Topic 5 Rotational and Vibrational Spectroscopy

7/29/2019 Topic 5 Rotational and Vibrational Spectroscopy

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SKA6014

ADVANCED ANALYTICAL CHEMISTRY

TOPIC 5Rotational and Vibrational Spectroscopy

Azlan Kamari, PhDDepartment of Chemistry

Faculty of Science and Mathematics

Universiti Pendidikan Sultan Idris


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Vibrational and Rotational Spectroscopy

Core techniques:

Infrared (IR) spectroscopy

Raman spectroscopy

Microwave spectroscopy


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The Electromagnetic Spectrum

The basic!

Microwave

Infrared (IR)


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The History of Infrared and Raman Spectroscopy

Infrared (IR) Spectroscopy:

First real IR spectra measured by Abney and Festing in 1880s

Technique made into a routine analytical method between 1903-

1940 (especially by Coblentz at the US NBS)

IR spectroscopy through most of the 20th century is done with

dispersive (grating) instruments, i.e. monochromators

Fourier Transform (FT) IR instruments become common in the1980s, led to a great increase in sensitivity and resolution

Raman Spectroscopy:

In 1928, C. V. Raman discovers that small changes occur the

frequency of a small portion of the light scattered by molecules.

The changes reflect the vibrational properties of the molecule

In the 1970s, lasers made Raman much more practical. Near-IR

lasers (1990s) allowed for avoidance of fluorescence in many

samples.


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Infrared Spectral Regions

IR regions are traditionally sub-divided as follows:

Region Wavelength

(), m

Wavenumber

(), cm-1

Frequency

(), Hz

Near 0.78 to 2.5 12800 to 4000 3.8 x 1014to

1.2 x 1014

Mid 2.5 to 50 4000 to 200 1.2 x 1014to

6.0 x 1012

Far 50 to 1000 200 to 10 6.0 x 1012to

3.0 x 1011

After Table 16-1 of Skoog, et al. (Chapter 16)


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What is a Wavenumber?

Wavenumbers (denoted cm-1) are a measure of frequency

For an easy way to remember, think waves per centimeter

Relationship of wavenumbers to the usual frequency and

wavelength scales:

Image from www.asu.edu

100001 cm

Converting

wavelength () to

wavenumbers:


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Rotational and Vibrational Spectroscopy: Theory

Overview:

Separation of vibrational and rotational contributions toenergy is commonplace and is acceptable

Separation of electronic and rovibrational interactions

Basic theoretical approaches: Harmonic oscillator for vibration

Rigid rotor for rotation

Terminology:

Reduced mass (a.k.a. effective mass):21

21

mm

mm


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Rotational Spectroscopy: Theory Rotational energy levels can be

described as follows:

DJBJJ 3)1()1()(

crhB 2028/

23 /4 cBD

Where:c is the speed of light

k is the Hookes law force constantr0 is the vibrationally-averaged bond length

The rotational constant:

The centrifugal distortion coefficient:

u

k

cc

2

1

Example for HCl:B0 = 10.4398 cm

-1D0 = 0.0005319 cm

-1

r0 = 1.2887

is the reduced mass

his Plancks constant

0 = 2990.946 cm-1 (from IR)

k = 5.12436 x 105 dyne/cm-1

ForJ= 0, 1, 2, 3


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Vibrational Spectroscopy: Theory

Harmonic oscillatorbased on the classical spring

mhvE 2

1

m is the natural frequency of the oscillator (a.k.a. the fundamental vibrational wavenumber)kis the Hookes law force constant (now for the chemical bond)

u

km

2

1

v is the vibrational quantum numberhis Plancks constant

Since vmust be a whole number.

The potential energy function is:

2

21 )()( eHO rrkrE

NoteallEare

potential energies (V)!

or 2221 )()2()( emHO rrcrE

khhE m

2

k12103.5

and

ris the distance (bond distance)re is the equilibrium distance


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Vibrational Spectroscopy: Theory

Potential energy of a harmonic oscillator:


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Anharmonic Corrections

Anharmonic motion:when the restoring force is not

proportional to the displacement.

More accurately given by the Morse potential functionthan by the harmonic oscillator equation.

