Chapter 16 Infrared Spectrometry
Problems:1, 2, 3, 6, 11, 12
Intro
Infrared 12,800-10 cm-1
.780-1000 :m
780-1,000,000nm
Convenient to break into 3 somewhat arbitrary regions
Near- .78-2.5:m use a vis spectrometer, maybe with a different source
used in quantitation for industrial and agricultural process control
Mid- 2.5-50 use to be a dispersive or diffraction monochrometer designed for IR,
now use FT-IR machines. With older machines was used qualitatively
only. With FTIR 10x better S/N so now quantitative as well + surface
techniques
far- 50-1000 used to be difficult, with FTIR now easier, so relatively new field
Actually region most used is 2.5 to 15
Our machine 4000-500 cm-1
2.5-20 :m
16A Theory
IR E corresponds to E for transitions between vibrational and rotational states
Will focus on absorption, but emission and reflection also are important
16A-1 Introduction
Figure 16-1 typical IR output
Y is Transmittance
X is usually wave # in cm-1
With modern computer driven machines don’t have to stick to this can do
Absorbance vs wavelength, this is just holdover from earlier times
X in a frequency unit it preferred because frequency directly proportional
to E. Hz because exponents on numbers are so big. Remember cm-1 is
not truly a frequency, it is just a number that is proportional to frequency.
Note change in X scale about ½ way through spectrum. Right hand en of
spectrum usually has more narrower peaks, to so this tends to spread the
peaks out more. Not all machine do this. Our machine does not.
Dipole changes during Vibrations and Rotations
IR E not large enough for change molecule’s electron orbital
Molecule only changes vibration or rotation state
How does this allow E to be absorbed?
2
Molecule must undergo a net change in dipole moment
Rotational Transitions
How do EM radiation and a change in dipole interact?
EM radiation Electric field alternating + then Rotation is easy - if molecule has a dipole, dipole will try to
line up with electric field, If can rotate at same frequency as
light, will do so. And will absorb that E to make the molecule
rotate. (Note if molecule has do dipole will not absorb E!)
E needed is slight
100cm-1, 8>100:m, only about 1000kJ/mol
In gas phase many discrete, well defined lines
In liquids or solids blur into a continuum
Vibrational Transitions
Let’s start with simplest vibration
H-Cl
Again EM radiation is alternating +/- electric field
So will alternately want to push and pull the H (positive part
of dipole) back and forth.
Bond between atoms is like a spring
There is a preferred position, but with just the right E
you can get the spring to oscillate back an forth
So when E of Em radiation matches E of bond, you get the
atoms vibrating back and forth
Also note each position also has a different dipole moment
Lots of other motions are similar
Atoms can rotate around single bonds
Chair/boat conformations in cyclic compounds
When have lots of atoms have lots of simultaneous changes and
lots of different motions
Break down into some general categories of motion
Stretching (need 2 atoms)
Continuous change in distance between atoms along
a bond
But direction of bond remains the same
Dipole stays pointed same direction, but changes in
magnitude
Bending (need 3 or more atoms)
Angle between 2 bonds changes
3
Scissoring
Rocking
Wagging
Twisting (figure 16-2)
Can also have complex coupling of all of the above with
each other
In next section will look at simplest model for this system, harmonic
oscillators then at adjustments to this model
16A-2 Mechanical Model of a Stretching Vibration
Nice, simple model
2 masses connected by a spring
pull one of the masses along the axis of the spring (line connecting two masses)
And release. What happens, atoms vibrate back and forth along the axis.
The heaviest moves a little, the lightest mas moves the most
Let’s make even simpler, eliminate one mass by hanging spring from a hook
Figure 16-3
Back to physics Force of a spring determined by Hooke’s Law
F=-ky
spring force tends to restore mass to original position
As distance Y increases + force will be increasing in opposite
direction to restore to original position. As distance goes -, force
will be positive, again to restore to original position.
Potential E of a Harmonic oscillator
skip differential and integral equations this year, may want to put back in
for future
dE= –Fdy
-F=ky
dE=kydy
integrate
E = ½ ky2
Show plot of E in figure 16-3
Higher E as spring is displaced from middle
0 E when weight is sitting still.
Nice and symmetric
4
Vibrational Frequency
Now that we know the E as a function id distance, we can look at
motion
F=ma (newton’s second law)
A = acceleration = d2y/dt2
(Second derivative of y with respect to time
Using F=-ky
ma=-ky
m d2y/dt2=-ky
M times second derivative = y
How can a function’s second derivative = the original function?
