application of „lightwaves“...
TRANSCRIPT
Bruker Optik
Application of „Lightwaves“
FT-IR-Spektroscopy
Content
• Bruker Optik
• Infrared Spectroscopy and Molecular Vibration
• FT-IR spectrometer
• Interferometer
• FT-IR Measurements
• Measurement Techniques (ATR)
• Data evaluation
• Examples
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Infrared SpectroscopyMolecular Vibrations
Electromagnetic radiation
Incident light beamIncident light beam
Reflection
Matter
Photoluminescence
Scattering
TransmissionAbsorptionAbsorption
2. Interaction of Radiation and Matter
Absorbance A:CdA ⋅⋅= ε
(Beer‘s law)
ε: molar absorptivity
d: thickness of sample
C: molar concentration
Interaction between light and matter
Excitation of molecular vibration
Interaction of radiation and matter
IR spectroscopy is based on the absorption of infrared light by the substance to be measured. This absorption excites molecular vibrations and rotations, which have frequencies that are the same as those within the infrared range of the electromagnetic spectrum.
The following simple model of a harmonic oscillator used in classical physics describes IR absorption. If atoms are considered to be particles with a given mass, then the vibrations in a diatomic molecule (e.g. HCl) can be described as follows:
Mechanical model of a vibrating diatomic molecule
Vibration Theory (1)
2. Vibration Theory (2)
ν: vibrational frequency
k: spring constant
µ: reduced mass
m1: mass of molecule 1
m2: mass of molecule 2
0dtd
2
2
=⋅+ rkrµ
Differential Equation:
CLASSICAL DESCRIPTION:
3 absorption peaks for different force constants. Note that by convention, in infrared spectroscopy wavenumbers are plotted
right-to-left; i.e. highest wavenumber to the left.
2. Vibration Theory (3)
Effect of different spring constants k:
3 absorption peaks for different atomic masses. Note that by convention, in infrared spectroscopy wavenumbers are plotted
right-to-left; i.e. highest wavenumber to the left.
2. Vibration Theory (4)
Effect of different atomic masses m:
2. Vibration Theory (5)QUANTUM MECHANICAL DESCRIPTION:
Potential energy curve for a harmonic oscillator
( ) ψψVdr
ψd2 2
2
⋅=⋅+ Ermh (Schrödinger Equation)
h: Planck‘s constant
V: harmonic potential
E: energy
ψ: wave function
Potential energy curve for an anharmonic oscillator
2. Vibration Theory (6)Improvement of the model: The Anharmonic Oscillator
2. Vibration Theory (7)
What kind of molecules absorb infrared light?
Heteronuclear diatomic molecule
IR active
Homonuclear diatomic molecule
IR inactive
An accurate model of a molecule is given by the anharmonicoscillator. The potential energy is then calculated by the Morse equation, and is asymmetric. The energy levels are no longer equally spaced, and are given by:
Ev=(v + ½) h • ν - (v + ½)2 xGl h • ν
where xGl is the anharmonicity constant.
The anharmonic oscillator model allows for two important effects:1) As two atoms approach each other, the repulsion increases very rapidly.
2) If a sufficiently large vibrational energy is reached the molecule will dissociate (break apart). This is called the dissociation energy.
In the case of the anharmonic oscillator, the vibrational transitions no longer only obey the selection rule ∆v = ±1. This type of vibrationaltransition is called fundamental vibration. Vibrational transitions with ∆v = ±1, ±2, ±3, ... are also possible, and are termed overtones.
Potential energy curve for an anharmonic oscillator
Vibration Theory (8)
Which kind of vibrations?
Stretching vibrations
Symmetric stretching vibration Anti-symmetric stretching vibration
For example: water
Deformation vibrations
Which kind of vibrations?