Primarily caused by Coulombic (electrostatic)

repulsion as atoms approach

Effects: at higher quantum numbers, Egets smaller, and the ( =

+/-1)selection rule can be broken

Double ( = +/-2), triple ( = +/-3), and higher order transitions

can occur, leading toovertone bandsat higher frequencies(NIR)

2)( )1()( erraeMorse ehcDrE

Deis the dissociation energy

e

m

hcD

ca

2

)2( 2


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Vibrational Coupling

Vibrations in a molecule may couple changing each

others frequency. In stretching vibrations, the strongest coupling occurs

between vibrational groups sharing an atom

In bending vibrations, the strongest coupling occurs

between groups sharing a common bond

Coupling between stretching and bending modes can occur

when the stretching bond is part of the bending atom

sequence.

Interactions are strongest when the vibrations have similar

frequencies (energies) Strong coupling can only occur between vibrations with the

same symmetry (i.e. between two carbonyl vibrations)


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Vibrational Modes and IR Absorption

Number of modes:

Linear: 3n 5 modes Non-linear: 3n 6 modes

Types of vibrations:

Stretching Bending

Examples:

CO2 has 3 x 3 5 = 4normal modes

SymmetricNo change in dipole

IR-inactive

Asymmetric

Change in dipoleIR-active

ScissoringChange in dipole

IR-active

IR-active modes require dipole changes during rotations and

vibrations!


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Vibrational Modes: Examples

IR-activity

requires dipole

changes during

vibrations!

InactiveActive

Active

Active

Inactive

Inactive

Active


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IR Spectra: Formaldehyde

Certain types of vibrations have distinct IR frequencies

hence the chemical usefulness of the spectra

The gas-phase IR spectrum of formaldehyde:

Formaldehyde spectrum from: http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/InfraRed/infrared.htm#ir2Results generated using B3LYP//6-31G(d) in Gaussian 03W.

Tables and simulation results can help assign the vibrations!

(wavenumbers, cm-1)


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Rayleigh and Raman Scattering

Only objects whose dimension is ~1-1.5 will scatter EM

radiation.

Rayleigh scattering:

occurs when incident EM radiation induces an oscillating dipole in

a molecule, which is re-radiated at the same frequency

Raman scattering: occurs when monochromatic light is scattered by a molecule, and

the scattered light has been weakly modulated by the

characteristic frequencies of the molecule

Raman spectroscopy measures the difference between

the wavelengths of the incident radiation and the

scattered radiation.


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The Raman Effect

Polarization changes are

necessary to form the

virtual state and hence

the Raman effect

This figure depicts

normal (spontaneous)Raman effects

hv1

Scattering timescale ~10-14 sec(fluorescence ~10-8 sec)

Virtual state

Virtual state

hv1

Ground state(vibrational)

The incident radiation excites virtual states (distorted

or polarized states) that persist for the short timescaleof the scattering process.

Excited state(vibrational)

hv1hv2

Stokes line

hv1hv2

Anti-Stokes line


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More on Raman Processes

The Raman process: inelastic scattering of a photon when it is

incident on the electrons in a molecule

When inelastically-scattered, the photon loses some of itsenergy to the molecule (Stokes process). It can then be

experimentally detected as a lower-energy scattered

photon

The photon can also gain energy from the molecule (anti-

Stokes process)

Raman selection rules are based on the polarizability of the

molecule

Polarizability: the deformability of a bond or a molecule in

response to an applied electric field. Closely related to the

concept of hardness in acid/base chemistry.

P. W. Atkins and R. S. Friedman,Molecular Quantum Mechanics, 3 rdEd. Oxford: 1997.


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More on Raman Processes

Consider the time variation of the dipole moment induced by incident

radiation (an EM field):

)()()( ttt

P. W. Atkins and R. S. Friedman,Molecular Quantum Mechanics, 3 rdEd. Oxford: 1997.

EM fieldInduced dipole moment

Expanding this product yields:

tttt )cos()cos(cos)( intint041

0

Rayleigh line Anti-Stokes line Stokes line

polarizability

If the incident radiation has frequency and the polarizability of the

molecule changes between min and max at a frequency int as a result

of this rotation/vibration:

ttt coscos)( 0int21

mean polarizability = max - min


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The Raman Spectrum of CCl4

Figure is redrawn from D. P. Strommen and K. Nakamoto, Amer. Lab., 1981, 43 (10), 72.