This works for periodic functions like sin or cosine
Y = A cos 2B<mt
Where <m is called the natural harmonic frequency
A is the amplitude of the motion
The second derivative is:
-4B2<m2A cos 2B<mt
And substituting in we have
m -4B2<m2A cos 2B<mt= -k A cos 2B<mt
And cancelling out common terms
m -4B2<m2= -k
<m2= k/4B2m
<m2=1/2B sqrt(k/m)
Note the natural frequency depends only on the force constant of
the spring and the mass, NOT on the energy! The only thing the
energy changes is the amplitude of the vibration
If we change the system to reflect 2 masses tied together by a
spring we need to substitute a reduced mass for the original m
: = m1m2/(m1+m2)
5
Then
<m=1/2B sqrt[k(m1+m2)/m1m2]
The last equation we can use in molecular systems. We can
substitute the mass of the two atoms into the equation. Set < to the
frequency of interest, and k becomes a measure of the ‘stiffness’ of
the bond
16A-3 Quantum Treatment of vibrations
If we really want to model an atom, then we have to shift to quantum mechanics
to show the quantitized nature of the molecular vibrations.
Using the harmonic oscillator couples with a quantum vibration we get:
Where h is Planck’s constant
v is the vibrational quantum number (positive integers 0,1,2...)
And the rest is the same
Note how similar ths is to the harmonic oscillator model
Substituting one equation into the other to get rid of the common terms we have:
E=(v+1/2)h<m
At RT most of the molecules with be in the ground state so:
E = 1/2h<m
Promotion to the 1st excited state will be to
E=3/2 h<m
And the )E = 3/2-1/2 = h<m
E=h< we then have
h<=h<m = 1/2Bsqrt(k/:)
6
Since the frequency is usually in wavenumbers, and there are some other
constants we can get lump together we can get the equation:
< (bar) is the wavenumber of the absorption peak
K is the force constant of the bond in Newtons/m
: is the reduced mass in kg
Using this equation we find that
K is usually between 3 x102 and 8 x102 N/m, and is usually about
5x102
K for a double bond is about 2x as much (10x102 = 103)
K for a triple bond is 3x About 1.5x103
Try a sample calculation
A CH stretching frequency is 2900 cm-1
2900=5.3x10-12sqrt(k/:)
:=m1m2/(m1+m2)
m1=C = 12x10-3 kg/mol / 6.02x1023atom/mol = 2x10-26kg/atom
m2 = H =1x10-3/6,02x1023 = 1.7x10-27
:= 2x10-26 x 1.7x10-27 /(2x10-26 + 1.7x10-27)
=3.4x10-53/3.7x10-27
=.9x10-26
2900=5.3x10-12sqrt(k/.9x10-26 )
2900/5.3x10-12 = sqrt(k/0.9x10-26)
5.5x1014 = sqrt(k/0.9x10-26)
(5.5x1014)2 = k/0.9x10-26
3x1029 = k/0.9x10-26
3x1029 x 0.9x10-26 = k
7
2.1x103 =k This is a little higher than expected, is there an error?
Selection Rules
Quantum theory indicates that only )v =+/- 1 are allowed
So only ever see 1 absorption peak for a given vibration
Anharmonic Oscillator
Real atomic forces aren’t nice and symmetric like springs
As the atoms get too close the inter atomic repulsion skyrockets,
and as the atoms get too far away the bond force weakens. A
more realistic E potential is shown in figure 16-3b. We can more
properly model this system with more quantum theory, but at this
point the math becomes very complex. If we use what is called an
anharmonic oscillator model we can get a model that is simpler
mathematically, and more realistic
The anharmonic oscillator has some interesting ramifications
1. The E level between vibrations are no longer identical
Because of this selection rules allow v=+/-2 or even +/- 3
transitions. This means that we can begin to see ’overtone’
vibrations
These are weak lines and may not be observed
2. Two different frequencies can interact to give additional
frequencies at sums and difference of the fundamental frequencies
as well.
16A-4 Vibrational Modes
for simple diatomic or triatomic molecules can figure out number and kinds of
vibrations that will be present
For more complicated molecules many different kinds of vibrations so can’t
figure them all out
Can figure out the total number of possible vibrations
3 coordinates needed to fix an atom in space (X, Y, Z)
Each coordinate is one degree of freedom
so with N atoms have 3N degrees of freedom
Three kinds of motion to think about
Translation of entire molecule through space
Rotation of entire molecule around it’s center of gravity
Individual vibrations within the molecule
8
The translation take up 3 degrees of freedom
The rotation take up another 3 degrees of freedom
So we are left with 3N-6 degrees of freedom (of possible different
vibrations)
Linear molecules are slightly different
Since are linear, rotation about axis doesn’t cost a degree fo
freedom
So for linears have 3N-5 degrees of freedom
3N-6 or 3N-5 degrees of freedom, called the ‘normal modes’ of vibrations
each normal mode will have a potential well like we developed earlier
each will have its selection rules
so if the vibration changes the dipole of the molecule, it will have an
absorption
Often will have less absorption peaks than normal modes
1. Symmetry of molecule is such that dipole of molecule doesn’t change
2. Energies of 2 or more vibrations are nearly the same so they overlap
3. absorption is so low that it can’t be observed
4. Vibrational wavelength outside the range of the instrument
Occasionally more absorption bands than expected
1. Overtones (as discussed earlier)
2. Combination bands - a photon excites 2 different vibration modes
simultaneously
16A-5 Vibrational Coupling
The E of a vibration (frequency or wavelength of a vibration) may be coupled
(influenced) by other vibrators in the molecule
1.
