Instrumental Analysis:
Spectrophotometric Methods II
FTIR, AS and Quantitative analysis
2007
By the end of this part of the course, you should be able to:
•
Understand interaction between light and matter
(absorbance, excitation, emission, luminescence,fluorescence, phosphorescence)
•
Describe the main components of a spectrophotometer,
(sources, monochromators, detectors, interferometer, grating, ATR, ICP, )
•
Make calculations using Beer’s Law
(analyse mixture absorption)
•
Understand the mechanism and application of UV-Vis, FTIR, Luminescence, atomic
spectroscopy
Last week’s lecture:
(Instruments based on light interaction with matter)
•
•
•
•
Properties of light
Molecular electronic structures
Interaction of photons with molecules
Spectrophotometer components
• Light sources
• Single and double beam instruments
• Monochrometers
• Detectors
Fluorescence spectroscopy
•
Today’s lecture:
•
•
•
Fourier transformed infrared spectroscopy
• Interferometer
Atomic spectroscopy
Quantitative analysis
• Beer’s law
• Method validation
• Dilution and spike
Survey of spectrophotometric methods learning assessment
Concept
known
before
100% need more
understand explaination
to be covered
in workshop
need check
book myself
completely
lost
electronic structure of molecules and
molecular spectrum
7
singlet/triplet
5
8
4
diffraction/Grating
PMT/photodiode/CCD
5
Luminescence
Beer's law
absorbance/transmittance
3
7
3
6
6
6
1
5
3
1
2
5
1
dilution
5
2
5
spike
4
4
8
analysis of mixture
1
3
8
2
10
isosbestic point
6
Beer’s law is the fundation for quantitative analytical chemistry
Basic principles before Beer’s law
Qualitative vs quantitative analysis
What is inside and how much is inside?
Sensitivity vs resolution
How can we balance the sensitivity vs resolution?
S/N ratio ratio control
Improve the Signal/Noise ratio by repeat.
Background correction
Control the background (stabilise) and numerically subtract.
Peak shape control
Minimum artificial distortion.
Chemical environment control
Improve the reproducibility.
Selectivity
Improve the uniqueness of the quality analysis.
A = ebc
Beer’s law
Absorption A = ebc
where b =>path length
c =>molar concentration
e =>molar absorptivity
A
Absorption vs Transmittance
Transmittance T = P/Po
where T => transmittance
P => power of transmitted radiation
Po => power of incident radiation
%T = (P/Po)*100
Where %T => percent transmittance
With constant b
c
A = - log10T = - log10 (P/Po)
and T=10-A
A
With constant c
b
b
Readout
Absorbance
Detector
Source
Sample
What is the units for A, b, c, T, P and e ?
Cuvets or Cuvettes
Error in Beer’s Law
Spectrophotometric measurements involve:
i. an adjustment for P/Po = 0 i.e. for no light through
ii. an adjustment for P/Po = 100% i.e. for all the light through
iii. an adjustment of P/Po with sample in place
Scale the spectrometer
Consider the effect of a 1% error in T (P/Po)
ii. when c is large:
error now corresponds to a large
uncertainty in c
1%
error
1%
error
Dc
DC
P/Po %
i. when c is small:
Dc is also small but it is large
proportion of c
DC
In practice: the measure A should be
between:
1.0 (T = 10%)  0.1 (T = 79.4%)
1% error
1% error
concentration(c)100%
Dc
Quantitative methods:
Part 1. Methods validation:
Specificity: the ability of a method to distinguish the analyte from others in the sample Check resolution
Linearity:
How well a calibration curve follows a straight line. Square of correlation coefficient
Accuracy: nearness to truth, check with different methods and spiking
Precision: reproducibility, standard deviation
Range: concentration interval over which linearity, accuracy and precision are all good
Detection Limits: defined by signal detection limit: 3s (standard deviation), minimum concentration:
3s/m, m is the slope of the linear curve.
Quantitative methods:
Part 2: Dilution
Concentration-dilution formula
A very versatile formula that you
absolutely must know how to use
C1 V1 = C2 V2
where C = conc.; V = volume
How to prepare 100ml of 0.1M NaCl
solution from 2.0M stock?
Calculations:
The total NaCl molecules:
V1x2.0M =100mlx0.1M
Cconc Vconc = Cdil Vdil
So, V1=100mlx0.1M/2.0M
=5ml (needed from stock)
where “conc” refers to the concentrated solution
and “dil” refers to the dilute solution
QuickTime™ and a
TIFF (Uncompress ed) dec ompres sor
are needed to s ee this pic ture.
How to do it:
Chef:
Measure 5ml of stock with teaspoon
Add 95ml of water
Chemist:
transfer 5ml stock with a 5ml pipet into a
100ml volumetric flask.