IR-Spectrum of water
15002000250030003500wavenumber cm-1
6065
7075
8085
9095
100
Tran
smis
sion
[%]
Hexane
More than 50 different vibrations
Hexane
1000150020002500300035004000wavenumber cm-1
2040
6080
100
Tran
smis
sion
[%]
C-H stretch C-H deformation
„Fingerprint region“
IR absorption of different organic molecular classes 2. IR Absorption of organic molecules
2. The Infrared Spectrum is ...
Each molecule has got itsown individual spectrum
„ ... like aFingerprint “
Fingerprint range:1430 ... 1000 cm-1
FT-IR Spectrometer
Dispersive IR spectrometer FT-IR spectrometer
Principle layout of IR spectrometer
Layout of an FT-IR spectrometer
Electronic Source compartment
Sample compartment
Sample position
Detector
Interferometer compartment
Aperture wheelFilter wheel
Interferometer
Michelson Interferometer
Source
Detector
Movingmirror
Fixedmirror
∆x
Beamsplitter
L
L + ∆x
x=0
Optical Retardation
Inte
nsity
Detector signal
Frequency
Inte
nsity
Spectrum
Monochromatic source
Monochromatic source detector signal
3. Origin of the interferogram (1)Constructive interference:
Destructive interference:
Detector signal,symmetric cos-Wave:
222 λ
⋅=∆⋅ kx
( )2
122 λ⋅+=∆⋅ kx
( ) ( ) ( )xx ∆⋅⋅=∆ νπν 2cosSI
( ),...2,1,0=k
e.g. He-Ne laser
Optical retardation
Inte
nsity
Nine waves with different wavelengths
Frequency
Inte
nsity
Spectrumconsisting of 9 single frequencies
Optical retardation
Inte
nsity
Resulting detector signal:
3. Origin of the interferogram (2)
Dephasing for polychromatic light
Example for an wavelength-independent light modulator:
The interferometer is a wavelength-dependend„light modulator“.
Resulting detector signal
Frequency
Inte
nsity
IR-source
Optical retardation
Inte
nsity
Frequency distribution of a black body source
3. Origin of the interferogram (3)
„center burst“„interferogram peak“„ZPD“
3. Example: Interferograms and SpectraInterferogram and Spectrumð „Reciprocal Relationship“
Comparison between „Raman Naphtalene“ and „White Light“:
Dispersive IR spectrometer
FT-IR spectrometer
IR spectrometer principle3. Advantages of FT-IR Spectroscopy
1) Connes´ advantage:precision of wavenumber axis scale
2) Jacquinot´s advantage:large throughput withcircular apertures
3) Fellgett´s advantage:multiplexed measurement
3. The Michelson Interferometer
RockSolid Interferometer
State-of-the-art technology:
RockSolidTM Interferometer
• CubeCorner mirrors:
permanently aligned
Angle accuracy:
better than 0,001°
(=1cm on 1km)
• Wearless bearings based on
steel springs,
like a clockwork
US Patent No 5.309.217
Using zero crossings: fixed sampling,
but: Undersampling / Spacing Variation and
Interpolating possible
Sampling with a He-Ne laser15798 cm-1, 633 nm, 474 THz:
Every ...thZero-Crossing
„0.25“
„0.5“
1
2
3
4
Spectral Band-width / cm-1
63192
31596
15798
7899
5266
3949
3. Sampling in FT-IR spectrometers (1)
3. Sampling in FT-IR spectrometers (2)
AD
FFT
SourceLaser
Laser detector A
Laser detector B
IR detector
Moveable mirror
3. Sampling in the time domain (1)-0.
3-0.
2-0.
