Transcript Instrumental Methods of Analysis

Chapter 16 – Infrared
Spectroscopy
Introduction
• Useful range from about 2.5 mm to 50 mm.
• Infrared used to determine the major functional groups present.
• Quantitative measurements possible but subject to large amount of
error.
• Atoms or groups of atoms in molecules are in continuous motion
with different modes of vibration relative to each other.
• Absorption of radiation changes amplitude of vibration but not
frequency.
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Chapter 16 - 2
Vibrational Modes
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Increased amplitude produces a change in
dipole moment.
m = q×r. where m = dipole moment, q =
change displacement, and r = displacement
from equilibrium.
Only vibrations that cause this change in
electric dipole moment will be associated
with an absorption of infrared radiation.
E.g. Symmetric and antisymmetric modes
of vibration are possible with CO2;
symmetric mode of vibration has no net
change in its dipole moment, while
antisymmetic mode has net change in
dipole moment. The antisymmetric mode
would be infrared active and the symmetric
mode would not.
O C O O C O
symmetric antisymmetric
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Chapter 16 - 3
VIBRATIONAL MODELS
• Mechanical model: spring connects
one or two moving bodies. Restoring
force, F, pulling on atoms to return to
initial positions.
• Force related to force constant
[stiffness of spring (bond)].
– F = ky. Negative sign means
restoring force. (Hook’s law)
– dE = Fdy or upon integrating
between equilibrium position and y
gives E = ½ky2.
• Potential energy curve parabolic;
maximum when spring is stretched
or compressed and minimum at
equilibrium position.
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Chapter 16 - 4
Vibrational frequency
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F = ma where a = acceleration and m =
mass of the substance moving.
2y
d
Acceleration is written as: a =
dt2
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F = ma = m
dt
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2
= ky
Solution: y = A cos 2pumt where
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.um = vibrational frequency and
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A = maximum amplitude of the motion.
k
1
k

2p
m
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Leads to m =
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Two moving particles: frequency uses reduced mass .
m =
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d2 y
m1m2
m1 + m2
4 p2 m
=
m =
Chapter 16 - 5
1 k
1 k(m1 + m2)
=
2p m
2p
m1  m2
Quantum Mechanical Vibrations
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Harmonic oscillator is used to obtain wave equation for potential
energy of oscillator.
1 h k

E = v  

2  2p m
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Quantum Mechanical Model of Atomic Movement only certain
energies are allowed.
near equilibrium position, molecular vibrations similar to mechanical
model..
Frequency of the vibration from the mechanical model as a
reasonable estimate of true vibrational frequency: .
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where v = vibrational quantum # (+ integer).
m =
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1 k
1 k(m1  m 2 )
=
2p m 2p
m1  m 2
But quantum mechanical energy is: .
1

E =  v +  h m

2
Quantum mechanical selection rule which states that Dv = ± 1 (due
to conservation of momentum of the combined photon and
molecular system).
1 k
h k
m 
and
where
DE  h m =
2p m
2p m
k = force constant (N/m) and m = reduced mass (kg).
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In wavenumbers:
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 = 5.3x 1012
k
m
Chapter 16 - 6
GROUP FREQUENCIES
Estimation of frequencies of vibration for various groups
possible when force constant known.
E.g.1 force constant of C=O bond is 1.23x103 N/m,
determine vibrational frequency of this C=O group.
12.0gC
1kgC
1molC

x1atomCx
= 1.99x 10 26 kgC
molC
6.02x 10 23 atomsC
1x 10 3 gC
mO = 2.66x 1026 kgO
26
26
mc 
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• reduced mass of
• Substituting:
• Units:
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m
1.99x 10
 2.67x 10
(1.99 + 2.67)x 10 26
 = 5.3x 10-12 s / cm
1.23x 103 N / m
1.13x 10
N
kg  m  s 2
1
1
 s 2
kg  m
kg  m
Chapter 16 - 7
-26 kg
kg = 1.13x 10 26 kg
= 1742 cm-1
Sample Problem
• E.g.2: C-H stretch of alkane occurs at  2900 cm1; determine
frequency of deuterated analog using mechanical equation:
• ratio of two equations for two forms of compound
C-H
=
C-D
or
m C-D
m C-H
m C-H
=
C-D
C-H
m C-D
reduced mass for each of two bonds will be: mC = 1.99x1026 kg,
• mD = 3.32x1027 kg, mH = 1.66x1027 kg and
• .mC-H = 1.53x1027 kg and mC-D = 2.84x1027 kg
• Substituting:
1.53x 1027 kg