Observed intypical

Raman

experiments

0 = 20492 cm-10 = 488.0 nm

Anti-Stokes lines

(inelastic scattering)

-218

Raman shift cm-1

0 = (s - 0)

-200

Stokes lines

(inelastic scattering)

-400400 200

218314

-314

-459

459

0

Rayleigh line

(elastic scattering)


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Raman-Active Vibrational Modes

Modes that are more polarizable are more Raman-active

Examples:

N2 (dinitrogen) symmetric stretch

cause no change in dipole (IR-inactive)

cause a change in the polarizability of the bond as the bond

gets longer it is more easily deformed (Raman-active)

CO2 asymmetric stretch

cause a change in dipole (IR-active)

Polarizability change of one C=O bond lengthening is

cancelled by the shortening of the other no net polarizability(Raman-inactive)

Some modes may be both IR and Raman-active, others

may be one or the other!


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The Raman Depolarization Ratio

Raman spectra are excited by linearly polarized radiation

(laser). The scattered radiation is polarized differently depending

on the active vibration.

Using a polarizer to capture the two components leads to

the depolarization ratiop:

I

Ip

The depolarization ratiop can be useful in interpreting theactual vibration responsible for a Raman signal.


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Why Build Instruments for Fourier Transform Work?

Advantages: The Jacqinot (throughput) advantage: FT instruments have

few slits, or other sources of beam attenuation Resolution/wavelength accuracy (Connes advantage):

achieved by a colinear laser of known frequency

Fellgett (multiplex) advantage: all frequencies detected atonce, signal averaging

These advantages are critical for IR spectroscopy The need for FT instruments is rooted in the detector

There are no transducers that can acquire time-varying signalsin the 1012 to 1015 Hz range they are not fast enough!

Why are FT instruments not used in UV-Vis? The multiplex disadvantage (shot noise) adversely affects

signal averaging it is better to multiplex with array detectors(such as the CCD in ICP-OES)

In some cases, technical challenges to building interferometerswith tiny mirror movements


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Inteferometers for FT-IR and FT-Raman

The Michelson

interferometer, the

product of a famous

physics experiment:

Produces

interferencepatterns from

monochromatic

and white light

Figures from Wikipedia.org


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Inteferometers

For monochromaticradiation, the

interferogram looks like

a cosine curve

For polychromaticradiation, each

frequency is encoded

with a much slower

amplitude modulation

The relationshipbetween frequencies:

Example: mirror rate = 0.3 cm/s modulates 1000 cm-1 light at 600 Hz

Example: mirror rate = 0.2 cm/s modulates 700 nm light at 5700 Hz

c

vf M

2

Where: is the frequency of the radiationc is the speed of light in cm/svm is the mirror velocity in cm/s


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The Basics of the Fourier Transform The conversion from time- to frequency domain:

50 100 150 200 250

-1

-0.5

0.5

1

50 100 150 200 250

0.5

1

1.5

2

FT

50 100 150 200 250

-1.5

-1

-0.5

0.5

1

1.5

2

50 100 150 200 250

0.5

1

1.5

2

2.5

1

0

/21 N

k

Nikn

kn edN

f

b

a

dtftKg )(),()( 1 )texp(),( itK Continuous:

Discrete:

FT

S


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FTIR Spectrometer Design

Michelson

Interferometer

IR Source

Sample

Moving MirrorFixed Mirror

Beamsplitter

Detector

Interferogram

Fourier Transform - IR Spectrum

It is possible to build a detector that detects multiplefrequencies for some EM radiation (ex. ICP-OES with CCD,UV-Vis DAD)

FTIR spectrometers are designed around the Michelsoninterferometer, which modulates each IR individualfrequency with an additional unique frequency:


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IR Sampling Methods: Absorbance Methods

Salt plates (NaCl): for liquids (a drop) and small amounts of

solids. Sample is held between two plates or is squeezed onto

a single plate.

KBr/CsI pellet: a dilute (~1%) amount of sample in the halide

matrix is pressed at >10000 psi to form a transparent disk.