10.0
0.10.2
time
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14
Reference laser fringes
Detector signal
Delta-Sigma-ADC sample times
fixed ∆Τ
Advantages:• Very high resolution
• No gain ranging
• No analog filters
• Low cost
3. Sampling in the time domain (2)Ultimate accuracy determined by:
1. Where to sample? 2. How to sample?
1.a) Analog comparator: measure time between laserzero crossings
Pros:
• Accuracy limited only by noise
and clock resolution (e.g. 20 ns)
• Values readily available
no delay, no computations
Cons:
• No noise averaging
t1 t2
Comparator output
AC-coupled laser fringes
0 Volt
Count ticks from fast master clock
+
-
3. Sampling in the time domain (3)Ultimate accuracy determined by:
1. Where to sample? 2. How to sample?
1.b) 2nd Delta-Sigma-ADC: fit a cubic to digitized laser fringes
Pros:
• Fit provides noise averaging
Cons:
• Wave form is critical
• Requires computational power
• High oversampling (x10)
limits scanner velocity
(typ. 10 kHz for 192 kHz ADC)
Cubic polynomial
3. Sampling in the time domain (4)
2. How to sample:
Bandwidth-limited signal (ωmax),
ð Convolution with sinc:
Ideal weighting function:
•Flat pass band
•High stop band rejection
•Low number of coefficients
•Linear phase
ADC samples
Pos. 0
Pos. 1 Pos. -1
0 99 512 Master clock ticks
Laser zero crossing
Weighting function (kernel)
( )
( ) ( )( )∑∞+
−∞=
−⋅
=
kK
K
kTtkTx
tx
maxsinc ω
3. Sampling in the time domain (5)
Frequency response of carefully designed kernel (64 coefficients):(phase response is linear, leading to a constant delay)
dB
1 2 3 4 5 6 7 8 9-160
-140
-120
-100
-80
-60
-40
-20
0
f/f00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-5
-4
-3
-2
-1
0
1
2
3
4
5
f/f0
10-4 dB
FT-IR measurements
Resulting detector signal
Frequency
Inte
nsity
IR light source
∆X, moving mirrorIn
tens
ity
Origin of the interferogram
Transmission spectrum
1.) In the empty sample compartment an Interferogram is detected. The result of the FOURIER transformation is R(ν).
FourierFourier--TransformationTransformation
5001000150020002500300035004000wavenumber cm-1
0.10
0.20
0.30
0.40
Sing
le c
hann
elin
tens
ity
∆X, moving mirror
Det
ecto
rint
ensi
ty
2.) A second interferogram is detected with the sample placed in the sample compartment. The result of the FOURIER transformation is S(ν). S(ν) shows similarities to the reference spectrum R(v), but has lower intensities at the regions the sample absorbs radiation.
FourierFourier--TransformationTransformation
5001000150020002500300035004000wavenumber cm-1
0.10
0.20
0.30
0.40
Sing
le c
hann
el in
tens
ity
∆X, moving mirror
Det
ecto
r int
ensi
ty
Transmission spectrum
The transmission spectrum T(ν) is calculatedas the ratio of the sample and referencesingle channel spectra:
T(ν) = S(ν)/R(ν).
5001000150020002500300035004000wavenumber cm-1
0.10
0.20
0.30
0.40
Sing
le c
hann
elin
tens
ity
5001000150020002500300035004000wavenumber cm-1
4060
8010
0Tr
ansm
issi
on [%
]20
ratioratio
Transmission spectrum
Two separated lines with the distance
d in the spectrum lead to a periodic
signal in the interferogram with a
distance 1/d.
RAYLEIGH criterion:
∆X ≥ 1/d
wavenumber cm-1
d IR Spectrum
Interferogram
Spectral resolution
source
detector
movablemirror M2
fixedmirror M1
∆x
Beam splitter
L
L + ∆x
x=0
0.5
0.6
0.7
0.8
0.9
1.0
Sing
le c
hann
el0.
50.
60.
70.
80.
91.
0Si
ngle
cha
nnel
High spectral resolution
Low spectral resolution
ATRAttentuated Total Reflection
ATR TheoryAttenuated Total Reflection
sample
ATR crystal
ATR crystal
n1
sample
n2
sample
ATR crystal
ΘRefractive index
n1 > n2
λ = wavelength, np = refractive index of crystalθ = Einfallswinkelnsp = ratio of refractive index
sample/crystal.