1
 2130 cm1 Q.E.D.
C-D = 2900 cm

27
2.84x
kg
10
• Deuterating convenient way to confirm presence of particular type
of bond, since frequency shift is relatively large and predictable.
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Chapter 16 - 8
INSTRUMENTATION
• Instrumentation is same as for other absorption instruments except
that the sources, detector and the optical material are designed
specifically for this spectral region.
• Sources: We have mentioned these detectors in our discussion of
general features of the absorption spectrophotometer.
• Nernst Glower = cylinder composed of rare-earth oxides which is
heated to some temperature before current can be passed directly
through it.
– Since it has a negative temperature coefficient, it is necessary to
regulate the current (T kept at about 1800K)..
• Globar = SiC rod (T kept at about 1600K) kept at desired
temperature by passing current through it; positive temperature
coefficient..
• Both of these sources suffer from having low intensities (  107 109 W) and has led authors to claim that source is energy limited.
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Chapter 16 - 9
Detectors
• Low flux of photons and low energy of infrared
radiation make it more difficult to detect.
• photon detector- based upon photoconductive effect
that occurs in certain semiconductor materials.
Absorption of light causes resistance to decrease.
Voltage drop across load resistor measured: HgCdTe
must be cooled to 77K and PbS2 can be operated at
room temperature.
– Photon detectors (also called quantum detectors) have rapid
response and thus are used with FTIR .
• Material deposited on surface of a nonconducting
material and is sealed in an evacuated tube to protect
the semiconductor from reaction with the atmosphere.
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Chapter 16 - 10
Thermal Detectors
• Absorption of IR radiation produces a heating effect which
alters a physical property of the detector. Thermal detectors are
usable over a wide wavelength range.
• Thermocouple or therompile.Instrumental Methods of
Analysis, Willard, Merritt, Dean & Settle, p. 193.thermocouplespiece of blackened foil placed over 2 wires made of dissimilar
metals.
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detector is placed inside vacuum to improve its response (minimize
heat loss due to conduction).
Several thermocouples in series = thermopile; has higher
sensitivity since voltages of individual thermocouples are additive.
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Temperature differences of about 106 K can be determined
this way.
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Thermocouple is low impedance circuit so that high impedance
preamplifier is necessary to avoid signal modification by the
amplifier circuitry. The response time of these detectors is on
order of 100 ms. 2s
• Null Point Wheatsone Bridg
• thermistor or bolometer- change in resistance is measured and
related to amount of photons hitting detector.
• Resistance measured with Wheatstone bridge
• Radiation falls on R1;R2 adjusted until circuit balanced (no
voltage drop between C and D. Then R1/R2 = R3/R4
• Knowledge of all other resistances makes it possible to
determine R1
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Chapter 16 - 11
Thermocouple or therompile.
Instrumental Methods of Analysis, Willard,
Merritt, Dean & Settle, p. 193.
Null Point Wheatsone Bridge,
Undergraduate Instrumental
Analysis ,Robinson, p. 141.
INSTRUMENTS
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Dispersive instruments: have been the traditional instrument design for IRs; high resolution is
possible, FT-IR is essentially the same in modern instruments. The FT-IR has a much higher
sensitivity which is very important due to the low signal levels in the IR region. This extra
sensitivity makes it possible to use the FT-IR for quantitative work.
Sample Handling: Solids, liquids and gases can be analyzed with IR.
Gases are generally are often constructed with a cylindrical glass body and are usually about 10
cm in length.
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The pressure can be from a few mm Hg up to several atm. depending upon the absorption characteristics of
sample.
Liquids and solutions:
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–
–
b=
DN
2(  2  1)
Only a short pathlength (1mm) is required for liquids.
Some solvents absorb in IR region interfering with signal from sample.
Pathlength of thin IR sample holder can be determined by observation of the interference patterns
associated with constructive interference from reflection of light from the two internal surfaces of cell: .
E.g. Determine the pathlength from the fringes below:
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Chapter 16 - 12
FT-IR
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Michaelson Interferometer.
– Laser-fringe reference system
provides sampling-interval. Signal
averaging can only be
accomplished if the positioins of
the mirror are precisely know. This
is achieved by using a helium-neon
laser as a reference. Radiation at
exactly 632.8 nm traverses the
same optical path as the IR beam.
– A separate detector measures the
interferogram produced, giving a
sinusoidal signal with maxima
separated by the laser frequency at
15,803 cm-1.
– This signal is used to trigger the
sampling of the IR signal very
reproducibly
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IR Source
Detector
Chem 422
Chapter 16 - 13
Quantitative Analysis
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IR has traditionally been used for qualitative
analysis.
Difficult to use quantitatively due to chemical
or instrumental effects.
Large sloping background often interferes
with normal spectrum.
The base line method corrects involves
selection of absorption band of the
substance under analysis which is
sufficiently separated from other matrix
peaks and corrected as shown below.
Mixtures can be determined by same
methods described earlier. Need to set up
the correct number of simultaneous
equations.
Convenient for measuring concentrations of
gases
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Chapter 16 - 14
Instrumental Analysis, Christian & O’Reilly, p. 241.