Transcript Theory of Infrared Absorption Spectroscopy

Infrared Spectroscopy
Theory of Infrared Absorption Spectroscopy
• IR photons have low energy. The only transitions that have
comparable energy differences are molecular vibrations and rotations.
Theory of Infrared Absorption Spectroscopy
• In order for IR absorbance to occur two conditions must be met:
1. There must be a change in the dipole moment of the molecule as a
result of a molecular vibration (or rotation). The change (or
oscillation) in the dipole moment allows interaction with the
alternating electrical component of the IR radiation wave.
Symmetric molecules (or bonds) do not absorb IR radiation since
there is no dipole moment.
2. If the frequency of the radiation matches the natural frequency of
the vibration (or rotation), the IR photon is absorbed and the
amplitude of the vibration increases.
Theory of Infrared Absorption Spectroscopy
• In order for IR absorbance to occur two conditions must be met:
1. There must be a change in the dipole moment of the molecule as a
result of a molecular vibration (or rotation). The change (or
oscillation) in the dipole moment allows interaction with the
alternating electrical component of the IR radiation wave.
Symmetric molecules (or bonds) do not absorb IR radiation since
there is no dipole moment.
2. If the frequency of the radiation matches the natural frequency of
the vibration (or rotation), the IR photon is absorbed and the
amplitude of the vibration increases.
DE = hn
• There are three types of molecular transitions that occur in IR
a) Rotational transitions
• When an asymmetric molecule rotates about its center of mass, the
dipole moment seems to fluctuate.
• DE for these transitions correspond to n < 100 cm-1
• Quite low energy, show up as sharp lines that subdivide vibrational
peaks in gas phase spectra.
b) Vibrational-rotational transitions
• complex transitions that arise from changes in the molecular dipole
moment due to the combination of a bond vibration and molecular
rotation.
c) Vibrational transitions
• The most important transitions observed in qualitative mid-IR
spectroscopy.
• n = 13,000 – 675 cm-1 (0.78 – 15 mM)
Vibrational Modes
1. Stretching - the rhythmic movement along a bond axis wit a subsequent
increase and decrease in bond length.
2. Bending - a change in bond angle or movement of a group of atoms with
respect to the rest of the molecule.
The Vibrational Modes of Water
Mechanical Model of Stretching Vibrations
1. Simple harmonic oscillator.
• Hooke’s Law (restoring force of a spring is proportional to the
displacement)
F = -ky
Where: F = Force
k = Force Constant
(stiffness of spring)
y = Displacement
• Natural oscillation frequency of a mechanical oscillator depends on:
a) mass of the object
b) force constant of the spring (bond)
• The oscillation frequency is independent of the amount of energy
imparted to the spring.
• Frequency of absorption of radiation can be predicted with a modified
Hooke’s Law.
1 k
 
n 
2c  m 
m
Mx My
Mx  My
1
2
Where: n = wavenumber of the abs. peak (cm-1)
c = speed of light (3 x 1010 cm/s)
k = force constant
m = reduced mass of the atoms
Where: Mx = mass of atom x in kg
My = mass of atom y in kg
• Force constants are expressed in N/m (N = kg•m/s2)
- Range from 3 x 102 to 8 x 102 N/m for single bonds
- 500 N/m is a good average force constant for single bonds when
predicting k.
- k = n(500 N/m) for multiple bonds where n is the bond order
Example 1: Calculate the force constant of the carbonyl bond in the
following spectrum.
Example 2: Predict the wavenumber of a peak arising from a nitrile
stretch.
Anharmonic oscillators
• In reality, bonds act as anharmonic oscillators because as atoms get
close, they repel one another, and at some point a stretched bond
will break.
IR Sources and Detectors
Sources - inert solids that heat electrically to 1500 – 2200 K.
• Emit blackbody radiation produced by atomic and molecular oscillations
excited in the solid by thermal energy.
• The inert solid “glows” when heated.
• Common sources:
1. Nernst glower - constructed of a rod of a rare earth oxide (lanthanide)
with platinum leads.
2. Globar - Silicon carbide rod with water cooled contacts to prevent
arcing.
3. Incandescent wire - tightly wound wire heated electrically. Longer life
but lower intensity.
Detectors – measure minute changes in temperature.
1. Thermal transducer
• Constructed of a bimetal junction, which has a temperature dependant
potential (V). (similar to a thermocouple)
•
Have a slow response time, so they are not well suited to FT-IR.
2. Pyroelectric transducer
• Constructed of crystalline wafers of triglycine sulfate (TGS) that have a
strong temperature dependent polarization.
• Have a fast response time and are well suited for FT-IR.
3. Photoconducting transducer
• Constructed of a semiconducting material (lead sulfide,
mercury/cadmium telluride, or indium antimonide) deposited on a glass
surface and sealed in an evacuated envelope to protect the
semiconducting material from the environment.
•
Absorption of radiation promotes nonconducting valence electrons to a
conducting state, thus decreasing the resistance (W) of the semiconductor.
•
Fast response time, but require cooling by liquid N2.
Multiplexing (FT) Spectrometers
• Collect data in the time domain and convert to the frequency domain by
Fourier Transform.
• Detectors are not fast enough to respond to power variations at high frequency
(1012 to 1015 Hz) so the signal is modulated by a Michelson interferometer to a
lower frequency that is directly proportional to the high frequency.
B. Multiplexing (FT) Spectrometers
1. Michelson Interferometer
• The source beam is split into two
beams.
• One beam goes to a stationary
mirror and the other goes to a
moveable mirror.
• Movement of the mirror at a
constant rate and recombination of
the two beams results in a signal
that is modulated by constructive
and destructive interference
(Interferogram).
Multiplexing (FT) Spectrometers
• The frequency of the
radiation (n) is directly
related to the frequency
of the interferogram (f).
2n m
f 
n
c
n = frequency of radiation
f = frequency of inteferogram
nm = velocity of the mirror
c = speed of light (3.00 x 1010
cm/s)
• FT-IR spectrometers use a polychromatic source and collect the entire
spectrum simultaneously and decode the spectrum by Fourier Transform.
Multiplexing (FT) Spectrometers
2. FT-IR instrument
•
Mirror length of travel ranges
from 1 to 20 cm.
• Scan rates from 0.1 to 10 cm/s
• Detectors are usually pyroelectric
or photoconducting.
• Use multiple scans and signal
averaging to improve S/N.
• Cost $10,000 - $20,000
• Have virtually replaced
dispersive instruments.
Performance Characteristics
•
Range: 7800 to 350 cm-1 (less expensive)
25,000 to 10 cm-1 (Near to far IR, expensive)
•
Resolution: 8 cm-1 to 0.01 cm-1
•
Qualitative: Very good, functional groups are identifiable
•
Quantitative: Dispersive – poor
FTIR - fair