2/12sp
2p )(sinn2 n
dp−
=θπλ
Penetration depth
*: calculated for a sample with n = 1.4 @ 1000cm-1
MaterialRefractive index
@ 1.000 cm-1
Dp *
[µm] @ 45°
Diamant 2.4 1.66
Ge 4 0.65
Si 3.4 0.81
ZnSe 2.4 1.66
Dp *
[µm] @ 60°
AMTIR** 2.5 1.46 0.96
1.04
0.5
0.61
1.04
Calculated penetration depth for some typicalATR materials
**: AMTIR: Ge33As12Se55 - Glass
The penetration depth Dp depends on the following parameters:
1.) angle of incidence
2.) refractive index
3.) wavelength of light
Penetration depth
100015002000250030003500wavenumber cm-1
0.0
0.2
0.4
0.6
0.8
1.0
Abso
rban
ce
Transmission
ATR
Penetration depth
The penetration depth Dp depends on the following parameters:
1.) angle of incidence
2.) refractive index
3.) wavelength of light
sample
wavelength wavelength
Not penetrated sample
Evaluation of IR spectra
Infrared spectroscopy is an extremely efficient analytical method due to modest operating expenditure. The analytical results are provided within a short period of time without the need of extensive sample preparation. In particular, infrared spectroscopy provides data which can be evaluated by quantity as well as by quality. The following will describe the qualitative and quantitative evaluation of acquired spectra.
•Qualitative evaluation of spectra
1. Identify an unknown substance2. Check the identification of a known substance
•Quantitative evaluation of spectra
Evaluation of spectra
A functional group within a molecule is considered as a harmonic oscillator (see vibration theory) which in a first approximation vibrates without being affected by the rest of the molecule. This results in the fact that a particular functional group shows IR absorption bands within characteristic spectral ranges: this is called group vibrations. This fact serves as the basis for spectral interpretation, whereby the position, (relative) intensity and half-width of a band decide whether a band can be assigned to a specific structural group.
Many functional groups of organic molecules show characteristic vibrations corresponding to absorption bands within defined ranges of the IR spectrum. These molecular vibrations are mainly restricted to the functional group and do not affect the remaining molecule, i.e. such functional groups can be identified by their absorption band. This circumstance, apart from a straightforward acquisition technique, makes IR spectroscopy to be one of the simplest, fastest and most reliable methods when assigning a substance to its specific class of compounds. The position and intensity of the absorption bands are extremely specific in the case of a pure substance. This enables the IR spectrum, similar to the human fingerprint, to be used as a highly characteristic feature for identification.
Identify an unknown substance
a) Structural determination by interpreting spectra
5001,0001,5002,0002,5003,0003,5004,000Wavenumber / cm-1
4060
8010
0Tr
ansm
issi
on [%
]20
IR absorption of different organic molecular classes
Besides basic spectral interpretation, various comprehensive digital spectral libraries have been compiled according to different chemical classes and groups of substance. These are provided, for example, by companies like Bruker and Sadtler. Apart from working with existing spectral libraries, it is possible to create your own libraries using modern spectroscopic software,see OPUS/SEARCH. Different spectra regarding the number of bands and half-width, may require different search algorithms. Therefore, OPUS/SEARCH has the flexibility in providing various search options.
b.) Comparing with spectral libraries
Identify an unknown substance
Infrared spectroscopy is a perfect analytical tool for quality control. It gives the answer to the following question: “Does the quality of the raw material delivered to the receiving department comply with the specifications?” The underlying concept is very easy:
identical material = identical IR spectrum
The identification is done by comparing measured spectra with reference spectra already saved. The method is based upon the following considerations:
•chemically different materials result in different spectra
•real spectral differences exceed the reproducibility of repeated measurements
•reference samples represent the expected sample variations caused by supplier, batch, season, purity, grain size etc.
It is important to note that the reference samples can vary to a certain degree, a circumstance that is experienced within quality control every day. The spectrum of the material to be identified is compared with the reference sample by means of a valid tolerance previously defined. How to create a reference library and to compare spectra will be described in the following.