Topup to 100ml mark. Shake not stirred
Can you tell the difference between a chef and a chemist?
Quantitative methods:
Part 3: spike:
a known quantity of analyte add to the sample to test
accuracy and linearity
The unknown sample: V1, A1
Spiked with V2, c2 and A2.
The solutions are diluted to volume V.
Without dilution of the unknown
unknown: (V1cx), absorbance A1
A1=eb (V1cx)
Spiked: (V1cx+v2c2)/ V, absorbance A2
A2=eb (V1cx+v2c2)/ V
The final concentration:
V1Cx
V1Cx
+V2C2
Dilute unknown: (V1cx)/ V, absorbance A1
A1=eb (V1cx)/ V
Diluted to
V
Spiked: (V1cx+v2c2)/ V, absorbance A2
A2=eb (V1cx+v2c2)/ V
Absorbance difference A2-A1=ebV2c2/ V (spike dilution)
So the molar absorbance e can be measured, which will in turn give cx
Analysis of a mixture and isosbestic point
A solution of mixture of M and N
Pure N
Pure M
What is in my soup?
A mixture of flavours.
Fig. 14-14, pg. 345 Principles of Instrumental Analysis Fifth Edition, by Skoog-Holler-Nieman
Analysis of Mixtures of Absorbing Substances
The interaction between substance A and B is so weak that the
presence of A(B) does not affect the molar absorbance of B(A). A
linear addition of individual absorbance is equal to the total
absorbance.
Assumption
Solution of Binary Mixture
two
With
Wavelength 1
Am,l1 = a1,l1*b*c1 + a2,l1*b*c2
Wavelength 2
Am,l2 = a1,l2*b*c1 + a2,l2*b*c2
In
Need
variables
two
two measurements at wavelength 1 and 2
equations
How to get the answer c1 and c2?
Simple, just eliminate c2 to get c1.
What happens if we do more than two wavelength measurements?
Two vaiables in N equations
Classically, we can solve each pairs of equation to get c1 and c2, then
we average the c1 and c2 to reduce the errors in each measurment
With computer, a least square fitting to find the best solution of c1
and c2 by minimising the standard deviation (least square).
If the solution is a mixture of N substances, how many
minimum measurements are required at different energy?
Analysis of a mixture: Isosbestic point
Changing of experimental conditions
A=e1bc1+e2bc2
When e1=e2=e
A=eb(c1+c2)=ebc
A is a function of c=(c1+c2),
but not c1 or c2 individually
If absorption curves at different conditions always cross at one wavelength, that cross point
is called isosbestic point.
This suggests:
There are only two principal species in the solution.
At this point, absorption coefficient are equal for different species in the solution.
At this point, total concerntration can be measured.
Analysis of mixture: equilibrium constant
With constant total concerntration P0
A simple classical situation:
Adding [X] to achieve different equilibrium (titration).
P+X
PX Equilibrium constant k=[PX]
[P][X]
Complicated considerations:
P, X and PX all have absorbance at l wavelength.
Only P and PX have absorbance at l wavelength.
Only PX has absorbance at l wavelength.
P0=[P]+[PX]
A=e1[P]+e2[X]+e3[PX]
What we measure: [X], A
Target: get rid off [P] and [PX] with a function of known A and [X]
[P]=P0-[PX]
A=e P0- e [PX] +e [X]+e [PX]
1
1
2
3
Analysis of mixture: equilibrium constant
A=e1P0- e1[PX] +e2[X]+e3[PX]
Here: A0= e1P0
k[P][X]=[PX]
[PX]=(A-A0-e2[X])
e3-e1
Further more: DA=A-A0, De31= e3-e1
[P]=P0-[PX]=P0-(DA-e2[X])/ De31
At last:
Or:
k[P]=k{P0-(DA-e2[X])/ De31}= (DA-e2[X])
De31[X]
kP0-k(DA-e2[X])/ De31= (DA-e2[X])
De31[X]
x= (DA-e2[X])/ De31
What is the intercept?
y= (DA-e2[X])
De31[X]
y
Slope=-k
x
Fourier Transform Infrared Spectroscopy (FTIR)
Traditional dispersive spectroscopy problems:
Low sensitivity in IR
Slow (relatively)
low resolution
FTIR
Large optical throughout, high sensitivity
Fast
And high resolution
Solution:
Interferometer,
mechanical modulation
Jean-Baptiste-Josephde Fourier (1768-1830)
Key element of FTIR
Michelson Interferometer
Purpose: incident beam modulation through interference
Interference of waves
In-phase: constructive
Out-of-phase: destrictive
Michelson Interferometer
-Mirror moves with Velocity V
-Two beams recombine before detector
-Monochromatic beam of frequency n gives an interferogram (cosine curve with
wavelength proportional to 1/n)
-The interferogram contains the spectrum of the source (reference sample) minus the
spectrum of the sample
-Recorded as
intensity as a
function of
distance [I(d)]
versus the
distance (d)
-V is usually 1.5
cm s-1
-To distinguish
two frequencies
n1 and n2:
distance, d,
≥ 1/(n1 – n2)
Fourier Transform Infrared Spectroscopy
Fourier Transform Infrared Spectroscopy
Normal spectrum: plot of I(n) vs n
Intensity as a function of frequency vs.
