1 / 29

Introduction to Infrared Spectrometry Chap 16

Introduction to Infrared Spectrometry Chap 16. Quantum Mechanical Treatment of Vibrations Required to include quantized nature of E From solving the wave equations of QM:. Selection rule for vib. transitions. Quantum Mechanical Treatment of Vibrations. Plot of potential energy:.

herb
Download Presentation

Introduction to Infrared Spectrometry Chap 16

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Infrared SpectrometryChap 16

  2. Quantum Mechanical Treatment of Vibrations • Required to include quantized nature of E • From solving the wave equations of QM: Selection rule for vib. transitions

  3. Quantum Mechanical Treatment of Vibrations • Plot of potential energy: • where level spacings: hvres • All vib levels spaced • equally for HO only Interatomic distance, r →

  4. 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)

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

  6. Anharmonic Oscillator (AHO) • Three consequences: • (1) Harmonic at low v levels • (2) ΔE becomes smaller at high v levels • (3) Selections rule fails: Δv = ±1 and ±2... • referred to as overtones

  7. 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)

  8. 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

  9. Examples N2 CO2 H2O CH3-C(O)-CH3

  10. Vibrations of CO2 Fig 16-10 667 cm-1 2350 cm-1 } 1388 cm-1 Doubly degenerate No dipole change Dipole change Dipole change

  11. Vibrations of H2O 3657 cm-1 1595 cm-1 3766 cm-1

  12. IR Sources and Transducers Sources (1200 – 2200 K)

  13. Spectral emission from a Nernst glower at ~ 2200 K Fig 16-16

  14. IR Sources and Transducers Sources (1200 – 2200 K)

  15. Transducers • IR beam 10-7 - 10-9 W, ΔT at transducer mK-µK

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

  17. 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

  18. Single- and Double-Beam Spectra of the Atmosphere Fig. 16-9

  19. 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

  20. 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):

  21. S/N improves with more scans (noise is random, signal is not!) Fig. 5-10

  22. (2) Multiplex (or Fellget) advantage • Simultaneously measure entire spectrum Components of Fourier Transform Instruments • Based on Michelson Interferometer • Converts frequency signal to time signal

  23. Fig. 7-41 (p 207) Time domain Frequency domain

  24. Time Domain Signal of a Source Made Up of Many Wavelengths Fig. 7-42 (p 207)

  25. 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(δ) • δ ≡ retardation, difference in pathlengths • of the two beams

  26. Michelson Interferometer Fig. 7-43 (p 208) Single Frequency Source

  27. Computer needed to turn complex interferogram into spectrum: Fig. 7-43 (p 188) Single Frequency:

  28. Two Frequencies: Many Frequencies:

  29. Advantages to FT Instruments • High S/N ratios - high throughput • • Rapid (<10 s) • • Reproducible • • High resolution (<0.1 cm-1) • • Inexpensive (relatively!)

More Related