Strong coupling between stretching vibrations where one atoms is
common to both stretches
2.
Interactions between bending vibrations involving a common bond
between vibrating groups
3.
Stretching and bending can couple if the bond that is stretching
forms one side of the angle that is bending
4.
Interactions are greater when the E of the 2 energies are about
equal
5.
Little or no interactions between groups separated by 2 or more
bond
6.
Coupling requires that vibrations must be of the same symmetry
species
What does this all mean? Let’s look at CO2 O=C=O
9
3 atoms, linear, 3N-5, 9-5, expect 4 normal modes or bands
Diagrams page 388&389
Since contains C=O bonds, expect vibration like C=O in other
carbonyls
(Like ketones)
1700 cm-1 6:m
Actually observe 2 bands
2330 cm-1 (4.3 :m)
677 cm-1 (15 :m)
Can see 2 stretching vibrations
Symmetric - non change in dipole - no absorption
Asymmetric change in dipole should absorb this is the 2330
cm-1 band
2 remaining modes are scissoring , either in plane or out of plane
Since same motion, but in different directions, the E’s are
the same
If the E’s are the same, the quantum states are degenerate
This is the 677 cm-1 band
So you have accounted for all normal modes of vibrations!
Look at non-linear SO2 (lone pair on the S makes sp2 hybridization)
Again 3 atoms, but nonlinear so 3N-6 for 9-6 = 3 vibrational modes
(Shown in diagram)
Here symmetric stretching does change dipole so does absorb
3650 cm-1
Asymmetric stretching 3760 cm-1
Because 3 atoms are non-linear they define the scissoring plane,
so have only 1 scissoring motion, so only 1 vibration
For water this is at 1595 cm-1
I don’t see what it is for SO2
Note, the presence of 1 or 2 scissoring can be used to determine
molecular structure, linear or nonlinear, so there is structural
information here
Coupling of vibrations can shift things around as well
C-O Stretch
Methanol 1034 cm-1
Ethanol 1053 cm-1
2 butanol 1105 cm-1
Changed due to C-H, C-C-OH or C-COH-C coupled motions
So assignment of frequencies to specific groups can have some
uncertainties
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16B Infrared Sources and Transducers
Need a continuum source of IR radiation and a sensitive detector. Discussed
briefly in earlier chapter, now here are details
16B-1 Sources
Inert solid heated to 1500-2200 K where produce blackbody continuum radiation
At these temps max intensity 5000-5900 cm-1
See figure 6-18 page 134
To long 8 side falls off smoothly, to about 1% at 670cm-1
To short 8 side decreases more rapidly, 1% at 10,000 cm-1
Note: most organic IR 650-4000 cm-1
Nernst Glower Cylinder f rare earth oxides 1-2 mm diameter, 20 mm length
Platinum leads
Pass current through to heat to 1200-2200 K
Large negative T coefficient of electrical resistance
IE high resistance when cold, can’t pass enough current through it
to make it hot, so need an external heat source. Once is it warm
enough, now lower resistance, so it lets more current through, and
it stays warm. Electronic design problem. Must limit current. If you
don’t as more current passes gets warmer, resistance decreases,
to lets more current through, that will make warmer, etc until the
machine burns out!
Spectral output at 2200K. General blackbody like, small peaks and
dips due to composition
Globar
Silicon carbide rod
5 mm diameter, 50 mm length
Again heat with electrical current
+ coefficient of resistance
So current limits itself, no fancy electronics
Need to water cool contacts, otherwise will arc
Energy similar to Nernst, but has better output <5:m
Incandescent wire
Lower intensity but longer life
Tightly wound Nichrome wire
Again pass current to heat until glows about 1100K
Mercury Arc
11
The above 3 don’t put out much when 8>50:m (far IR)
Here high pressure Hg Arc works
Current causes arc that forms plasma that yields IR continuum
Tungsten Filament
Ordinary bulb, good in near IR 4000-12,800 cm-1
CO2 Laser
100 closely spaced lines between 900 and 1100 cm-1 (about 1/10
of usual IR range)
Can tune laser to any 1 line
Use in instrument designed to monitor a specific compound. Very
bright, several orders of magnitude brighter than other sources, but
not flexible
16B-2 IR Transducers
3 main types
1.