frequency
Fourier transform: plot of I(t) vs t
Intensity as a function of frequency vs
frequency (remember: t = 1/n)
Called the Fourier Transform of the frequency spectrum
Spectrum may be collected in the frequency domain as function of n
or in the time domain as a function of t
Each version of the spectrum contains the same information
Conversion to one form to the other can be accomplished by a computer
Transfer interferogram to absorption spectrum
FFT: Fast Fourier Transformation
Fourier Transform Infrared Spectroscopy
- sample interferogram is transformed into sample spectrum
- background spectrum is subtracted
from sample spectrum
Beyond stabdard transmission FTIR
Atomic spectroscopy
A tool for
Quantitative and qualitative elementary analysis.
Atomic Spectroscopy: Overview
Number of spectral lines for each
element can be large!
Hydrogen
Helium
Mercury
Uranium
http://library.thinkquest.org/19662/low/eng/model-bohr.html
Atomic Spectroscopy: Overview
-
Samples vaporized at 2000 – 6000 K  decompose
into atoms
Concentration of atoms in the vapor are measured
Very sensitive: ppm (mg/g) to ppt (pg/g) levels
-
Can measure up to 60 elements at a time:
Molecular spectroscopy has a bandwidth of at least
10 nm
Atomic spectroscopy has a bandwidth of 0.001 nm
-
1 – 2% precision
Atomic Absorption, Emission and Fluorescence
Hollow-Cathode Lamps
-
Hollow-Cathode lamps (HCL) contains the vapor of the element of interest (i.e. Na)
Positive ions from a noble gas bombard the cathode and give metal atoms by sputtering
Metal atoms absorb energy by colliding with fast-moving filler gas ions, are elevated to
excited electronic states, and return to ground state (emission)
-
-
Spectrum consist of discrete lines from the metal and gas (chosen so that interference is
minimized)
The lines have a bandwidth of 0.001 nm
Atoms in the flame are mainly in the ground state

Only those HCL lines terminating in the ground state can be used for
absorption
measurements
Lines are separated by a monochrometer
-
Sometimes can use the same lamp for 2 – 3 elements (e.g. Ca/Mg)
-
Simplest system: Flame Atomization
-
Nebulizer: converts the liquid into aerosol
-
Typical temperature of flame = 2200 ºC
-
Typical fuel: acetylene (can use H2)
-
Typical oxidant: air (can use N2O or O2)
Background Correction
Background correction:
A.
B.
Corrections performed by alternate sampling from the HCL & D2 lamp
D2 lamp will give the background
Alternatively, beam chopping or modulation of the HCL is used to
distinguish between signal from flame (emission) and atomic line of
element
Source is usually modulated (e.g. at 325 Hz)  detector arranged so that
only the modulated signal is recorded
Modulation cuts down noise!
Inductively Coupled Plasma Spectrophotometer
-
Sample and Ar are aspirated into concentric
quartz tubes surrounded by a lead coil
-
Inner tube has sample aerosol and Ar support
gas
Outer tube has flow gas to keep the tubes cool
-
Oscillating current is produced in induction
coil  oscillating magnetic field is created
-
Magnetic field creates an oscillating current in
the ions and electrons of the support gas (a
plasma)
These ions and electrons collide with other
atoms in the support gas
-
Temperatures of 6000 – 10000 K are generated
-
Atoms or ions are almost all excited

emission rather than absorption is
measured
From:
http://www.chemistry.adelaide.edu.
au/external/soc-rel/content/icp.htm
Interference: An example
Sn has to major emission lines at 189.927 nm and 235.485 nm
Element added at
50mg/L
None
Ca
Mg
P
Si
Cu
Fe
Mn
Zn
Cr
[Sn] (mg/L), 189.927
nm emission line
100.0
96.4
98.9
106.7
105.7
100.9
103.3
99.5
105.3
102.8
Interference: An example
Sn has to major emission lines at 189.927 nm and 235.485 nm
Element added at
50mg/L
None
Ca
Mg
P
Si
Cu
Fe
Mn
Zn
Cr
[Sn] (mg/L), 189.927
nm emission line
100.0
96.4
98.9
106.7
105.7
100.9
103.3
99.5
105.3
102.8
Which elements interfere at both wavelengths?
Which wavelength is preferred for analysis?