Disadvantages: dilution required, can cause changes in

sample

Mulls: Solid dispersion of sample in a heavy oil (Nujol)

Disadvantages: big interferences

Cells: For liquids or dissolved samples. Includes internalreflectance cells (CIRCLE cells)

Photoacoustic (discussed later)


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IR Sampling Methods: Reflectance Methods Specular reflection: direct

reflection off of a flat surface.

Grazing angles

Attenuated total reflection

(ATR): Beam passed through

an IR-transparent material

with a high refractive index,causing internal reflections.

Depth is ~2 um (several

wavelengths)

Diffuse reflection (DRIFTS): atechnique that collects IR

radiation scattered off of fine

particles and powders. Used

for both surface and bulk

studies.

Figures from http://www.nuance.northwestern.edu/KeckII/ftir7.asp

ATR

DRIFTS


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IR Sources

Nernst glower: a rod or cylinder made from several

grams of rare earth oxides, heated to 1200-2200K by an

electric current.

Globar: similar to the Nernst glower but made from

silicon carbide, electrically heated. Better performance at

lower frequencies.

Incandescent Wires: nichrome or rhodium, low intensity

Mercury Arc: high-pressure mercury vapor tube, electric

arc forms a plasma. Used for far-IR

Tungsten filament: used for near-IR

CO2 Lasers (line source): high-intensity, tunable, used for

quantitation of specific analytes.

IR D t t


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IR Detectors Thermal transducers

Response depends upon heating effects of IR radiation

(temperature change is measured)

Slow response times, typically used for dispersive instrumentsor special applications

Pyroelectric transducers

Pyroelectric: insulators (dielectrics) which retain a strong electric

polarization after removal of an electric field, while they stay

below their Curie temperature.

DTGS (deuterated triglycine sulfate): Curie point ~47C

Fast response time, useful for interferometry (FTIR)

Photoconducting transducers

Photoconductor: absorption of radiation decreases electricalresistance. Cooled to LN2 temperatures (77K) to reduce thermal

noise.

Mid-IR: Mercury cadmium telluride (MCT)

Near-IR: Lead sulfide (NIR)


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Raman Spectrometers

The basic design dispersive Raman scattering system:

Special considerations:

Sources: lasers are generally the only source strong enough toscatter lots of light and lead to detectable Raman scattering

Avoiding fluorescence: He-Cd (441.6 nm), Ar ion (488.0 nm,

514.5 nm), He-Ne (632.8), Diode (782 or 830), Nd/YAG (1064)

SampleWavelength

Selector

Detector

(photoelectric transducer)

Radiation

source

(90 angle)


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More on Raman

Raman can be used to study aqueous-phase samples

IR is normally obscured by H2O modes, these happen to be lessintense in Raman

However, the water can absorb the scattered Raman light and

will damp the spectrum, and lower its sensitivity

Raman has several problems: Susceptible to fluorescence, choice of laser important

When used to analyze samples at temperatures greater than

250C, suffers from black-body radiation interference (so does

IR)

When applied to darkly-colored samples (e.g. black), the Ramanlaser will heat the sample, can cause decomposition and/or

more black-body radiation


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Applications of Raman Spectroscopy

Biochemistry: water is not strongly detected in Raman experiments,

so aqueous systems can be studied. Sensitive to e.g. protein

conformation.

Inorganic chemistry: also often aqueous systems. Raman also can

study lower wavenumbers without interferences.

Other unique examples:

Resonance Raman spectroscopy: strong enhancement (102

106 times) of Raman lines by using an excitation frequency close

to an electronic transition (Can detect umol or nmol of analytes).

Surface-enhanced Raman (SERS): an enhancement obtained for

samples adsorbed on colloidal metal particles.

Coherent anti-Stokes Raman (CARS): a non-linear technique

using two lasers to observe third-order Raman scattering used

for studies of gaseous systems like flames since it avoids both

fluorescence and luminescence issues.


