Introduction to Infrared Spectrometry Chap 16

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Introduction to Infrared SpectrometryChap 16
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• Quantum Mechanical Treatment of Vibrations
• Required to include quantized nature of E
• From solving the wave equations of QM

Selection rule for vib. transitions
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Quantum Mechanical Treatment of Vibrations

• Plot of potential energy

• where level spacings

hvres

• All vib levels spaced
• equally for HO only

Interatomic distance, r ?
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• Problems with Harmonic Oscillator (HO) Model
• Real vib levels coalesce as v levels increase
• Does not allow for dissociation of bond
• Repulsion is steeper at small r
• Appears as if atoms can pass through
• each other during vibrational amplitude

Solution
Anharmonic Oscillator (AHO)
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Anharmonic Oscillator (AHO)
Fig. 16-3
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Anharmonic Oscillator (AHO)

• Three consequences
• (1) Harmonic at low v levels
• (2) ?E becomes smaller at high v levels
• (3) Selections rule fails ?v 1 and 2...
• referred to as overtones

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Vibrational Modes

• Approach
• Each atom in a molecule can be located
• with three coordinates (degrees of freedom)
• A molecule with N atoms then has 3N DOF
• Translational motion defined by center-of-
• mass coordinates (COM)

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• Linear Molecules
• 3 DOF to define translation
• 2 DOF to define rotation
• 3N 5 number of vibrational modes
• Nonlinear Molecules
• 3 DOF to define translation
• 3 DOF to define rotation
• 3N 6 number of vibrational modes

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Examples N2 CO2 H2O CH3-C(O)-CH3
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Vibrations of CO2
Fig 16-10
667 cm-1
2350 cm-1

1388 cm-1
Doubly degenerate
No dipole change
Dipole change
Dipole change
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Vibrations of H2O
3657 cm-1
1595 cm-1
3766 cm-1
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IR Sources and Transducers
Sources
(1200 2200 K)
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Spectral emission from a Nernst glower at 2200
K
Fig 16-16
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IR Sources and Transducers
Sources
(1200 2200 K)
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Transducers

• IR beam 10-7 - 10-9 W, ?T at transducer mK-µK

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IR Instrumentation
Dispersive Grating IR Instruments
Fig 16-11
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IR Instrumentation

• Dispersive Grating IR Instruments
• Similar to UV-Vis spectrophotometer
• BUT sample after source and before
  monochromator in IR
• Sample after monochromator in UV- Vis - less
  incident light
• Grating 10-500 blazes per mm
• Single beam and double beam (DB in time and
  space)
• DB eliminates atmospheric gas interference

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Single- and Double-Beam Spectra of the Atmosphere
Fig. 16-9
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• Fourier Transform IR Instruments
• FTIR has largely displaced dispersive IRs
• A multiplex instrument (e.g., diode array)
• Beam is split and pathlength is varied
• to produce interference patterns
• Signal converted from frequency
• domain to time domain
• Fourier transform then converts clean
• signal back to frequency domain

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• Fourier Transform Instruments (Section 7-I) have
  two advantages
• Throughput (or Jaquinot) advantage
• Few optics, no slits, high intensity
• Usually, to improve resolution, decrease slit
  width but less light makes spectrum "noisier"
• i.e., signal-to-noise ratio (S/N) decreases (p.
  110-111)

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S/N improves with more scans (noise is random,
signal is not!)
Fig. 5-10
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• (2) Multiplex (or Fellget) advantage
• Simultaneously measure entire spectrum

Components of Fourier Transform Instruments

• Based on Michelson Interferometer
• Converts frequency signal to time signal

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Fig. 7-41 (p 207)
Time domain
Frequency domain
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Time Domain Signal of a Source Made Up of Many
Wavelengths
Fig. 7-42 (p 207)
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• Frequencies of IR photons 100 THz
• No detector can respond on 10-14 s time scale
• Need to modulate high freq signal ? lower freq
• without loss of P(t) relationships
• Interferometer
• Splits beam equally in power
• Recombines them such that variations
• in power can be measured as P(d)
• d retardation, difference in pathlengths
• of the two beams

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Michelson Interferometer Fig. 7-43 (p 208)
Single Frequency Source
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Computer needed to turn complex interferogram
into spectrum
Fig. 7-43 (p 188)
Single Frequency
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Two Frequencies
Many Frequencies
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Advantages to FT Instruments

• High S/N ratios - high throughput
• Rapid (lt10 s)
• Reproducible
• High resolution (lt0.1 cm-1)
• Inexpensive (relatively!)