm-1
Ultraviolet (UV)
∆Evib ≈ 0.1 eV
λ ≈ 10 µm
σ ≈ 1000 cm-1
Infrared (IR)
∆Erot ≈ 10-4 eV
λ ≈ 1 cm
σ ≈ 1 cm-1
Microwaves
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Diatomic Molecule: Rotation
• Rotation:
• Classical mechanics:
Z
2
L
E=
2I
M1
E: Energy
L: Angular momentum
I : Moment of inertia
M2
R
J (J + 1)h 2
• Quantum mechanics: E =
2I
J: Quantum number of rotation
J = 0, 1 …
h=h/2π
h =6,62607×10-34 J s Planck´s constant
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Diatomic Molecule: Vibration
Z
• Nuclei in the field of the electrons
⇒ Attracting Force
M1
M2
• Coulomb-force (Nuclei positive)
⇒ Repelling Force
R
2
• Potential energy:
Energy (De)
1.5
Repelling force
1
0.5
Attracting Force
0
0.5
1
0
1
2
3
Distance R (Ro)
4
5
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Diatomic Molecule
Z
• Description of Vibration
M1
•
M2
Morse-Potential: empirical formula for the potential energy
E pot ( R ) D e . e
2. α. R
R0
2. e
α. R
R
R0
2
• Approximation for R ≈ R0: harmonic oscillator
R0
• Eigenvalues of the energy :
E
•
υ
1 . .
hω
2
ν = 0,1....
• Energy levels are equidistant
(harmonic oscillator)
1
2
Epot (De)
2
E pot ( R ) D e . α . R
ES
0
1
0
1
2
3
Distance
R/R
Kernabstand
R (Ro)
0
4
5
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Spectra of Molecules
• Transitions between energy levels
• Vibrational spectra contain rotational fine structure
• Selection rules
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Vibration-Rotation Spectrum
Selection rules (harmonic oscillator):
∆J = +- 1 (exception: ∆J = 0, +- 1 if electronic
quantum number of angular momentum
Λ ≠ 0)
∆ν = +- 1
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Vibration-Rotation Spectrum of HCl
0.08
Absorption
0.06
0.04
0.02
0
Relation between Energy
and frequency of radiation:
E’- E’’ = h·f = h·c·σ
Absorption
0.02
2600
2800
2900
3000
Wavenumber (cm-1)
P-Branch
(Q-Branch) R-Branch
3100
3200
0.05
0
2900
Upper state
Lower state
2700
2920
2940
2960
2980
3000
3020
Wavenumber (cm-1)
h: Planck’s constant, c: velocity of light, σ: Wavenumber
3040
3060
3080
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Polynuclear Molecules
• Calculation of resonance frequencies
• Description of positions of nuclei of the molecule by 3N – 6 coordinates,
N: number of nuclei
(Linear molecule: 3N – 5)
• 3N – 6 (5) coupled equations of motion
• Calculation of eigenvalues and eigenvectors
• Diagonalisation: Decoupling of equations
• 3N – 6 (5) normal modes
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Absorption Lines of CO2
0.8
Absorption
0.6
0.4
0.2
0
620
640
660
680
Wavenumber σ / cm-1
700
720
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Group Frequencies
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/InfraRed/infrared.htm
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Summary: Vibration-Rotation Spectra of Molecules
• Allowed energy states of molecules are quantized
• In the infrared spectral region, transitions between vibrational
states of molecules are observed
• Rotational structure of vibrational transition (band)
• All molecules except diatomic homonuclear molecules (e.g. N2,
O2) have significant characteristic signatures in the infrared
spectral region
• Property that allows observation by spectroscopy: Dipole
moment is (non-constant) function of nuclear positions
• Functional groups have specific absorption bands
• Molecule with N nuclei has 3N-6 normal modes, i.e. 3N-6
(possible) absorption bands (linear molecule: 3N-5)