Ir

Infrared Spectroscopy The portion of the infrared region most useful for analysis of organic compounds is not immediately adjacent to the visible spectrum, but is that having a wavelength range from 4000 to 600 cm-1, with a corresponding frequency range.

Region

Wavelength (λ) Wavenumber (νbar) Range, μm Range, cm-1

Frequency (ν) Range, Hz

near middle

0.78 - 2.5

12800 - 4000

3.8 x 1014 - 1.2 x 1014

2.5 - 50

4000 - 200

1.2 x 1014 - 6.0 x 1012

far most used

50 - 1000

200 - 10

6.0 x 1012 - 3.0 x 1011

2.5 - 15

4000 - 670

1.2 x 1014 - 2.0 x 1013

The Health Sciences Center

Mechanical model of Stretching Vibration Consider the vibration of a mass attached to a spring. If the mass is displaced a distance y by application of a force, the restoring force is proportional to the displacement (Hooke’s Law) where k is the force constant

The potential energy of a vibrating spring ( a harmonic oscillator) is E = (1/2) ky2

parabolic

The potential energy of a vibrating spring ( a harmonic oscillator) is given by

Potential Energy, E

F = -ky

-A

0 y

+A

1 k -A 0 +A νm = Displacement, y 2π m For a system consisting of two masses m1 and m2 connected by a spring ( which approximates two atoms connected by a bond), € - the mass m above is replaced by reduced mass, µ.

m1m2 µ= m1 + m2 The vibrational frequency for such a system is given by

1 νm = € 2π

k 1 = µ 2π

k ( m1 + m2 ) m1m2

Quantum Mechanical Treatment of Vibrations Solutions of the equations for PE of harmonic oscillator is given by

€

 1 h E = v +   2  2π

k µ

where h is Planck’s constant and v is vibrational quantum number (v = 0, 1, 2 ...)

Thus QM vibrators can take only certain discrete values. Note that the € last two terms (less h) is equal to the natural frequency, νm. Thus,

 1 E = v + hν m  2

The transitions in vibrational energy levels can be brought about by radiation, provided the energy of radiation exactly matches the difference in energy levels (ΔE) between vibrational quantum states. (and provided the vibration causes a fluctuation in dipole)

E radiation

h = hν = ΔE = hν m = 2π

k µ

If we wish to express the radiation in wavenumber (vbar) in unit of cm-1,

1 k k −12 ν= = 5.3x10 2πc µ µ

€ k is about

€

500 N/m for single bonds 1000 N/m for double bonds 1500 N/m for triple bonds

N = kg m/s2

Example Calculate the approximate wavenumber of the fundamental absorption peak due to the stretching vibration of a carbonyl group (C=O).

Solution The mass of the carbon atom on kilograms is given by mC = 12 x 10-3 kg/mol x 1 atom = 2.0 x 10-26 kg 6.0 x 10²³ atoms/mol

Similarly, for oxygen mO = 16 x 10-3 kg/mol x 1 atom = 2.7 x 10-26 kg 6.0 x 10²³ atoms/mol

and the reduced mass µ is given by µ = (2.0 x 10-26 kg) x (2.7 x 10-26 kg) = 1.1 x 10-26 kg (2.0+2.7) x 10-26 kg

The force constant for the typical double bond is about 1 x 10³ N/m. Substituting this value and µ v = 5.3 x 10-12 s/cm x sqrt[(1 x 10³ N/m)/1.1 x 10-26 kg

v = 1600 cm-1 The carbonyl stretching band is found experimentally to be in the region of 1600 to 1800 cm-1.

SELECTION RULES

The only transitions that can take place are those in which the vibrational quantum number changes by unity

Δv = ±1 Since the vibrational levels are equally spaced, only a single absorption peak should be observed for a given molecular vibration.

In reality, as two atoms approach each other, coulombic repulsion between them occurs, thus the PE rises as r approaches zero. At the other extreme, as the two atoms move away from each other at distances where the dissociation occurs, the PE does not rise continuously. The curve takes the anharmonic form.

Potential Energy, E

ANHARMONIC OSCILLATOR Dissociation energy

0 Interatomic distance, r

Anharmonicity leads to deviations of two kinds: 1. At higher quantum numbers, ΔE becomes smaller and the selection rule is not rigorously followed.

Δv = ±2 or ±3

are observed

These are responsible for the appearance of overtone lines. Overtone lines occur at frequencies 2 to 3 times that of fundamental line; but low in intensity and may not be observed.