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Applications of Raman Spectroscopy

Raman in catalysis research:

Useful for the study of zeolite interiors Fluorescence can be a problem, but one approach is to use

UV light (257 nm) which avoids it just like switching to the

IR (but at the risk of decomposition)

Raman microscopy:

offers sub-micrometer lateral resolution combined with depth-

profiling (when combined with confocal microscopy)

C i f IR d R S t


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Comparison of IR and Raman Spectroscopy

Advantages of Raman over IR:

Avoids many interferences from solvents, cells and sample

preparation methods Better selectivity, peaks tend to be narrow

Depolarization studies possible, enhanced effects in some cases

Can detect IR-inactive vibrational modes

Advantages of IR over Raman: Raman can suffer from laser-induced fluorescence and

degradation

Raman lines are weaker, the Rayleigh line is also present

Raman instruments are generally more costly

Spectra are spread over many um in the IR but are compressed

into several nm (20-50 nm) in the Raman

Final conclusion they are complementary techniques!

I t t ti f IR d R S t


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Interpretation of IR and Raman Spectra

General Features:

Stretching frequencies are greater (higher wavenumbers) than

corresponding bending frequencies It is easier to bend a bond than to stretch it

Bonds to hydrogen have higher stretching frequencies than those

to heavier atoms.

Hydrogen is a much lighter element

Triple bonds have higher stretching frequencies than doublebonds, which have higher frequencies than single bonds

Strong IR bands often correspond to weak Raman bands and

vice-versa

I t t ti f IR d R S t


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Interpretation of IR and Raman Spectra

Characteristic Vibrational Frequencies for Common Functional Groups

Frequency (cm-1) Functional Group Comments

3200-3500 alcohols (O-H)

amine, amide (N-H)

alkynes (CC-H)

Broad

Variable

Sharp

3000 alkane (C-C-H)

alkene (C=C-H)

2100-2300 alkyne (CC-H)nitrile (CN-H)

1690-1760 carbonyl (C=O) ketones, aldehydes,

acids

1660 alkene (C=C)

imine (C=N)

amide (C=O)

Conjugation lowers

amide frequency

1500-1570

1300-1370

nitro (NO2)

1050-1300 alcohols, ethers,

esters, acids (C-O)

IR and Raman Spectra of an Organic Compound


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The IR and Raman spectra of

flufenamic acid (an analgesic/anti-

inflammatory drug):

CF3

O OH

FT-IR Flufenamic acid Aldrich as recd

0.05

0.10

0.15

0.20

0.25

0.30

Ab

s

FT-Raman Flufenamic acid Aldrich as recd

0

10

20

30

40

50

60

Int

500100015002000250030003500

Raman shi ft (cm-1)



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The IR and Raman spectra of

flufenamic acid (an analgesic/anti-

inflammatory drug):

CF3

O OH

FT-IR Flufenamic acid Aldrich as recd

0.05

0.10

0.15

0.20

0.25

0.30

Abs

FT-Raman Flufenamic acid Aldrich as recd

0

10

20

30

40

50

60

Int

2004006008001000120014001600

Wavenumbers (cm-1)

Notematerials

usually limit IRin this region


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IR F i d H d B di Eff t


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IR Frequencies and Hydrogen Bonding Effects

IR frequencies are sensitive to

hydrogen-bonding strength and

geometry (plots of relationshipsbetween crystallographic distances

and vibrational frequencies):

G. A. Jeffrey,An Introduction to Hydrogen Bonding, Oxford, 1997.


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T h t S t


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Terahertz Spectroscopy

A relatively new technique, addresses an unused portion of the

EM spectrum (the terahertz gap):

50 GHz (0.05 THz) to 3 THz (1.2 cm-1 to 100 cm-1)

Made possible with recent innovations in instrument design,

accesses a region of crystalline phonon bands

Applications of Near IR Spectroscopy


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Applications of Near IR Spectroscopy

Near IR heavily used in process chemistry

Amenable to quantitative analysis usually in conjunction withchemometrics (calibration requires many standards to be run)

While not a qualitative technique, it can serve as a fast and useful

quantitative technique especially using diffuse reflectance

Accuracy and precision in the ~2% range

Examples:

On-line reaction monitoring (food, agriculture, pharmaceuticals) Moisture and solvent measurement and monitoring

Water overtone observed at 1940 nm

Solid blending and solid-state issues

N IR S t


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Near IR Spectroscopy


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Near IR Spectrum of Water (1st Derivative)


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Near IR Spectrum of Water (1st Derivative)

1st derivative (and 2nd derivative) allows for easier identification of

bands

Photoacoustic Spectroscopy


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Photoacoustic Spectroscopy

First discovered in 1880 by A. G. Bell

The IR version of photoacoustic sampling is generally

applied to two types of system (UV-Vis spectrometrycan also be performed):

All gas (or all-liquid)

systems:

The solid-gas system:

Solid

IR-Transparent Gas

Gas:

IR Radiation

IR Radiation

The Photoacoustic Effect for Solid Gas Systems


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The Photoacoustic Effect for Solid-Gas Systems

The photoacoustic effect is produced when intensity-

modulated light hits a solid surface (or a confined gas

or liquid).