[Sn] (mg/L), 235.485
nm emission line
100.0
104.2
92.6
104.6
1029
116.2
intense emission
126.3
112.8
76.4
Dealing with Interference: Standard Addition
-
Measure the absorbance (AX) of sample of unknown concentration (cX)
-
Add a known amount of standard to give a new concentration (cS) and measure new
absorbance (AT)
-
From Beer’s Law:
AX = k V1Cx /V
AT = k(V1Cx + V2Cs)/V
-
For better accuracy add several
different known amounts to
generate a plot
V1Cx
V1Cx
+V2Cs
Diluted to
V
Ax
-
Intercept = -V1Cx
0
[Added analyte]=V2Cs
Some Practical Considerations
Flame photometry is used when looking at the most sensitive spectral lines (looks at emission)
> 300 – 350 nm (e.g. Na 589.0 nm, K 766.5 nm and Ca 422.7 nm)
- good for relatively high concentrations
Atomic Absorption Spectrophotometry:
- Slightly more expensive than flame photometry, but can look at more elements
- Good for relatively high concentrations (routine analysis)
- Most AA spectrometers have facilities for recording emission spectra (HCL taken out of
circuit)
ICP
- Many lines of varying intensity from both atoms and ions are available
- Since dealing with hotter temperatures, can get more interference
- BUT…. ICP gives sharper lines  more elements can be measured at once with several
slits and monochromators
- VERY VERY SENSITIVE!!! NEED TO DILUTE  ERROR
Some Practical Considerations: Temperature Effects
-
Number of atoms in the excited state is temperature dependent
Boltzmann Distribution
N/N0 = (g/g0) exp(-DE/kT)
N, N0, g, g0 = #’s in and degeneracies of the excited and ground states
DE = energy difference
T = Temperature
k = Boltzmann Constant (1.39 x 10-23)
N
e.g. Na: g1 = 6, g0 = 2
- At 2500 K, N/N0 = 1.74 x 10-4
- At 2510 K, N/N0 = 1.79 x 10-4
 4% difference!
Element
Cs
Na
Ca
Fe
Cu
Mg
Zn
g/g0
2
2
3
2
3
3
Absorption
Excited state
Emission
Ground state
N0
N/N0
2000 K
4.44 x 10-4
9.89 x 10-6
1.21 x 10-7
2.29 x 10-9
4.82 x 10-10
3.35 x 10-11
7.45 x 10-15
3000K
7.24 x 10-3
5.88 x 10-4
3.69 x 10-5
1.31 x 10-6
6.65 x 10-7
1.50 x 10-7
5.50 x 10-10
What we have learned today:
• Beer’s law, absorbance and transmittance
• Explain why the most accurate data are obtained when the absorbance is between 0.1
and 1.0.
• Quantitative methods, validation, dilution and spike.
• Mixture analysis and isosbestic point
• Explain with diagram how a FTIR spectrometer works
• atomic emission and absorption spectrophotometers work
• Describe an Inductively Coupled Plasma (ICP) spectrophotometer
• Explain the use of a deuterium lamp to obtain background corrections in AAS
• Explain the standard addition method
• Explain why higher temperatures give stronger emission lines
Atomic and x-ray fluorescence
For atomic spectroscopy, the light sources generally needs to be stronger than HCL in order to
get a strong fluorescence signal
- lasers commonly used (see http://science.howstuffworks.com/laser.htm for a nice
description on how lasers work)
- vacuum discharge vessels also used
Sample needs to be viewed at an angle (generally 90)
- differentiate between incident light (P) and fluorescence
- prevent swamping out of the detector with the high intensity laser beam
LASER
source
or other light source if
looking at molecular
fluorescence
A
F
Sample
sample
90o
detector
Monochrometer
and Detector
Advantages:
- much better sensitivity (up to 1000 times greater that atomic absorption)
- can even count individual atoms (Mark Osborn looks at single molecules using
fluorescence spectroscopy)
- good for biological and medical applications
X-ray fluorescence
-
Similar to fluorescence, but uses X-rays instead of photons
-
Incoming X-ray ejects an electron from an inner-shell
-
A lower energy X-ray is released when an electron replaces the lost inner-shell electron
-
Energy of the resulting X-ray is atom dependent
-
Number of characteristic X-rays is proportional to the concentration of the element
X-ray2
-
Excited electron e
e-
ee-
E0
Incoming
radiation
X-ray1
X-ray3
X-ray fluorescence uses
-
Non-destructive
Multi-element
Fast
Metallurgical industry
Geochemistry and mineralogy: qualitative and quantitative
Environmental science: measurement of sediments, aerosols, water
Paint industry: lead analysis
Jewellery: precious metals
Fuel industry: contaminant monitoring
Food industry: toxic metal analysis
Agriculture: trace metal analysis
Archaeology
Arts: analysis of paintings and sculptures
Lead analysis