2. Two different vibrations in a molecule can interact to give peaks with frequencies that are sums or differences of their fundamental lines. Again, the intensities of combination and difference peaks are low.

Vibrational Modes

The number of possible vibrations in a polyatomic molecule is

normal modes = 3N - 6 where N is the number of atoms in the molecule.

A molecule containing N atoms is said to have 3N degrees of freedom. The location of each atom requires three coordinates (x, y, z). Thus to fix N atoms requires 3N coordinates.

The six degrees of freedom subtracted from 3N is due to the translational and rotational motions of the molecule. The molecule may move along x, y, or z (translation) or rotate about x, y, or z (rotation) for a total of 6 degrees of freedom.

For a linear molecule, rotation about the bond axis will not count (it will not affect the energy of the molecule) normal modes = 3N - 5 Four Factors that tend to produce fewer peaks

1. The symmetry of the molecule is such that no change in dipole results from a particular vibration. (no dipole change, no IR absorption) 2. The energies of two or more vibrations are identical or nearly identical.

3. The absorption intensity is so low as to be undetectable, 4. The vibrational energy is in a wavelength region beyond the range of the instrument. Factors that tend to produce more peaks

1. Overtone lines 2. Combination bands Vibrational coupling possibly occurs when there is common atom or bond involved between vibrating groups and their energy and symmetry are favorable.

Example Consider the IR spectrum of CO2. Normal modes = 3(3) - 5 = 4 If no coupling occurs, a band is expected at 1700 cm-1 for vC=O. Experimentally two peaks are observed (at 2330 cm-1 and 667 cm-1). The peak at 2330 cm-1 is due to asymmetric stretching vibration of two C=O bonds which are vibrationally coupled. The peak at 667 cm-1 is due to two bending vibrations (scissoring) which are degenerate. The 4th mode is symmetric stretch, which is IR inactive.

Different Vibrational Modes

Gas Phase IR Spectrum of Formaldehyde, H2C=O

Infrared spectrum of a compound is a unique reflection of its molecular structure. An example of such a spectrum is that of the flavoring agent vanillin, shown below.

The inverted display of absorption, compared with UV-visible spectra , is characteristic. Thus a sample that did not absorb at all would record a horizontal line at 100% transmittance (top of the chart).

Some General Trends: i) Stretching frequencies are higher than corresponding bending frequencies. (It is easier to bend a bond than to stretch or compress it.) ii) Bonds to hydrogen have higher stretching frequencies than those to heavier atoms. iii) Triple bonds have higher stretching frequencies than corresponding double bonds, which in turn have higher frequencies than single bonds. (Except for bonds to hydrogen).

Typical Infrared Absorption Frequencies Functional Class

Stretching Vibrations Range (cm-1) Intensity

Bending Vibrations

Assignment Range (cm-1) Intensity

Assignment

1350 - 1470 1370 - 1390 720 - 725

medium medium weak

CH2 & CH3 deformation

Alkanes

2850 - 3000

strong

CH3, CH2 & CH 2 or 3 bands

medium variable strong

(=CH) and =CH2 C=C (sym) C=C (assym)

880-995 780-850 675-730

strong medium medium

(=CH) and =CH2

Alkenes

3020 - 3100 1630 - 1680 1900 - 2000

Alkynes

3300 2100-2250

strong variable

C-H C≡C

600-700

strong

C-H deformation

Arenes

3030 1600 & 150

variable med-weak

C-H (sevrl bands) C=C (2 to 3 bands)

690-900

strong-med

C-H bending & ring puckering

Alcohols and Phenols

3580-3650 3200-3550 970-1250

variable strong strong

O-H (free) O-H (H-bonded) C-O

1330-1430 650-770

medium var-weak

O-H (in-plane) O-H (out-of-plane)

Amines

3400-3500 3300-3400 1000-1250

weak weak medium

N-H (1o) 2 bands N-H (2o) C-O

1550-1650 660-900

CH3 deformation CH2 rocking

(out-of-plane bending)

cis-RCH=CHR

med - strong NH2 (sciss, 1o) variable NH2 N-H (wag)

Typical Infrared Absorption Frequencies Functional Class

Aldehydes and Ketones

Stretching Vibrations Range (cm-1) Intensity 2690-2840 1720-1740 1710-1720 1690 1675 1745

2500-3300 (acids) 1705-1720 (acids) 1210-1320 (acids) Carboxylic 1785-1815 acid and 1750 & 1820 derivatives 1040-1100 1735-1750 (esters) 1000-1300 1630-1695(amides) ( acyl halides)