Thermal transducers
2.
Pyroelectric transducer (very specialized thermal transducer)
3.
Photoconducting transducer
Thermal Transducers
response depends on heating effect of radiation
radiation is absorbed by a small amount of material, measure temperature
rise
E hitting transducer 10-7 to 10-9 W
Need very small amount of material so T rise is maximal
Make detector as small as possible
Focus light as tightly as possible
T rise still only.001 K or so
Detecting heat is also a problem because fo thermal noise
(Everything else is warm so has make thermal noise)
House transducer in vacuum, so other heat can’t get to it
Use chopper electronics to minimize drift
Keep detector at constant T
Thermocouples
2 junction at 2 metals
A potential difference develops when 2 junctions are at different T’s
12
Use either ver fine wires or metals evaporated onto nonconducting
support
Again, seal in vacuum to shield from outside heat
House both junctions in same spot, but only shine IR radiation on
one
Again chop signal and compare one to the other
But don’t need to keep at a constant T
Can put several thermocouple in series for better sensitivity -called
a thermopile
Well designed can detect )T of 10-6K
Bolometers
Not used as much in mid IR, but good in 5-400 cm-1 region
Strips of metal like Pt or Ni, or semiconducting thermisters
Resistance has large change with heat
Measure resistance of circuit
Pyroelectric Transducers
Single crystals of pyroelectric materials
Insulators with special thermal and electrical properties
Most common triglycine sulfate
(NH2CH2COOH)3 @ H2SO4
Usually deuteratred, with a few alanines
Is a dielectric material, does not conduct E, but material within dielectric
will orient with external electric field
Usually polarization disappears when field removed
In pyroelectric substance polarization remains for a while
And polarization is T dependent
So use like a capacitor, Charge it up and watch current flow out of
it
Very fast response
So used in most FTIR machines
Photoconducting Transducers
Thin film of semiconducting material sealed in vacuum to protect
from air
When light hits, moves electrons into conducting orbitals, starts to
conduct E
PbS widely used in near IR (10,000-333 cm-1) operates at RT
13
In mid and far IR use Hg/Cd Te, cooled under liquid N2 (77K)
Also has fast response for FT machine
Probably best overall detector, if you can afford the liquid N2
16C Infrared Instruments
First IR machines were dispersive, used until 1980's now largely replaced by
FTIR machines
16C-1 FTIR Spectrometers
Actually two different designs the interference design and the Hadamard
design. The latter isn’t used much so will stick to the interference
Original FT machines big, bulky >100,000 and some mechanical
adjustments
Now 15-20K and largely maintenance free
Components
Figure 7-42 page 186
Figure 16-6
Drive
For interferometer need to know speed and position of
moving mirror at all time to within a fraction of a 8
In far IR (50-1000 :m, 200-10 cm-1)
This can be accomplished with a motor driven
micrometer screw
Near and mid IR need more precision
Mirror floated on an air bearing
Held in close fitting stainless steel sleeve
DC coil pushes plunger back and forth
Drive length 1 to 20 cm-1
Scan rate .01 to 10 cm/s
Need to sample signal at precise intervals
Need to know zero retardation point exactly
One way to do this is to have 3 interferometers built into
same moving mirror
1st system is the IR sampling system
14
2nd system uses a helium/neon laser
Has a single frequency
Creates a simple sine wave pattern
Use to keep track of mirror speed
Used to trigger sampling electronics
Called laser-fringe reference system
3rd system called the white-light system
Tungsten source and visible transducer
Polychromatic source so largest signal is at
zero position
As get off zero, some light interferes and
intensity decreases
Look for max signal, know where zero position
is
Triple system extremely accurate and reproducible
Current instruments use a single interferometer with a
laser, and get zero position from max of IR
signal
Beam Splitters
IR transparent material with refractive materials that reflect
50% of light and transmit 50%
Usually thin film of Mylar between 2 plates
Sources
Already covered
Designs
Single beam 16-20K
Since single beam need a reference run
Usually stable so only need occasional reference runs
Performance Characteristics
Less expensive 7800-350 cm-1
Resolution of 4 cm-1
(Check specs on our machine)
More expensive
Interchangeable splitters, sources, transducers
For IR through vis
Resolution from 8 to .01 cm-1
15
Advantages
10x better S/N than dispersive machines
Gets even better with signal averaging
High resolution and highly accurate frequency determination
Much higher E throughput because not using classical
monochrometer
A bit of a trade off is that high speed e\detector is not as
sensitive as other detectors
No equivalent of stray light problems
Has really been useful in
1.
high resolution work on gases
2.
study of samples with high absorbance
3.
study of samples with weak absorbance
4.
fast kinetic studies
5.
small sample
6.
IR emission studies
16C-2 Dispersive - skip
16C-3 Non dispersive - skip