Gas

Solid

Modulated IR Radiation

x

PA Cell

Thermal Wave (attenuates rapidly)

Microphone

P(x)

P0

IR is absorbed by a vibrational transition,

followed by non-radiative relaxation

P R P ex

R

P

surface

( )(

1 0

0

+ )

surface reflectivity

incident IR beam power

- absorption coefficient- thermal diffusion length

1

(Psurface)

Th Th l Diff i L th


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The Thermal Diffusion Length

The thermal diffusion length is:

PET

PVF2

0.15 cm/sec IR 1.2 cm/sec IR

-thermal diffusion length = / 2

The thermal diffusivity a is:

The variable , the modulation frequency of the IRradiation, is directly proportional to interferometer mirror

velocity, and is defined as:

(cm/sec)eterinterferomMichelsonofocityMirror vel

rs)(wavenumbeFrequencyIR

4

M

M

ak

C

k

C

thermal conductivity

density

specific heat

2a


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A Typical Photoacoustic FTIR Spectrum


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A Typical Photoacoustic FTIR Spectrum

A PA-FTIR Spectrum of a silicone sealant:

The spectrum shows peaks where the IR radiation is beingabsorbed due to vibrational energy level transitions.

IR Modulation

frequency is high

IR Modulation

frequency is low

Differences between a PA-FTIR spectrum and a regular IRspectrum:

IR modulation frequency effects (weak CH3 and CH2 bands)

Saturation of strong bands in the spectrum


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Photoacoustic Saturation

Strong bands in PA-FTIR spectraoften show saturation.

Saturation occurs when the

vibrational transition is beingpumped to its excited state faster

than it can release energy.

A high absorption coefficientcoincides with faster saturation.

A Saturated Band


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Depth-Profiling Studies with PA-FTIR

Thermal diffusion length

allows for IR depthprofiling with PA-FTIR

Example: a layer ofpoly(vinylidine fluoride

(PVF2) on poly(ethyleneterephthalate) (PET)

PET

PVF2

PVF2 top layer is 6 micrometers thick.The carbonyl band, due to the PET, is marked with a red dot ().Data acquired with a Digilab FTS-20E with a home-built PA cell.

0.15 cm/sec IR 1.2 cm/sec IR

-thermal diffusion length = / 2

Applications of FT Microwave Spectroscopy


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Applications of FT Microwave Spectroscopy Under development for: real-time, sensitive monitoring of

gases evolved in process chemistry, plant and vehicle

emissions, etc

Current techniques have limits (GC, IR, MS, IMS)

Normally use pulsed-nozzle sources and high-precision Fabry-

Perot interferometers (PNFTMW)

Diagram from http://physics.nist.gov/Divisions/Div844/facilities/ftmw/ftmw.html

Compound Detection Limit

(nanomol/mol)

Acrolein 0.5

Carbonyl sulfide 1

Sulfur dioxide 4

Propionaldehyde 100

Methyl-t-butyl ether 65

Vinyl chloride 0.45

Ethyl chloride 2

Vinyl bromide 1

Toluene 130

Vinyl cyanide 0.28

Acetaldehyde 1

Hybrid/Hyphenated Techniques: Interfaces
http://physics.nist.gov/Divisions/Div844/facilities/ftmw/ftmw.htmlhttp://physics.nist.gov/Divisions/Div844/facilities/ftmw/ftmw.html


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Hybrid/Hyphenated Techniques: Interfaces

Interfaces between vibrational spectrometers and other

analytical instruments

GC-FTIR: gaseous column effluent passed through light

pipes

Similar Technique: TGA-IR, for identification of evolved

gases from thermal decomposition

Topic 5 Rotational and Vibrational Spectroscopy

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