(anhydrides)

Nitriles

2240-2260

Assignment Range (cm-1) Intensity

medium strong strong strong strong strong

C-H (aldehyde) C=O (satd ald) C=O (satd ket) aryl ketone α, β-unsaturation cyclopentanone

strong strong med - str strong strong strong strong strong strong

O-H (very broad) 1395-1440 C=O (H-bonded) O-C C=O C=O (2-bands) O-C C=O O-C (2-bands) 1590-1650 C=O (amide) 1500-1560

medium

C≡N (sharp)

medium

N=C=O, -N=C=S -N=C=N-, -N3, C=C=O

Isocyanates,Iso thiocyanates, Diimides, Azides & Ketenes

2100-2270

Bending Vibrations

1350-1360 1400-1450 1100

Assignment

strong strong medium

α-CH3 bending α-CH2 bending C-C-C bending

medium

C-O-H bending

medium medium

N-H (1¡-amide) N-H (2¡-amide)

INFRARED SOURCES Infrared sources consist of an inert solid that is heated electrically resulting in continuous radiation approximating that of a blackbody.

1. Nernst Glower

Platinum leads are sealed to the ends to permit passage of electricity.

Energy, arbitrary unit

Composed of rare earth oxides formed into a cylinder having a diameter of 1 to 2 mm and a length of 20 mm. It is heated to 1200 to 2200 K.

1

3

5

7

λ, µm

9

11

Spectral distribution of energy from a Nernst glower operated at 2200 K.

2. Globar Globar is a SiC rod, about 50 mm in length and 5 mm in diameter. It is also electrically heated (1300 to 1500 K); has the advantage of positive coefficient of resistance. Its spectral energy is comparable to that of Nernst glower except at 5 µm where Globar provides greater output.

3. Incandescent wire source 1. Nichrome wire (Ni + Cr) - tightly wound spiral heated to 1100 K; - lower intensity but longer life. 2. Rhodium wire (Rh) - sealed in a ceramic cylinder; has similar properties.

4. Mercury arc This is for far IR region (λ > 50 µm); high pressure Hg arc is used; The device consists of a quartz-jacketed tube containing Hg vapor at <1 atm pressure. Passage of electricity forms an internal plasma source that emits far IR.

5. Tungsten lamp An ordinary W filament lamp is a convenient source for NIR region (4000 to 12800 cm-1)

6. CO2 laser A CO2 laser produces a band in the 900 to 1100 cm-1 range Consists of about 100 closely spaced discrete lines; any one of these lines can be chosen by tuning the laser.

INFRARED DETECTORS

3 General Types 1. Thermal detectors 2. Pyroelectric detectors 3. Photoconducting detectors

Thermal Detectors The responses of thermal detectors depend on the heating effect of radiation.

1. Thermocouple A thermocouple consists of a pair of junctions fromed when two pieces of a metal (e.g. Bi) is fused to either end of a dissimilar metal (e.g. Sb). A potential develops between the two junctions that varies with their difference in temperature.

A well-designed thermocouple is capable of responding to T differences of 10-6 K.

Thermopile is composed of thermocouples connected in series; this enhances sensitivity. 2. Bolometers A type of resistance thermometer constructed of strips of metals such as Pt or Ni, or from a semiconductor.

Thermistors are bolometers constructed from semiconductors. These materials exhibit large change in resistance as a function of temperature.

Pyroelectric Detectors These are constructed from single crystalline wafers of pyroelectric materials, which are insulators (dielectric materials) with special thermal and electrical properties. Example : Triglycine sulfate (NH2CH2COOH)3.H2SO4

A temperature-dependent capacitor is produced if a pyroelectric crystal is sandwiched between two electrodes. Irradiating with IR changes the charge distribution across the crystal, which can be detected as current.

Photoconducting Detectors They consist of a semicon material (e.g. PbS, HgCdTe, InSb) deposited on a nonconducting glass surface and sealed into an evacuated envelope. Absorption of IR by these materials promotes nonconducting valence electrons to a higher E conducting state electrical resistance decreases A photoconductor is placed in series with a V source and load resistor, and the V drop across the resistor serves as a measure of the power of the beam.

Synchronous motor Chart

Reference

Synchronous motor

Attenuator

Grating

Source

Detector

Chopper Sample

Filter, modulator,

amplifier

Monochromator

Synchronous rectifier

Preamp