Check the identity of a known substance
2.) Calculate average spectrum & threshold values
3.) Library structure & validation
••
•
••
•
•
•• •
•
•••
•••
•
•••
••
•• • •
1.) Measure reference sample
Wavenumber / cm-1
Abso
rban
ce
Wavenumber / cm-1
Abso
rban
ce
Reference library structure
Identified sample:
material X
1.) Measure new samples
2.) Compare with library
Identifying new samples
3.) Identify material
The basic principle for quantitative evaluation in optical spectroscopy as well as in IR spectroscopy is the Bouguer-Lambert-Beer Law which had already been defined in 1852. Quantitative determinations by means of IR spectroscopy are preferably performed in solution. Transmission T of a sample is defined as:
T = I / I0
Io is the intensity of the incident light beam, I is the intensity of the light beam leaving the sample. The percentage transmission (%T) is 100 • T. When traversing the measurement cell, the light intensity decreases exponentially:
I = I0 • exp(-2.303ε • c • b)
Where ε is the molar absorption coefficient (in L mol-1 cm-1), c is the sample concentration (in mol L-1) and b the thickness of the measurement cell (in cm). The absorption coefficient ε is a value which depends on either the wavelength or the wavenumber, which is typical for the compound analyzed. From the equation above, it follows that:
log (I / I0) = -ε • c • b, or:A = log (I0 / I) = ε • c • b
where A is the absorbance. Because of the Bouguer-Lambert-Beer Law, the relationship between absorbance and concentration of the absorbing substance is a linear function.
Quantitative evaluation of spectra
In practice the relationship between concentration and absorbance is empirically determined by calibration. Calibrating means finding the mathematical connection between concentration and the measurement values.
In the first step, spectra of substances with known composition are recorded. Then, these acquired spectra and the data available from a reference analysis (concentration or substance properties) areused to determine a calibration function. The software package OPUS/QUANT provides several algorithms to do this.
In the second step, spectra of substances with an unknown composition are measured and then used to determine the properties of interest by means of the calibration function.
There are two different forms of calibration:
Univariate calibration (OPUS)
Correlates just one piece of spectral information (e.g. peak height or peak area) with the reference values of the calibration set.
Multivariate calibration (OPUS/QUANT)
Correlates considerably more spectral information using larger spectral ranges with the reference values of the calibration set. This leads to a higher degree of precision and reduced chance of error. Partial Least Squares ((PLS) is an example of this method and isimplemented in OPUS/QUANT.
X
Analysis
1
2
3
4
Abso
rban
ceConcentration
X
1
3
2
4
Abs o
rban
ce
Wavelength
Calibration
Quantitative evaluation of spectra
Examples
Industrial Applications
1) Compensation of velocity variations
2) Compensation of source fluctuations
Trace impurities in theatmosphere
4. FT-IR Spectroscopy at exotic sites
The Observatory on the Jungfraujoch, the “Sphinx”, 3700m altitude.
4. Size of the IFS 120
FT-IR Spectroscopy at exotic sites
The “The “PolarsternPolarstern” of the Alfred” of the Alfred--WegenerWegener--InstitutInstitut, , BremerhavenBremerhaven
Bruker OptikSpectrometer
Forensics / Pharmaceuticals – Chinese SFDA
§ State Food and Drug Administration (SFDA) of the People's Republic of China.§ 300+ FT-NIR spectrometers
integrated into mobile laboratory vehicles.§ Deployment across China for the
rapid screening of pharmaceutical products.
Forensics / Pharmaceuticals – Chinese SFDA
Vice Premier of China, Wu Yi, inspecting the NIR testing
Real Counterfeit
Real example of counterfeit drugs
JungfraujochJungfraujoch Observatory, SwitzerlandObservatory, Switzerland3.700 m above sea level3.700 m above sea level
An exotic place for an FT-IR spectrometer